math problem solving questions grade 10

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Problems with Solutions and Answers for Grade 10

Grade 10 math word problems with answers and solutions are presented.

A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?

• An airplane flies against the wind from A to B in 8 hours. The same airplane returns from B to A, in the same direction as the wind, in 7 hours. Find the ratio of the speed of the airplane (in still air) to the speed of the wind.

Solutions to the Above Problems

• 6% x = 8,880 : x = selling price of house. x = $148,000 : solve for x.
• 3000 revolutions / minute = 3000×360 degrees / 60 seconds = 18,000 degrees / second
• L × W = 300 : area , L is the length and W is the width. 2 L + 2 W = 70 : perimeter L = 35 - w : solve for L (35 - W) × W = 300 : substitute in the area equation W = 15 and L = 20 : solve for W and find L using L = 35 - w.
• Let h be the height of the trapezoid. area = (1/2) × h × (10 + 10 + 3 + 4) = 270 h = 20 : solve for h 20 2 + 3 2 = L 2 : Pythagora's theorem applied to the right triangle on the left. L = sqrt(409) 20 2 + 4 2 = R 2 : Pythagora's theorem applied to the right triangle on the right. R = sqrt(416) perimeter = sqrt(409) + 10 + sqrt(416) + 17 = 27 + sqrt(409) + sqrt(416)
• 400 rev / minute = 400 × 60 rev / 60 minutes = 24,000 rev / hour 24,000 × C = 72,000 m : C is the circumference C = 3 meters
• Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat. 4x + 4y + 2z = 560 : 9x + 9y + 6z = 1,290 3x + 3y + 2z = 430 : divide all terms of equation C by 3 x + y = 130 : subtract equation D from equation B 3(x + y) + 2z = 430 : equation D with factored terms. 3*130 + 2z = 430 z = 20 : solve for z x + y + z = 130 + 20 = $150
• x : the total number of toys x/10 : the number of toys for first child x/10 + 12 : the number of toys for second child x/10 + 1 : the number of toys for the third child 2(x/10 + 1) : the number of toys for the fourth child x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x x = 30 toys : solve for x
• Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above. [sum(Xi) + sum(Yi)] / 20 = 70 : class average sum(Xi) / n = 50 : average for less that 60 sum(Yi) / N = 75 : average for 60 or more 50n + 75N = 1400 : combine the above equations n + N = 20 : total number of students n = 4 and N = 16 : solve the above system
• f(x) = -3(x - 10)(x - 4) = -3 x 2 + 42 x - 120 : expand and obtain a quadratic function h = -b/2a = - 42/(-6) = 7 : h is the value of x for which f has a maximum value f(h) = f(7) = 27 : maximum value of f.
• (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100) = (9/10)(10/11)(11/12)...(98/99)(99/100) = 9/100 : simplify
• Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B. d = 3(S + r) : boat travelling down river d = 5(S - r) : boat travelling up river 3(S + r) = 5(S - r) r = S / 4 : solve above equation for r d = 3(S + S/4) : substitute r by S/4 in equation B d / S = 3.75 hours = 3 hours and 45 minutes.
• Let: S be the speed of the airplane in still air, r be the speed of the wind and d the distance between A and B. d = 8(S - r) : airplane flies against the wind d = 7(S + r) : airplane flies in the same direction as the wind 8(S - r) = 7(S + r) S/r = 15

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Sample Test Questions

Grade 10 math questions and solutions.

The Smarter Balanced Assessment Consortium (SBAC) is a standardized test that includes a variety of new technology-enhanced questions.

Some of them are Multiple choice-single correct responses, Multiple choice-multiple correct responses, Matching Tables, Drag and Drop, Hot text, Table Fill in, Graphing, Equation/numeric, Extended constructed response, Short answer, and many more.

This page contains several sample questions along with practice test links for Grade 10 Math that gives you an idea of questions that your students are likely to see on the test. After each sample question, an answer explanation follows. The explanation includes essential aspects of the task that you may need to consider for the skills, processes, and information your students need to know.

Domain: Grade 10 >> Number and Quantity – The Real Number System

Sample Question: Evaluate 9 150/300

Answer Explanation: 9 150/300 = 9 1/2 = square root of 9 = 3. In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. However, in this problem the exponent can be reduced, so we should reduce that first. The exponent 150/300 = 1/2. So the problem becomes 9 to the 1/2 power. The denominator is 2 so we take the square root of 9 which is 3. The numerator is 1 so we raise 3 to the 1st power and the answer is 3.

Standards: HSN.RN.A.1

Click here to practice: Number and Quantity – The Real Number System Questions on Grade 10 Math

Domain: Grade 10 >> Number and Quantity – Quantities

Sample Question: Rewrite x 1/2 in radical form.

Answer Explanation: In a problem with a rational exponent, the numerator tells you the power, and the denominator the root. Since the problem is, x 1/2 , the denominator is 2 indicating we should take a square root and the numerator is 1 so we would raise that to the first power or there will be no exponent since an exponent of 1 is rarely used. That makes the answer the square root of x, written as √x.

Click here to practice: Grade 10 Number and Quantity – Quantities Questions

Domain: Grade 10 >> Number and Quantity – The Complex Number System

Sample Question: Simplify completely i(7−i)

Answer Explanation: i(7−i)=i*7−i*i=7i−i 2 =7i−(−1)=7i+1=1+7i

Start by using the distributive method. Now simplify −i 2 =1 by definition. Now rearrange and put the real part first and the imaginary part last so that it looks like this a+bi.

Standards: HSN.CN.A.2

Click here to practice: Grade 10 Math Number and Quantity – The Complex Number System Questions

Domain: Grade 10 >> Number and Quantity – Vector & Matrix Quantities

Sample Question: A vector in standard form has components . What is the initial point?

• Not enough information given

Answer Explanation: Since the vector is in standard position, we know that the initial point is (0, 0) or the origin.

Standards: HSN.VM.A.2

Click here to practice: Number and Quantity – Vector & Matrix Quantities Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Seeing Structure in Expressions

Sample Question: Which expression is equivalent to 9x 2 – 16y 2 ?

• (3x – 4y) (3x – 4y)
• (3x + 4y) (3x + 4y)
• (3x + 4y) (3x – 4y)
• (3x – 4y) 2

Answer Explanation: Student must recognize the expression is the difference of two perfect squares

Standards: HSA.SSE.A.2

Click here to practice: Algebra – Seeing Structure in Expressions Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Arithmetic with Polynomials & Rational Expressions

Sample Question: Evaluate f(x)=−a 3 +6a−7 at a = – 1 and state the remainder.

Answer Explanation: student must substitute – 1 into the function as follows −(−1) 3 +6(−1)−7=−12 and find the value to get the remainder

Standards: HSA.APR.B.2

Click here to practice: Algebra – Arithmetic with Polynomials & Rational Expressions Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Creating Equations

Sample Question: The ratio of staff to guests at the gala was 3 to 5. There were a total of 576 people in the ballroom. How many guests were at the gala?

Answer Explanation: Setup a proportion of guests to the total number of people, 8/5 = x/576. Solve by cross multiplying. 8x = 2880. Divide both sides by 8. So x=360.

Standards: HSA.CED.A.3

Click here to practice: Algebra – Creating Equations Questions for Grade 10 Math

Domain: Grade 10 >> Algebra – Reasoning with Equations & Inequalities

Sample Question: Solve the quadratic x 2 +10x=−25.

Answer Explanation: This problem can be easily solved by rearranging the equation so that it is solved for zero and then factoring as shown:

x 2 +10x=−25

x 2 +10x+25=0

(x+5)(x+5)=0

Since both factors are exactly the same, you will only have one solution to this problem.

Standards: HSA.REI.B.4

Click here to practice: Algebra – Reasoning with Equations & Inequalities Questions for Grade 10 Math

Domain: Grade 10 >> Functions – Interpreting Functions

Sample Question: Which graph could represent the graph of f(x)=sin(x)?

Answer Explanation: The sin function always graphs to look like a wave. The only one that could be the sin function is D.

Standards: HSF.IF.C.7

Click here to practice: Functions – Interpreting Functions Questions for Grade 10 Math

Domain: Grade 10 >> Functions – Building Functions

Sample Question: Describe how the graph of g(x)=x 3 – 5 can be obtained by shifting f(x) = x 3 + 2.

• Shift right 7 units
• Shift left 7 units
• Shift up 7 units
• Shift down 7 units

Answer Explanation: The only thing that changed in the two equations is the y-intercept which controls the vertical shift (up or down). To get the graph of g(x) by shifting the graph of f(x), you would shift f(x) down 7 units to change from +2 to -5.

Standards: HSF.BF.B.3

Click here to practice: Functions – Building Functions Questions for Grade 10 Math

Sample Question: Solve 3 x =12 using logarithmic form.

• x = ln12/ln3
• None of these

Answer Explanation: Solve using logs as follows 3 x =12 x=log(base 3) 12 x=ln12/ln3

Standards: HSF.LE.A.4

Domain: Grade 10 >> Functions – Trigonometric Functions

Sample Question: In the unit circle, one can see that tan(5π/4)=1 . What is the value of cos(5π/4)?

Standards: HSF.TF.A.2

Click here to practice: Functions – Trigonometric Functions Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Congruence

Sample Question: What would be the coordinates of point S after applying the following rule: (x+3, y -2)?

Answer Explanation: Answer: B Explanation: The transformation rule that is give is to translate the point 3 units to the right and 2 units down as shown by the following diagram:

Click here to practice: Geometry – Congruence Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Similarity, Right Triangles, & Trigonometry

Sample Question: By what property can the angles BAX and TSX be found to be congruent?

• Corresponding angles
• Vertical angles
• Alternate interior angles
• Congruent angles

Answer Explanation: Answer: A

Although they are congruent angles, the question is asking for the property. Since they are in corresponding locations with the transversal (AX) the correct answer is A

Standards: HSG.SRT.A.3

Click here to practice: Geometry – Similarity, Right Triangles, & Trigonometry Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Circles

Sample Question: What is the translation rule and the scale factor of the dilation as Circle F→Circle F′ ?

• (x,y)→1/4(x,y+10)
• (x,y)→4(x,y+10)
• (x,y)→1/4(x+10,y)
• (x,y)→1/4(x,y−10)

Answer Explanation: The original circle F has its center at the point (−5,−6) with a radius of 4 units. The translated/dilated circle F’ has its center at the point (−5,4) with a radius of 1 units. This means the center was translated up 10 units. As a transformation, this translation is written as (x,y)→(x,y+10). Circle F was also dilated by a factor of 1/4 because the radius was reduced from 4 units to 1 units. As a transformation, this dilation is written as (x,y)→1/4(x,y). Putting the translation and dilation together, the rule is (x,y)→1/4(x,y+10).

Click here to practice: Geometry – Circles Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Expressing Geometric Properties with Equations

Sample Question: What value on the number line in the figure below divides segment EF into two parts having a ratio of their lengths of 3:1?

Answer Explanation: Point E is at -7 on the number line in the figure, and pointF is at 1. Thus, the length of segment EF is 8. To divide the segment into two parts with a ratio of their lengths of 3:1, change the ratio to 3x:1x to allow variation in the location on the number line. Next, set the sum of the two parts equal to 8 and solve for x. 3x+1x=8;4x=8;x=2.Now, that you know that x=2, find 3x, which equals 6. Find the value on the number line by adding 6 to the position of point E. −7+6=−1.The value on the number line that divides segment EF in a ratio of 3:1 is -1.

Standards: HSG.GPE.B.6

Click here to practice: Geometry – Expressing Geometric Properties with Equations Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Geometric Measurement & Dimension

Sample Question: What is the volume of the prism shown below?

Answer Explanation: Use the formula for volume of a pyramid:

V=1/2.a.c.h

In this case the length is 15cm, the base is 10 cm in length, and the height is 9 cm. Therefore :

V=1/2.15.10.9=675cm 3

Standards: HSG.GMD.A.3

Click here to practice: Geometry – Geometric Measurement & Dimension Questions for Grade 10 Math

Domain: Grade 10 >> Geometry – Modeling with Geometry

Sample Question: A company ships spherical paperweights in cubic boxes. The circumference of the paperweight is 9π cm. If the box fits the sphere exactly with the sides of the sphere touching the box, what is the volume of the smallest box the company can use for shipping.

• 1009 π cm 3

Standards: HSG.MG.A.3

Click here to practice: Geometry – Modeling with Geometry Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Interpreting Categorical & Quantitative Data

Sample Question: Given the scatter plot below, what type of function expresses the correlation between the two variables?

• Exponential

Answer Explanation: Notice that the trend of the graph (in red) between the data points forms a line.

Standards: HSS.ID.A.4

Click here to practice: Statistics & Probability – Interpreting Categorical & Quantitative Data Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Making Inferences & Justifying Conclusions

Sample Question: In a research project about pet behavior, a random sample of 400 cats was chosen. The study showed that 60% of the cats preferred to sleep inside the house. Chicken was the favorite food for 35% of those cats. The study also showed that 85% of the cats that preferred to sleep outside the house had a different favorite dish. How many cats in the sample liked chicken the best and preferred to sleep inside?

Answer Explanation: If the sample has 400 cats and 60% of the cats preferred to sleep inside, then 400.0.60=240 cats preferred to sleep inside and 160 cats preferred to sleep outside. Next, if the favorite dish of 35% of those cats that preferred to sleep inside was chicken, then, 240.0.35=84 cats in the sample preferred to sleep inside and had chicken as their favorite dish.

Standards: HSS.IC.B.6

Click here to practice: Statistics & Probability – Making Inferences & Justifying Conclusions Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Conditional Probability & the Rules of Probability

Sample Question: A student council has one upcoming vacancy. The school is holding an election and has eight equally likely candidates. The AP Statistics class wants to simulate the results of the election, so the students have to choose an appropriate simulation method. They intend to do trials with the simulation. Which of these methods would be the most appropriate?

• Spin a wheel with eight equal spaces
• Toss a coin eight times for each election
• Throw a dice
• Throw four die

Answer Explanation: The question states that there are eight equally likely candidates. This means that each candidate has the same chance of winning the election. Only the spinning wheel with eight equal spaces could simulation this situation because the wheel has an equal chance of landing on each space.

Standards: HSS.IC.A.1

Click here to practice: Statistics & Probability – Conditional Probability & the Rules of Probability Questions for Grade 10 Math

Domain: Grade 10 >> Statistics & Probability – Using Probability to Make Decisions

Answer Explanation: Simply count the data points in circles C and E. There are 8 of them out of 24 total data points and by reducing we get 8/24=1/3.

Standards: HSS.CP.B.7

Click here to practice: Statistics & Probability – Using Probability to Make Decisions Questions for Grade 10 Math

Sample Question: A statistician is working for Sweet Shop USA and has been given the task to find out what the probability is that the fudge machine malfunctions messing up a whole batch of fudge in the process. Each malfunction of the machine costs the company $250. The statistician calculates the probability is 1 in 20 batches of fudge will be lost due to machine malfunction. What is the expected value of this loss for one month if the company produces 20 batches of fudge each day?

Answer Explanation: Since most months have 30 days we will assume 30 days in a month. We can use E(x)=x1p1+x2p2+…+xipi or simply calculate as follows E(X)=.05*250*30=$375

Standards: HSS.MD.A.4

Looking for online practice tests? Here is the link to practice more of SBAC Grade 10 Math questions.

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Jenny Watson

2 thoughts on “ grade 10 math questions and solutions ”.

Pingback: Create 10 questions for Grade 1 Algebra with explainations and answer choice - Parent.wiki

https://www.lumoslearning.com/llwp/sample-test-questions/sbac-sample-questions-grade-10-math.html

8/5 = x/576 should read 5/8 = x/576 The rest of the solution is correct so it’s a simple typo.

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Tenth Grade (Grade 10) Problem Solving Strategies Questions

You can create printable tests and worksheets from these Grade 10 Problem Solving Strategies questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

• The cost of her other groceries.
• The number of mangoes she bought.
• The weight of each mango.
• The cost of each mango.
• 525,600 minutes
• 21,900 minutes
• 8,760 minutes
• 913 minutes
• Because this is dimensional analysis, regular rules of math do not apply.
• Since the necessary units cancel out, there is no problem.
• Because each of these factors is equal to one (the numerator and denominator are equal, but in different units).
• By the Multiplicative Property of Equality.
• One variable: C, the cost of moving.
• One variable: t, for the amount of time.
• Two variables: C, for the total cost, and t, for the amount of time.
• Two variables: t, for the amount of time, and d, for the distance traveled.
• One variable, the length of the side of the garden.
• One variables, the total perimeter of the garden.
• Two variables, the length and width of the garden.
• Two variables, the amount of fence he has, and the area of the garden.
• The rate of the water's increase, in liters per hour.
• The amount of water in the bucket, in liters.
• The amount of water in the bucket in liters and the amount of time that has passed in hours.
• The size of the bucket in liters and the rate of the drip in liters per hour.
• Yes, since [math]("N" * "m")/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx 1/("m") = "N"*"m"[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx 1/"kg" xx 1/"kg" xx "m"/1 = ("N" * "m"^3)/ ("kg"^4)[/math].
• No, since [math]("N" * "m"^2)/("kg"^2) xx "kg"/1 xx "kg"/1 xx "m"/1 = "N" * "m"^3[/math].
• Yes, this is the correct model, and there are no more important factors to consider.
• No, this model leaves out many important variables, such as climate, water currents, diseases, and many more.
• No, only the current number of penguins and the historic rate of population growth are important. All the other factors are simply over-complicating the problem.
• Neither correct nor incorrect. Any real world problem can be modeled in multiple ways and with varying degrees of complexity.
• Hockey skill.
• Number of classes a student is taking.
• What type of movies he likes.
• Whether the student intends on attending university after he graduates high school.
• Number of calls placed to 9-1-1 from this neighborhood.
• When calls to 9-1-1 are placed from this neighborhood.
• Names of people arrested in this neighborhood.
• Criminal history of people arrested in this neighborhood.
• Yes, she is correct.
• No. She assumed that all terms need to have the same units, when all terms need to be without units.
• No. Although the variable [math]t[/math] is squared, the units are not. Therefore, the units of the last term are m/s, which are different than the rest of the terms.
• No. Jillian did the dimensional analysis incorrectly. The units of the second term on the right side come out to [math]"m"//"s"^2[/math] and the units of the last term are [math]"m"//"s"^4[/math].
• [math]3 xx 778 xx 26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 1/26.4 xx 2.5[/math]
• [math]1/3 xx 778 xx 1/26.4 xx 1/2.5[/math]
• Just one variable, the average cost of a baked good.
• Two variables, one for the cost to make the baked goods, and another for the total revenue of the baked goods.
• Two variables, one for the total number of turnovers sold, and another for the total number of cupcakes sold.
• Two variables, one for the cost of a turnover, and one for the cost of a cupcake.
• Amount of sunlight the plant will get.
• The size of the apartment.
• Whether she will put the plant on the floor or on a table.
• Average temperature of her apartment.
• The average number of tomatoes a tomato plant produces.
• The average weight of tomatoes a tomato plant produces.
• How long it takes to can one pound of tomatoes.
• The average weight of one can of tomatoes.
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Unit 2: Solving equations & inequalities

About this unit, linear equations with variables on both sides.

• Why we do the same thing to both sides: Variable on both sides (Opens a modal)
• Intro to equations with variables on both sides (Opens a modal)
• Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
• Equation with variables on both sides: fractions (Opens a modal)
• Equation with the variable in the denominator (Opens a modal)
• Equations with variables on both sides Get 3 of 4 questions to level up!
• Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!

Linear equations with parentheses

• Equations with parentheses (Opens a modal)
• Reasoning with linear equations (Opens a modal)
• Multi-step equations review (Opens a modal)
• Equations with parentheses Get 3 of 4 questions to level up!
• Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
• Reasoning with linear equations Get 3 of 4 questions to level up!

Analyzing the number of solutions to linear equations

• Number of solutions to equations (Opens a modal)
• Worked example: number of solutions to equations (Opens a modal)
• Creating an equation with no solutions (Opens a modal)
• Creating an equation with infinitely many solutions (Opens a modal)
• Number of solutions to equations Get 3 of 4 questions to level up!
• Number of solutions to equations challenge Get 3 of 4 questions to level up!

Linear equations with unknown coefficients

• Linear equations with unknown coefficients (Opens a modal)
• Why is algebra important to learn? (Opens a modal)
• Linear equations with unknown coefficients Get 3 of 4 questions to level up!

Multi-step inequalities

• Inequalities with variables on both sides (Opens a modal)
• Inequalities with variables on both sides (with parentheses) (Opens a modal)
• Multi-step inequalities (Opens a modal)
• Using inequalities to solve problems (Opens a modal)
• Multi-step linear inequalities Get 3 of 4 questions to level up!
• Using inequalities to solve problems Get 3 of 4 questions to level up!

Compound inequalities

• Compound inequalities: OR (Opens a modal)
• Compound inequalities: AND (Opens a modal)
• A compound inequality with no solution (Opens a modal)
• Double inequalities (Opens a modal)
• Compound inequalities examples (Opens a modal)
• Compound inequalities review (Opens a modal)
• Solving equations & inequalities: FAQ (Opens a modal)
• Compound inequalities Get 3 of 4 questions to level up!

GRADE  10 MATH QUESTIONS AND SOLUTIONS

Problem 1 :

Find greatest common factor of the following terms 

20x 3 , 36x 6

20  =  2 2  ⋅ 5

36  =  2 2  ⋅ 3 2

Greatest common factor  =   2 2  ⋅ 3 2  ⋅  5

  =  180

So, the g reatest common factor is  180 x 6 .

Problem 2 :

Simplify the following

p 2 - 1  =  (p+1) (p-1)

  =  [(p+1) (p-1)/p] ⋅ [p 3 /(p-1)]  ⋅ [1/(p+1)]

  =  p 2

Problem 3 :

Find the square root of 9801 by factor method.

So, the square root of 9801 is 99.

Problem 4 :

Solve 6x 2 + x - 1  =  0

6x 2  + x - 1  =  0

(3x - 1) (2x + 1)  =  0

So the solution is {-1/2, 1/3}.

Problem 5 :

The product of two consecutive odd number is 323. Find them.

Let x and x + 2 are two consecutive odd numbers. 

Product of two consecutive odd numbers =  323

x (x + 2)  =  323

x 2 + 2x  =  323

x 2  + 2x - 323  =  0

(x - 17)(x + 19)

x  =  17 and x  =  -19

So, the two odd numbers are 17 and 19.

Problem 6 :

Find two consecutive even integers whose product is 224.

Let x and x + 2 are two consecutive even integers.

Product of even integers  =  224

x(x + 2)  =  224

x 2 + 2x  =  224

x 2 + 2x - 224  =  0

(x + 16) (x - 14)  =  0

x  =  -16 and x  =  14

So, two consecutive even numbers are 14 and 16.

Problem 7 :

The length of the hall is 3 m more than its width. The numerical value of its area is equal to the numerical value of its perimeter. Find the length and width of the hall.

Let x be the width of the hall

length  =  x + 3

Area of the hall  =  Perimeter of the hall

x(x+3)  =  2(x+x+3)

x 2 + 3x  =  2(2x+3)

x 2  + 3x - 4x - 6  =  0

x 2  - 1x - 6  =  0

(x - 3)(x + 2)  =  0

x  =  3 and x  =  -2

x + 3  =  6

So, the width and length of the rectangle are 3 and 6 m.  

Problem 8 :

Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector approximately (use π = 3.14).

Area of major s ector  =  πr 2  - ( θ/360) πr 2

  =   π4 2  - (30 /360) π4 2

  =   π4 2 (1 - 1/12)

  =   π4 2 (11/12)

  =  (176/12)(3.14)

  =  46.05 cm 2

Problem 9 :

OACB is a quadrant of a circle with center O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region. 

Area of shaded region   =  Area of quadrant - Area of triangle ODB

  =   πr 2 - (1/2)  ⋅ base  ⋅ height

  =  (22/7)(3.5) 2  - (1/2)  ⋅ 3.5  ⋅ 2

  =  38.5 - 3.5

  =  35 cm 2

Problem 10 :

The wheels of a car are of diameter 80 cm each. Find how many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour.

Speed of the car  =  66 km/hr

 1000 m  =  1 km

  100 cm  =  1 m

66 km  =  6600000 cm

66 km/hr  =  6600000/60

  =  110000 cm/min

Distance covered  =  Time (Speed)

  =  10( 110000)

  =  1100000 

Radius of the wheel  =  40 cm

Number of revolutions

  =  Distance covered / Distance covered by 4 wheels

Distance covered by 4 whee l s  =  2 πr

  =  1100000 / [2 ( 3.14)  ⋅  40]

=  1100000/251.2

  =  4379

So, each wheel has to revolve 4379 times.

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Free Printable algebra Worksheets for 10th Grade

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4.5 Word problems

4.5 word problems (ema3d).

To solve word problems we need to write a set of equations that represent the problem mathematically. The solution of the equations is then the solution to the problem.

Problem solving strategy (EMA3F)

Read the whole question.

What are we asked to solve for?

Assign a variable to the unknown quantity, for example, \(x\).

Translate the words into algebraic expressions by rewriting the given information in terms of the variable.

Set up an equation or system of equations to solve for the variable.

Solve the equation algebraically using substitution.

Check the solution.

The following video shows two examples of working with word problems.

Video: 2FDX

Worked example 11: Solving word problems

A shop sells bicycles and tricycles. In total there are \(\text{7}\) cycles (cycles include both bicycles and tricycles) and \(\text{19}\) wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.

Assign variables to the unknown quantities

Let \(b\) be the number of bicycles and let \(t\) be the number of tricycles.

Set up the equations

Rearrange equation \(\left(1\right)\) and substitute into equation \(\left(2\right)\), calculate the number of tricycles \(t\), write the final answer.

There are \(\text{5}\) tricycles and \(\text{2}\) bicycles.

Worked example 12: Solving word problems

Bongani and Jane are friends. Bongani takes Jane's maths test paper and will not tell her what her mark is. He knows that Jane dislikes word problems so he decides to tease her. Bongani says: “I have \(\text{2}\) marks more than you do and the sum of both our marks is equal to \(\text{14}\). What are our marks?”

We have two unknown quantities, Bongani's mark and Jane's mark. Let Bongani's mark be \(b\) and Jane's mark be \(j\).

Set up a system of equations

Bongani has \(\text{2}\) more marks than Jane.

Both marks add up to \(\text{14}\).

Use equation \(\left(1\right)\) to express \(b\) in terms of \(j\)

Substitute into equation \(\left(2\right)\), rearrange and solve for \(j\), substitute the value for \(j\) back into equation \(\left(1\right)\) and solve for \(b\), check that the solution satisfies both original equations.

Bongani got \(\text{8}\) for his test and Jane got \(\text{6}\).

Worked example 13: Solving word problems

A fruitshake costs \(\text{R}\,\text{2,00}\) more than a chocolate milkshake. If \(\text{3}\) fruitshakes and \(\text{5}\) chocolate milkshakes cost \(\text{R}\,\text{78,00}\), determine the individual prices.

Let the price of a chocolate milkshake be \(x\) and let the price of a fruitshake be \(y\).

Substitute equation \(\left(1\right)\) into \(\left(2\right)\)

Rearrange and solve for \(x\), substitute the value of \(x\) back into equation \(\left(1\right)\) and solve for \(y\), write final answer.

One chocolate milkshake costs \(\text{R}\,\text{9,00}\) and one fruitshake costs \(\text{R}\,\text{11,00}\).

Worked example 14: Solving word problems

The product of two consecutive negative integers is \(\text{1 122}\). Find the two integers.

Let the first integer be \(n\) and let the second integer be \(n + 1\)

Set up an equation

Expand and solve for \(n\), find the sign of the integers.

It is given that both integers must be negative.

The two consecutive negative integers are \(-\text{34}\) and \(-\text{33}\).

Two jets are flying towards each other from airports that are \(\text{1 200}\) \(\text{km}\) apart. One jet is flying at \(\text{250}\) \(\text{km·h$^{-1}$}\) and the other jet at \(\text{350}\) \(\text{km·h$^{-1}$}\). If they took off at the same time, how long will it take for the jets to pass each other?

Let distance \(d_{1} = \text{1 200} - x\text{ km}\) and distance \(d_{2} = x\text{ km}\).

Speed \(s_{1}= \text{250}\text{ km·h$^{-1}$}\) and speed \(s_{2}= \text{350}\text{ km·h$^{-1}$}\).

Time is found by dividing distance by speed.

When the jets pass each other:

Now we know the distance travelled by the second jet when it passes the first jet, we can find the time:

It will take take the jets 2 hours to pass each other.

Two boats are moving towards each other from harbours that are \(\text{144}\) \(\text{km}\) apart. One boat is moving at \(\text{63}\) \(\text{km·h$^{-1}$}\) and the other boat at \(\text{81}\) \(\text{km·h$^{-1}$}\). If both boats started their journey at the same time, how long will they take to pass each other?

Notice that the sum of the distances for the two boats must be equal to the total distance when the boats meet: \(d_{1} + d_{2} = d_{\text{total}} \longrightarrow d_{1} + d_{2} = \text{144}\text{ km}\).

This question is about distances, speeds, and times. The equation connecting these values is \[\text{speed } = \frac{\text{distance }}{\text{time}} \quad \text{- or -} \quad \text{distance } = \text{speed } \times \text{time}\]

You want to know the amount of time needed for the boats to meet - let the time taken be \(t\). Then you can write an expression for the distance each of the boats travels: \begin{align*} \text{For boat 1:} \quad d_{1} &= s_{1} t \\ &= \text{63}t \\ \text{For boat 2:} \quad d_{2} &= s_{2} t \\ &= \text{81}t \end{align*}

Now we can substitute the two expressions for the distances into the expression for the total distance:

The boats will meet after \(\text{1}\) hour.

Zwelibanzi and Jessica are friends. Zwelibanzi takes Jessica's civil technology test paper and will not tell her what her mark is. He knows that Jessica dislikes word problems so he decides to tease her. Zwelibanzi says: “I have \(\text{12}\) marks more than you do and the sum of both our marks is equal to \(\text{148}\). What are our marks?”

Let Zwelibanzi's mark be \(z\) and let Jessica's mark be \(j\). Then \begin{align*} z &= j+\text{12} \\ z+j &= \text{148} \end{align*}

Substitute the first equation into the second equation and solve: \begin{align*} z+j &= \text{148} \\ (j+\text{12})+j &= \text{148} \\ 2j &= 148 - \text{12}\\ \therefore j &= \frac{\text{136}}{\text{2}}\\ &= \text{68} \end{align*}

Substituting this value back into the first equation gives: \begin{align*} z &= j+\text{12} \\ &= \text{68}+\text{12} \\ &= \text{80} \end{align*} Zwelibanzi achieved \(\text{80}\) marks and Jessica achieved \(\text{68}\) marks.

Kadesh bought \(\text{20}\) shirts at a total cost of \(\text{R}\,\text{980}\). If the large shirts cost \(\text{R}\,\text{50}\) and the small shirts cost \(\text{R}\,\text{40}\), how many of each size did he buy?

Let \(x\) be the number of large shirts and \(20 − x\) the number of small shirts.

Next we note the following:

• He bought \(x\) large shirts for \(\text{R}\,\text{50}\)
• He bought \(20 - x\) small shirts for \(\text{R}\,\text{40}\)
• He spent \(\text{R}\,\text{980}\) in total

We can represent the cost as:

Therefore Kadesh buys \(\text{18}\) large shirts and \(\text{2}\) small shirts.

The diagonal of a rectangle is \(\text{25}\) \(\text{cm}\) more than its width. The length of the rectangle is \(\text{17}\) \(\text{cm}\) more than its width. What are the dimensions of the rectangle?

Let length \(= l\), width \(= w\) and diagonal \(= d\). \(\therefore d = w + 25\) and \(l = w + 17\).

By the theorem of Pythagoras:

The width must be positive, therefore: width \(w = \text{28}\text{ cm}\) length \(l = (w + 17) = \text{45}\text{ cm}\) and diagonal \(d = (w + 25) = \text{53}\text{ cm}\).

The sum of \(\text{27}\) and \(\text{12}\) is equal to \(\text{73}\) more than an unknown number. Find the unknown number.

Let the unknown number \(= x\).

The unknown number is \(-\text{34}\).

A group of friends is buying lunch. Here are some facts about their lunch:

• a milkshake costs \(\text{R}\,\text{7}\) more than a wrap
• the group buys 8 milkshakes and 2 wraps
• the total cost for the lunch is \(\text{R}\,\text{326}\)

Let a milkshake be \(m\) and a wrap be \(w\). From the given information we get the following equations:

Substitute the first equation into the second equation and solve for \(w\):

Substitute the value of \(w\) into the first equation and solve for \(m\):

Therefore a milkshake costs \(\text{R}\,\text{34}\) and a wrap costs \(\text{R}\,\text{27}\).

The two smaller angles in a right-angled triangle are in the ratio of \(1:2\). What are the sizes of the two angles?

Let \(x =\) the smallest angle. Therefore the other angle \(= 2x\).

We are given the third angle \(=90°\).

The sizes of the angles are \(30°\) and \(60°\).

The length of a rectangle is twice the breadth. If the area is \(\text{128}\) \(\text{cm$^{2}$}\), determine the length and the breadth.

We are given length \(l = 2b\) and \(A = l \times b = 128\).

Substitute the first equation into the second equation and solve for \(b\):

But breadth must be positive, therefore \(b = 8\).

Substitute this value into the first equation to solve for \(l\):

Therefore \(b = \text{8}\text{ cm}\) and \(l = 2b = \text{16}\text{ cm}\).

If \(\text{4}\) times a number is increased by \(\text{6}\), the result is \(\text{15}\) less than the square of the number. Find the number.

Let the number \(= x\). The equation that expresses the given information is:

We are not told if the number is positive or negative. Therefore the number is \(\text{7}\) or \(-\text{3}\).

The length of a rectangle is \(\text{2}\) \(\text{cm}\) more than the width of the rectangle. The perimeter of the rectangle is \(\text{20}\) \(\text{cm}\). Find the length and the width of the rectangle.

Let length \(l = x\), width \(w = x - 2\) and perimeter \(= p\).

\(l = \text{6}\text{ cm}\) and \(w = l - 2 = \text{4}\text{ cm}\).

Stephen has 1 litre of a mixture containing \(\text{69}\%\) salt. How much water must Stephen add to make the mixture \(\text{50}\%\) salt? Write your answer as a fraction of a litre.

The new volume (\(x\)) of mixture must contain \(\text{50}\%\) salt, therefore:

The volume of the new mixture is \(\text{1,38}\) litre The amount of water (\(y\)) to be added is:

Therefore \(\text{0,38}\) litres of water must be added. To write this as a fraction of a litre: \(\text{0,38} = \frac{38}{100} = \frac{19}{50} \text{ litres}\)

Therefore \(\frac{19}{50} \text{ litres}\) must be added.

The sum of two consecutive odd numbers is \(\text{20}\) and their difference is \(\text{2}\). Find the two numbers.

Let the numbers be \(x\) and \(y\).

Then the two equations describing the constraints are:

Add the first equation to the second equation:

Substitute into first equation:

Therefore the two numbers are 9 and 11.

The denominator of a fraction is \(\text{1}\) more than the numerator. The sum of the fraction and its reciprocal is \(\frac{5}{2}\). Find the fraction.

Let the numerator be \(x\). So the denominator is \(x + 1\).

Solve for \(x\):

From this the fraction could be \(\frac{1}{2}\) or \(\frac{-2}{-1}\). For the second solution we can simplify the fraction to \(\text{2}\) and in this case the denominator is not 1 less than the numerator.

So the fraction is \(\frac{1}{2}\).

Masindi is \(\text{21}\) years older than her daughter, Mulivhu. The sum of their ages is \(\text{37}\). How old is Mulivhu?

Let Mulivhu be \(x\) years old. So Masindi is \(x + 21\) years old.

Mulivhu is \(\text{8}\) years old.

Tshamano is now five times as old as his son Murunwa. Seven years from now, Tshamano will be three times as old as his son. Find their ages now.

Let Murunwa be \(x\) years old. So Tshamano is \(5x\) years old.

In \(\text{7}\) years time Murunwa's age will be \(x + 7\). Tshamano's age will be \(5x + 7\).

So Murunwa is 7 years old and Tshamano is 35 years old.

If adding one to three times a number is the same as the number, what is the number equal to?

Let the number be \(x\). Then:

If a third of the sum of a number and one is equivalent to a fraction whose denominator is the number and numerator is two, what is the number?

Rearrange until we get a trinomial and solve for \(x\):

A shop owner buys 40 sacks of rice and mealie meal worth \(\text{R}\,\text{5 250}\) in total. If the rice costs \(\text{R}\,\text{150}\) per sack and mealie meal costs \(\text{R}\,\text{100}\) per sack, how many sacks of mealie meal did he buy?

There are 100 bars of blue and green soap in a box. The blue bars weigh \(\text{50}\) \(\text{g}\) per bar and the green bars \(\text{40}\) \(\text{g}\) per bar. The total mass of the soap in the box is \(\text{4,66}\) \(\text{kg}\). How many bars of green soap are in the box?

Lisa has 170 beads. She has blue, red and purple beads each weighing \(\text{13}\) \(\text{g}\), \(\text{4}\) \(\text{g}\) and \(\text{8}\) \(\text{g}\) respectively. If there are twice as many red beads as there are blue beads and all the beads weigh \(\text{1,216}\) \(\text{kg}\), how many beads of each type does Lisa have?

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Linear systems.

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Word problems with linear systems

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Midpoint and length of a line segment

Distance from a point to a line

Equation of median, altitude, perpendicular bisector (triangle)

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Properties of triangles and quadrilaterals

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Expanding product of binomials

Common factoring

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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

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120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

• Teaching Tools
• Subtraction
• Multiplication
• Mixed operations
• Ordering and number sense
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• Physical measurement
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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

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Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

• Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
• Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
• Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
• Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
• Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
• Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
• Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.