fractions and percentages problem solving

Decimals, Fractions and Percentages

Decimals, Fractions and Percentages are just different ways of showing the same value:

Here, have a play with it yourself:

Example Values

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:

Conversions!

From percent to decimal.

To convert from percent to decimal divide by 100 and remove the % sign.

An easy way to divide by 100 is to move the decimal point 2 places to the left :

Don't forget to remove the % sign!

From Decimal to Percent

To convert from decimal to percent multiply by 100%

An easy way to multiply by 100 is to move the decimal point 2 places to the right :

 Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

Example: Convert 2 5 to a decimal

Divide 2 by 5: 2 ÷ 5 = 0.4

Answer: 2 5 = 0.4

From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

Example: To convert 0.75 to a fraction

From fraction to percentage.

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

Example: Convert 3 8 to a percentage

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 37.5%

Answer: 3 8 = 37.5%

From Percentage to Fraction

To convert a percentage to a fraction , first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

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Published 2013 Revised 2019

Exploring Fractions

• The first group  gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children's current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. 
• The second group of tasks  focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills.   

• are applicable to a range of ages;
• provide contexts in which to explore the part-whole relationship in depth;
• offer opportunities to develop conceptual understanding through talk.

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Percentage Word Problems

Welcome to our Basic Percentage Word Problems. In this area, we have a selection of basic percentage problem worksheets designed for 6th grade students who are just starting to learn about percentages to help them to solve a range of simple percentage problems.

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Percentage Learning

Percentages are another area that children can find quite difficult. There are several key areas within percentages which need to be mastered in order.

Our selection of percentage worksheets will help you to find percentages of numbers and amounts, as well as working out percentage increases and decreases and converting percentages to fractions or decimals.

Key percentage facts:

• 50% = 0.5 = ½
• 25% = 0.25 = ¼
• 75% = 0.75 = ¾
• 10% = 0.1 = 1 ⁄ 10
• 1% = 0.01 = 1 ⁄ 100

How to work out Percentages of a number

This page will help you learn to find the percentage of a given number.

There is also a percentage calculator on the page to support you work through practice questions.

• Percentage Of Calculator

This is the calculator to use if you want to find a percentage of a number.

Simple choose your number and the percentage and the calculator will do the rest.

Basic Percentage Word Problems

Here you will find a selection of worksheets on percentages designed to help your child practise how to apply their knowledge to solve a range of percentage problems..

The sheets are graded so that the easier ones are at the top.

The sheets have been split up into sections as follows:

• spot the percentage problems where the aim is to use the given facts to find the missing percentage;
• solving percentage of number problems, where the aim is to work out the percentage of a number.

Each of the sheets on this page has also been split into 3 different worksheets:

• Sheet A which is set at an easier level;
• Sheet B which is set at a medium level;
• Sheet C which is set at a more advanced level for high attainers.

Spot the Percentages Problems

• Spot the Percentage 1A
• PDF version
• Spot the Percentage 1B
• Spot the Percentage 1C
• Spot the Percentage 2A
• Spot the Percentage 2B
• Spot the Percentage 2C

Percentage of Number Word Problems

• Percentage of Number Problems 1A
• Percentage of Number Problems 1B
• Percentage of Number Problems 1C
• Percentage of Number Problems 2A
• Percentage of Number Problems 2B
• Percentage of Number Problems 2C
• Percentage of Number Problems 3A
• Percentage of Number Problems 3B
• Percentage of Number Problems 3C

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

6th Grade Percentage Word Problems

The sheets in this area are at a harder level than those on this page.

The problems involve finding the percentage of numbers and amounts, as well as finding the amounts when the percentage is given.

• 6th Grade Percent Word Problems
• Percentage Increase and Decrease Worksheets

We have created a range of worksheets based around percentage increases and decreases.

Our worksheets include:

• finding percentage change between two numbers;
• finding a given percentage increase from an amount;
• finding a given percentage decrease from an amount.

Percentage of Money Amounts

Often when we are studying percentages, we look at them in the context of money.

The sheets on this page are all about finding percentages of different amounts of money.

• Money Percentage Worksheets

Percentage of Number Worksheets

If you would like some practice finding the percentage of a range of numbers, then try our Percentage Worksheets page.

You will find a range of worksheets starting with finding simple percentages such as 1%, 10% and 50% to finding much trickier ones.

• Percentage of Numbers Worksheets

Converting Percentages to Fractions

To convert a fraction to a percentage follows on simply from converting a fraction to a decimal.

Simply divide the numerator by the denominator to give you the decimal form. Then multiply the result by 100 to change the decimal into a percentage.

The printable learning fraction page below contains more support, examples and practice converting fractions to decimals.

• Converting Fractions to Percentages

• Convert Percent to Fraction

Online Percentage Practice Zone

Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.

You can choose your level of difficulty and test yourself with immediate feedback!

• Online Percentage Practice
• Ratio Part to Part Worksheets

These sheets are a great way to introduce ratio of one object to another using visual aids.

The sheets in this section are at a more basic level than those on this page.

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Fractions, Decimals and Percentages

Fractions, Decimals and Percentages are three different ways of expressing a part of a whole.

We can convert between fractions, decimals and percentages.

Converting between Decimals and Percentages

To convert a decimal to a percentage we multiply by 100.

Example 1: Convert 0.7 to a percentage

0.7 × 100 = 70 0.7 = 70%

Example 2: Convert 0.19 to a percentage

0.19 × 100 = 19 0.19 = 19%

To convert a percentage to a decimal we divide by 100 Dividing by 100 is the opposite of multiplying by 100

Example 3: Convert 25% to a decimal

To convert a percentage to a decimal we divide by 100.

25 ÷ 100 = 0.25 25% = 0.25

Example 4: Convert 9% to a decimal

9 ÷ 100 = 0.09 9% = 0.09

Converting between Percentages and Fractions

A percentage is out of 100. We can re-write any percentage as a fraction by writing it over 100.

Example 5: Convert 11% to a fraction.

A percentage is the same as a fraction out of 100.

We can write 11% as 11 ⁄ 100

Example 6: Convert 36% to a fraction. Give your answer in it simplest form.

We can write 36% as 36 ⁄ 100

We have written 36% as a fraction, but it is not in its simplest form. To simplify we need to find a times table that 36 and 100 are both in. 36 and 100 are both in the 2 and the 4 times tables. 4 is the biggest so we will divide the denominator and the numerator by 4.

36 = 4 × 9 100 = 4 × 25

36% = 9 ⁄ 25

We could have also halved the top and bottom, and then halved again:

36 ⁄ 100 = 18 ⁄ 50 = 9 ⁄ 25

To convert a fraction to a percentage we can change the denominator to 100.

Example 7: Convert 7 ⁄ 20 to a percentage.

To convert the fraction to a percentage we need to make the denominator 100.

We can make the denominator 100 by multiplying by 5. 20 × 5 = 100

We have to multiply the numerator by 5 too keep the fraction equivalent. 7 × 5 = 35

7 ⁄ 20 = 35 ⁄ 100 = 35%

When the denominator is not a factor of 100 it may be easier to convert the fraction to a decimal first, and then from a decimal to a percentage.

Converting between Fractions and Decimals

To convert from a fraction to a decimal we can divide the numerator by the denominator.

Example 8: Convert 3 ⁄ 8 to a decimal.

We can convert 3 ⁄ 8 to a decimal by calculating 3 ÷ 8.

We can use a calculator or short division to do the calculation.

3 ÷ 8 = 0.375

3 ⁄ 8 = 0.375

If we are using a calculator we can also use the SD button.

Example 9 : Convert 7 ⁄ 12 to a decimal.

We need to calculate 7 ÷ 12

7 ÷ 12 = \(0.58\dot3\)

The dot above the 3 means that the 3 is recurring (it goes on forever), 0.5833333333333333333...

7 ⁄ 12 = \(0.58\dot3\)

To convert a decimal to a fraction we can convert it to a percentage (by multiplying by 100) and then write it is a fraction out of 100.

Example 10: Convert 0.88 to a fraction. Give your answer in its simplest form.

To convert 0.88 to a percentage we multiply by 100. 0.88 × 100 = 88

88% = 88 ⁄ 100

We can simplify our answer by dividing top and bottom by 4.

88 ⁄ 100 = 22 ⁄ 25

0.88 = 22 ⁄ 25

If the decimal involves a recurring numbers we can type it into the calculator instead and the calculator will do the conversion for us. The recurring button looks like this:

It may be found (depending on your calculator) by pressing SHIFT then the square button:

Example 11: Convert \(0.7\dot3\) to a fraction. Give your answer in its simplest form.

We can type \(0.7\dot3\) into a calculator by pressing:

The calculator should give an answer of 11 ⁄ 15

Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions

Problem Solving using Fractions

Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less

Table of Contents

What are Fractions?

Types of fractions.

• Fractions with like and unlike denominators
• Operations on fractions
• Fractions can be multiplied by using
• Let’s take a look at a few examples

Solved Examples

• Frequently Asked Questions

Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.

For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction  \(\frac{1}{2}\) . 

Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .

Proper fractions

A fraction in which the numerator is less than the denominator value is called a  proper fraction.

For example ,  \(\frac{3}{4}\) ,  \(\frac{5}{7}\) ,  \(\frac{3}{8}\)   are proper fractions.

Improper fractions 

A fraction with the numerator higher than or equal to the denominator is called an improper fraction .

Eg \(\frac{9}{4}\) ,  \(\frac{8}{8}\) ,  \(\frac{9}{4}\)   are examples of improper fractions.

Mixed fractions

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.

We express improper fractions as mixed numbers.

For example ,  5\(\frac{1}{3}\) ,  1\(\frac{4}{9}\) ,  13\(\frac{7}{8}\)   are mixed fractions.

Unit fraction

A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .

Fractions with Like and Unlike Denominators

Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.

For example,  

\(\frac{1}{4}\)  and  \(\frac{3}{4}\)  are like fractions as they both have the same denominator, that is, 4.

\(\frac{1}{3}\)  and  \(\frac{1}{4}\)   are unlike fractions as they both have a different denominator.

Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.

There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.

Fractions can be Multiplied by Using:

Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor. 

Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

= \(\frac{5~+~12}{30}\)  

=  \(\frac{17}{30}\) 

( \(\frac{5}{2}~-~\frac{1}{6}\) )

= \(\frac{12~-~5}{30}\)

= \(\frac{7}{30}\)

Examples of Multiplication and Division

Multiplication:

(\(\frac{1}{6}~\times~\frac{2}{5}\))

= (\(\frac{1~\times~2}{6~\times~5}\))                                       [Multiplying numerator of fractions and multiplying denominator of fractions]

=  \(\frac{2}{30}\)

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\))                                     [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

= \(\frac{12}{5}\)

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

Let’s add \(\frac{7}{8}\)  and  \(\frac{2}{3}\)   using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.

\(\frac{7}{8}\) + \(\frac{2}{3}\)

= \(\frac{21~+~16}{24}\)    

= \(\frac{37}{24}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

Solution:  

Let’s subtract  \(\frac{12}{17}\) from \(\frac{11}{13}\)   using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.

\(\frac{11}{13}\) – \(\frac{12}{17}\)

= \(\frac{187~-~156}{221}\)

= \(\frac{31}{221}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

= \(\frac{270}{221}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25}{33}~\times~\frac{41}{45}\)                            [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\)  ]

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{1125}{1353}\)

Example 5: 

Sam was left with   \(\frac{7}{8}\)  slices of chocolate cake and    \(\frac{3}{7}\)  slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared   \(\frac{10}{11}\)  slices from the total number he had with his parents. What is the number of slices he has remaining?

To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,

=   \(\frac{7}{8}\) +   \(\frac{3}{7}\)   

=   \(\frac{49~+~24}{56}\)

=   \(\frac{73}{56}\)

To find out the remaining number of slices Sam has   \(\frac{10}{11}\)  slices need to be deducted from the total number,

= \(\frac{73}{56}~-~\frac{10}{11}\)

=   \(\frac{803~-~560}{616}\)

=   \(\frac{243}{616}\)

Hence, after sharing the cake with his friends, Sam has  \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had  \(\frac{243}{616}\)  slices of cake left with him.

Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of   \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?

First  \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters =  \(\frac{15}{8}\) x 1000 = 1875 ml

To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.

The number of oranges required for 1875 m l of juice =  \(\frac{1875}{25}\) ml = 75 oranges

To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has

=  \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups,   \(\frac{3}{8}\) th  of a cup cannot be sold alone.

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

What is a mixed fraction?

A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.

How will you add fractions with unlike denominators?

When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions. 

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PROBLEM SOLVING WITH FRACTIONS DECIMALS AND PERCENTAGES WORKSHEET

Problems with fractions.

(1)  A fruit merchant bought mangoes in bulk. He sold 5/8  of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy? 

(2)  A family requires 2 1/2 liters of milk per day. How much milk would family require in a month of 31 days?  

(3)  A ream of paper weighs 12 1/2 kg.  What is the weight per quire ?

(4)   It was Richard's birthday. He distributed 6 kg of candies to his friends. If he had given 1/8  kg of candies to each friend, how many friends were there ?

(5)  Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?

Answer Key :

(1)  960 mangoes

(2)   77 1/2 liter

(3)  5/8 kg

(4)   48 friends

(5)  1/5

Fraction Word Problems Mixed Operations

(1)  Linda walked 2 1/3 miles on the first day and 3 2/5   miles on the next day. How many miles did she walk in all ?                Solution

(2)   David ate 2 1/7 pizzas and he gave 1 3/14    pizzas to his mother. How many pizzas did David have initially ?

(3)   Mr. A has 3 2/3 acres of land. He gave 1 1/4 acres of land to his friend. How many acres of land does Mr. A have now ?          Solution

(4)   Lily added 3 1/3 cups of walnuts to a batch of trail mix. Later she added 1 1/3 cups of almonds. How many cups of nuts did Lily put in the trail mix in all? 

(5)   In the first hockey games of the year, Rodayo played 1 1/2 periods and 1 3/4 periods. How many periods in all did he play ?         Solution

(6)   A bag can hold 1 1/2 pounds of flour. If Mimi has 7 1/2 pounds of flour, then how many bags of flour can Mimi make ?        Solution

(7)   Jack and John went fishing Jack caught 3 3/4 kg of fish and while John  caught 2 1/5 kg of fish. What is the total weight of the fish they caught?

(8)   Amy has 3 1/2 bottles in her refrigerator. She used 3/5 bottle in the morning 1 1/4 bottle in the afternoon. How many bottles of milk does Amy have left over ?  

(9)   A tank has 82 3/4 liters of water. 24 4/5 liters of water were used and the tank was filled with another 18 3/4 liters. What is the final volume of the water in the tank ?

(10)   A trader prepared 21 1/2 liters of lemonade. At the end of the day he had 2 5/8 liters left over. How many liters of lemonade was sold by the Trader? 

Answer key :

Problems on Decimals

(1)  A chemist mixed 6.35 grams of one compound with 2.45 grams of another compound. How many grams were there in the mixture.      Solution

(2)   If the cost of a pen is $10.50, a book is $25.75 and a bag is $45.50, the  find the total cost of 2 books, 3 pens and 1 bag.         Solution

(3)    John wants to buy a bicycle that cost $ 450.75. He has saved $ 125.35. How much more money must John save in order to have enough money to buy the bicycle ?

(4)   Jennifer bought 6.5 kg of sugar. she used 3750 grams. How many kilograms of sugar were left ?

(5)   The inner radius of a pipe is 12.625 mm and the outer radius is 18.025 mm. Find the thickness of the pipe.          Solution

(6)   A copy of English book weighs 0.45 kg. What is the weight of 20 copies ?          Solution

(7)   Find the weight of 25.5 meters of copper wire in kilograms, if one meter weighs 10 grams.          Solution

(8)   Robert paid $140 for 2.8 kg of cooking oil. How much did 1 kg of the cooking oil cost ?         Solution

(9)   If $20.70 is earned in 6 hours, how much money will be earned in 5 hours ?            Solution

(10)   A pipe is 76.8 meters long. What will the greatest number of pieces of pipe each 8 meters long that can be cut from this pipe ?          Solution

Answers Key :

Problems on Percentage

(1)  In a particular store the number of TV's sold the week of Black Friday was 685. The number of TVs sold the following week was 500. TV sales the week following Black Friday were what percent less than TV sales the week of Black Friday ?

(A)  17%   (B)  27%   (C)  37%   (D)  47%

(2)  In March, a city zoo attracted 32000 visitors to its polar bear exhibit. In April, the number of visitors to the exhibit increased by 15%. How many visitors did the zoo attract to its polar bear exhibit in April ?

(A)  32150   (B)  32480   (C)  35200  (D)  36800

(3)  A charity organization collected 2140 donations last month. With the help of 50 additional volunteers, the organization collected 2690 donations this month. To the nearest tenth of a percent, what was the percent increase in the number of donations the charity organization collected ?

(A) 20.4%   (B)  20.7%    (C)  25.4%   (D)  25.7%

(4)  The discount price of a book is 20% less than the retail price. James manages to purchase the book at 30% off the discount price at the special book sale. What percent of the retail price did James pay ?

(A)  42%   (B)  48%    (C)  50%   (D)  56%

(5)  Each day, Robert eats 40% of the pistachios left in his jar at the time. At the end of the second day, 27 pistachios remain. How many pistachios were in the jar at the start of the first day ?

(A)  75   (B)  80   (C)  85  (D)  95

(6) Joanne bought a doll at a 10 percent discount off the original price of $105.82. However, she had to pay a sales tax of x% on the discounted price. If the total amount she paid for the doll was $100, what is the value of x ?

(A)  2   (B)  3   (C)  4  (D)  5

(7)  In 2010, the number of houses built in Town A was 25 percent greater than the number of houses built in Town B. If 70 houses were built in Town A during 2010, how many were built in Town B ?

(A)  56   (B)  50    (C)  48   (D)  20

(8)  Over two week span, John ate 20 pounds of chicken wings and 15 pounds of hot dogs. Kyle ate 20 percent more chicken wings and 40 percent more hot dogs. Considering only chicken wings and hot dogs, Kyle ate approximately x percent more food, by weight, than John, what is x (rounded to the nearest percent) ?

(A)  25   (B)  27    (C)  29   (D)  30

(9) Due to deforestation, researchers, expect the deer population to decline by 6 percent every year. If the current deer population is 12000, what is the approximate expected population size in 10 years from now ?

(A)  25000   (B)  48000    (C)  56000   (D)  30000

(10)  In 2000 the price of a house was $72600. By 2010 the price of the house has increased to 125598.

(A)  70%    (B)  62%    (C)  73%    (D)  90%

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Mixed Worded Fractions Decimals Percentages Questions (Exam Style)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

20 December 2017

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exactly what I was looking for thank you!

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Looks good, with a good mix. Thanks.

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Please could you provide the answers<br /> <br /> Thank you

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