compound presentation simple definition

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Chapter 27:  Compound Presentations

George Tawagi

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Prolapse of hand and arm or foot and leg.

• MANAGEMENT OF COMPOUND PRESENTATIONS
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A presentation is compound when there is prolapse of one or more of the limbs along with the head or the breech, both entering the pelvis at the same time. Footling breech or shoulder presentations are not included in this group. Associated prolapse of the umbilical cord occurs in 15 to 20 percent of cases.

Easily detectable compound presentations occur probably once in 500 to 1000 confinements. It is impossible to establish the exact incidence because:

Spontaneous correction occurs frequently, and examination late in labor cannot provide the diagnosis

Minor degrees of prolapse are detected only by early and careful vaginal examination

Classification of Compound Presentation

Upper limb (arm–hand), one or both

Lower limb (leg–foot), one or both

Arm and leg together

Breech presentation with prolapse of the hand or arm

By far the most frequent combination is that of the head with the hand ( Fig. 27-1 ) or arm. In contrast, the head–foot and breech–arm groups are uncommon, about equally so. Prolapse of both hand and foot alongside the head is rare. All combinations may be complicated by prolapse of the umbilical cord, which then becomes the major problem.

FIGURE 27-1.

Compound presentation: head and hand.

The etiology of compound presentation includes all conditions that prevent complete filling and occlusion of the pelvic inlet by the presenting part. The most common causal factor is prematurity. Others include high presenting part with ruptured membranes, polyhydramnios, multiparity, a contracted pelvis, pelvic masses, and twins. It is also more common with inductions of labor involving floating presenting parts. Another predisposing factor is external cephalic version. During the process of external version, a fetal limb (commonly the hand–arm, but occasionally the foot) can become “trapped” before the fetal head and thus become the presenting part when labor ensues.

Diagnosis is made by vaginal examination, and in many cases, the condition is not noted until labor is well advanced and the cervix is fully dilated.

The condition is suspected when:

There is delay of progress in the active phase of labor

Engagement fails to occur

The fetal head remains high and deviated from the midline during labor, especially after the membranes rupture

In the absence of complications and with conservative management, the results should be no worse than with other presentations.

Mechanism of Labor

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Types of Interest

Simple interest formula, compound interest formula, compounding periods.

• Other Related Concepts
• Compound Annual Growth Rate

Real-Life Applications

Additional interest considerations, the bottom line.

• Corporate Finance

Simple vs. Compound Interest: Definition and Formulas

Interest is defined as the cost of borrowing money, as in the case of interest charged on a loan balance. Conversely, interest can also be the rate paid for money on deposit, as in the case of a certificate of deposit. Interest can be calculated in two ways:  simple interest or compound interest .

• Simple interest is calculated on the principal , or original, amount of a loan.
• Compound interest is calculated on the principal amount and the accumulated interest of previous periods, and thus can be regarded as “interest on interest.”

There can be a big difference in the amount of interest payable on a loan if interest is calculated on a compound basis rather than on a simple basis. On the positive side, the magic of compounding can work to your advantage when it comes to your investments and can be a potent factor in wealth creation.

While simple interest and compound interest are basic financial concepts, becoming thoroughly familiar with them may help you make more informed decisions when taking out a loan or investing. Cumulative interest can also help you choose one bond investment over another.

Key Takeaways

• Interest can refer to the cost of borrowing money (in the form of interest charged on a loan) or to the rate paid for money on deposit.
• In the case of a loan, simple interest is only charged on the original principal amount.
• Simple interest is calculated by multiplying the loan principal by the interest rate and then by the term of a loan.
• Compound interest multiplies savings or debt at an accelerated rate.
• Compound interest is interest calculated on both the initial principal and all of the previously accumulated interest.

The formula for calculating simple interest is:

Simple Interest = P × i × n where: P = Principal i = Interest rate n = Term of the loan \begin{aligned}&\text{Simple Interest} = P \times i \times n \\&\textbf{where:}\\&P = \text{Principal} \\&i = \text{Interest rate} \\&n = \text{Term of the loan} \\\end{aligned} ​ Simple Interest = P × i × n where: P = Principal i = Interest rate n = Term of the loan ​

Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, then the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500.

Interest on this loan is payable at $500 annually, or $1,500 over the three-year loan term.

The formula for calculating compound interest in a year is:

A = P ( 1 + r n ) n t where: A = Final amount P = Initial principal balance r = Interest rate n = Number of times interest applied per time period t = Number of time periods elapsed \begin{aligned}&A=P\left(1+\frac{r}{n}\right)^{nt}\\&\textbf{where:}\\&A=\text{Final amount}\\&P=\text{Initial principal balance}\\&r=\text{Interest rate}\\&n=\text{Number of times interest applied}\\&\qquad\text{per time period}\\&t=\text{Number of time periods elapsed}\end{aligned} ​ A = P ( 1 + n r ​ ) n t where: A = Final amount P = Initial principal balance r = Interest rate n = Number of times interest applied per time period t = Number of time periods elapsed ​

Compound Interest = total amount of principal and interest in future (or future value ) less the principal amount at present, called  present value (PV). PV is the current worth of a future sum of money or stream of  cash flows  given a specified  rate of return . 

Continuing with the simple interest example, what would be the amount of interest if it is charged on a compound basis? In this case, it would be:

Interest = $ 10 , 000 ( ( 1 + 0.05 ) 3 − 1 ) = $ 10 , 000 ( 1.157625 − 1 ) = $ 1 , 576.25 \begin{aligned} \text{Interest} &= \$10,000 \big( (1 + 0.05) ^ 3 - 1 \big ) \\ &= \$10,000 \big ( 1.157625 - 1 \big ) \\ &= \$1,576.25 \\ \end{aligned} Interest ​ = $10 , 000 ( ( 1 + 0.05 ) 3 − 1 ) = $10 , 000 ( 1.157625 − 1 ) = $1 , 576.25 ​

While the total interest payable over the three-year period of this loan is $1,576.25, unlike simple interest, the interest amount is not the same for all three years because compound interest also takes into consideration the accumulated interest of previous periods. Interest payable at the end of each year is shown in the table below.

When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 of a loan over a certain period, the amount of interest accrued at 10% annually will be lower than the interest accrued at 5% semiannually, which will, in turn, be lower than the interest accrued at 2.5% quarterly.

In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year.

That is, within the parentheses, “i” or interest rate has to be divided by “n,” the number of compounding periods per year. Outside of the parentheses, “n” has to be multiplied by “t,” the total length of the investment.

Therefore, for a 10-year loan at 10%, where interest is compounded semiannually (number of compounding periods = 2), i = 5% (i.e., 10% ÷ 2) and n = 20 (i.e., 10 x 2).

To calculate the total value with compound interest, you would use this equation:

Total Value with Compound Interest = ( P ( 1 + i n ) n t ) − P Compound Interest = P ( ( 1 + i n ) n t − 1 ) where: P = Principal i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan \begin{aligned} &\text{Total Value with Compound Interest} = \Big( P \big ( \frac {1 + i}{n} \big ) ^ {nt} \Big ) - P \\ &\text{Compound Interest} = P \Big ( \big ( \frac {1 + i}{n} \big ) ^ {nt} - 1 \Big ) \\ &\textbf{where:} \\ &P = \text{Principal} \\ &i = \text{Interest rate in percentage terms} \\ &n = \text{Number of compounding periods per year} \\ &t = \text{Total number of years for the investment or loan} \\ \end{aligned} ​ Total Value with Compound Interest = ( P ( n 1 + i ​ ) n t ) − P Compound Interest = P ( ( n 1 + i ​ ) n t − 1 ) where: P = Principal i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan ​

The following table demonstrates the difference that the number of compounding periods can make over time for a $10,000 loan taken for a 10-year period. 

Other Compound Interest Concepts

Time value of money.

Since money is not “free” but has a cost in terms of interest payable, it follows that a dollar today is worth more than a dollar in the future. This concept is known as the time value of money and forms the basis for relatively advanced techniques like discounted cash flow (DFC) analysis. The opposite of compounding is known as discounting . The discount factor can be thought of as the reciprocal of the interest rate and is the factor by which a future value must be multiplied to get the present value.

The formulas for obtaining the future value (FV) and present value (PV) are as follows:

FV = P V × [ 1 + i n ] ( n × t ) PV = F V ÷ [ 1 + i n ] ( n × t ) where: i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan \begin{aligned}&\text{FV}=PV\times\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\text{PV}=FV\div\left[\frac{1+i}{n}\right]^{(n\times t)}\\&\textbf{where:}\\&i=\text{Interest rate in percentage terms}\\&n=\text{Number of compounding periods per year}\\&t=\text{Total number of years for the investment or loan}\end{aligned} ​ FV = P V × [ n 1 + i ​ ] ( n × t ) PV = F V ÷ [ n 1 + i ​ ] ( n × t ) where: i = Interest rate in percentage terms n = Number of compounding periods per year t = Total number of years for the investment or loan ​

The Rule of 72

The Rule of 72 calculates the approximate time over which an investment will double at a given rate of return or interest “i” and is given by (72 ÷ i). It can only be used for annual compounding but can be very helpful in planning how much money you might expect to have in retirement.

For example, an investment that has a 6% annual rate of return will double in 12 years (72 ÷ 6%).

An investment with an 8% annual rate of return will double in nine years (72 ÷ 8%).

Compound Annual Growth Rate (CAGR)

The compound annual growth rate (CAGR) is used for most financial applications that require the calculation of a single growth rate over a period.

For example, if your investment portfolio has grown from $10,000 to $16,000 over five years, then what is the CAGR? Essentially, this means that PV = $10,000, FV = $16,000, and nt = 5, so the variable “i” has to be calculated. Using a financial calculator or Excel spreadsheet , it can be shown that i = 9.86%.

Please note that according to cash flow convention, your initial investment (PV) of $10,000 is shown with a negative sign since it represents an outflow of funds. PV and FV must necessarily have opposite signs to solve “i” in the above equation.

CAGR is extensively used to calculate returns over periods for stocks, mutual funds, and investment portfolios. CAGR is also used to ascertain whether a mutual fund manager or portfolio manager has exceeded the market’s rate of return over a period. For example, if a market index has provided total returns of 10% over five years, but a fund manager has only generated annual returns of 9% over the same period, then the manager has underperformed the market.

CAGR can also be used to calculate the expected growth rate of investment portfolios over long periods, which is useful for such purposes as saving for retirement. Consider the following examples:

• A risk-averse investor is happy with a modest 3% annual rate of return on their portfolio. Their present $100,000 portfolio would, therefore, grow to $180,611 after 20 years. In contrast, a risk-tolerant investor who expects an annual rate of return of 6% on their portfolio would see $100,000 grow to $320,714 after 20 years.
• CAGR can be used to estimate how much needs to be stowed away to save for a specific objective. A couple who would like to save $50,000 over 10 years toward a down payment on a condo would need to save $4,165 per year if they assume an annual return (CAGR) of 4% on their savings. If they’re prepared to take on additional risk and expect a CAGR of 5%, then they would need to save $3,975 annually.
• CAGR can also be used to demonstrate the virtues of investing earlier rather than later in life. If the objective is to save $1 million by retirement at age 65, based on a CAGR of 6%, a 25-year-old would need to save $6,462 per year to attain this goal. A 40-year-old, on the other hand, would need to save $18,227, or almost three times that amount, to attain the same goal.

Make sure you know the exact annual percentage rate (APR) on your loan since the method of calculation and number of compounding periods can have an impact on your monthly payments. While banks and financial institutions have standardized methods to calculate interest payable on mortgages and other loans, the calculations may differ slightly from one country to the next.

Compounding can work in your favor when it comes to your investments, but it can also work for you when making loan repayments. For example, making half your mortgage payment twice a month, rather than making the full payment once a month, will end up cutting down your amortization period and saving you a substantial amount of interest.

Compounding can work against you if you carry loans with very high rates of interest, like credit card or department store debt. For example, a credit card balance of $25,000 carried at an interest rate of 20%—compounded monthly—would result in a total interest charge of $5,485 over one year or $457 per month. 

Which Is Better, Simple or Compound Interest?

It depends on whether you're investing or borrowing. Compound interest causes the principal to grow exponentially because interest is calculated on the accumulated interest over time as well as on your original principal. It will make your money grow faster in the case of invested assets. However, on a loan, compound interest can create a snowball effect and exponentially increase your debt. If you have a loan, you'll pay less over time with simple interest.

What Are Some Financial Products That Use Simple Interest?

Most coupon-paying bonds, personal loans, and home mortgages use simple interest. On the other hand, most bank deposit accounts, credit cards, and some lines of credit tend to use compound interest.

How Often Does Interest Compound?

Interest can be daily, monthly, quarterly, or annually. The higher the number of compounding periods, the larger the effect of compounding.

Is Compound Interest Considered Income?

Yes: on some types of investments, like savings accounts or bonds, compound interest is considered income.

Get the magic of compounding working for you by investing regularly and increasing the frequency of your loan repayments. Familiarizing yourself with the basic concepts of simple interest and compound interest will help you make better financial decisions, saving you thousands of dollars and boosting your net worth over time.

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Compound Definition in Chemistry

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The word "compound" has several definitions. In the field of chemistry, "compound" refers to a "chemical compound."

Compound Definition

A compound is a chemical species that is formed when two or more atoms join together chemically, with covalent or ionic bonds .

Compounds may be categorized according to the type of chemical bonds holding the atoms together:

• Molecules are held together by covalent bonds.
• Ionic compounds are held together by ionic bonds.
• Intermetallic compounds are held together by metallic bonds.
• Complexes are often held together by coordinate covalent bonds.

Note that some compounds contain a mixture of ionic and covalent bonds. Also note, a few scientists do not consider pure elemental metals to be compounds (metallic bonds).

Examples of Compounds

Examples of compounds include table salt or sodium chloride (NaCl, an ionic compound), sucrose (a molecule), nitrogen gas (N 2 , a covalent molecule), a sample of copper (intermetallic), and water (H 2 O, a covalent molecule) . Examples of chemical species not considered compounds include the hydrogen ion H + and the noble gas elements (e.g., argon, neon, helium), which do not readily form chemical bonds.

Writing Compound Formulas

By convention, when atoms form a compound, its formula lists the atom(s) acting as a cation first, followed by the atom(s) acting as the anion. This means sometimes an atom may be first or last in a formula. For example, in carbon dioxide (CO 2 ), carbon (C) acts as a cation. In silicon carbide (SiC), carbon acts as the anion.

Compound Versus Molecule

Sometimes a compound is called a  molecule . Usually, the two terms are synonymous. Some scientists make a distinction between the types of bonds in molecules ( covalent ) and compounds (ionic).

• Properties of Ionic and Covalent Compounds
• Compounds With Both Ionic and Covalent Bonds
• Molecules and Moles in Chemistry
• Examples of Polar and Nonpolar Molecules
• Ionic vs Covalent Bonds - Understand the Difference
• Formulas of Ionic Compounds
• Covalent or Molecular Compound Properties
• Double Displacement Reaction Definition and Examples
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• Polar Bond Definition and Examples
• The 6 Main Types of Solids
• Metallic Bond: Definition, Properties, and Examples
• Chemistry Vocabulary Terms You Should Know
• What Is a Covalent Bond in Chemistry?
• What You Should Know About Carbon Compounds
• Acid Definition and Examples

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Four Sentence Structures: Simple, Compound, Complex, & Compound-Complex

There are four sentence structures in English: Simple , Compound , Complex, and Compound-Complex . Here are examples of each:

• She ate lunch.  ( Simple : one independent clause)
• She ate lunch, but she was still hungry. ( Compound : two independent clauses joined by a coordinating conjunction ).
• She was still hungry even though she had eaten lunch . ( Complex : an independent clause + a dependent clause)
• She was tired, and she was still hungry even though she had eaten lunch ( Compound-Complex : two independent clauses joined by a coordinating conjunction and one dependent clause)

First: Understanding Clauses

A clause is a group of words that includes a subject and a verb . It's important to understand that there are two types of clauses:

Independent Clauses

A sentence must have at least one independent clause. An independent clause is a group of words that form a complete thought when you put them together. Here are some examples:

• She ate lunch. 
• The car drove on the road. 
• On Tuesday, I had my test. 

These sentences are complete thoughts , which means that no more information is needed to understand them completely.

Dependent Clauses (Subordinate Clauses)

Dependent clauses are incomplete thoughts. They depend on an independent clause in order for the sentence to have meaning. Dependent clauses begin with a subordinate conjunction . Here are some examples:

• when I got home (what happened?)
• because the restaurant was closed (what happened because it was closed?)
• whom I respect very much (whom are we talking about?)

As you can see, more information is needed. To create a complete sentence , you need to add an independent clause . Here are the examples again but written as complete sentences (known as complex sentences):

• I washed the dishes when I got home .
• We couldn't eat because the restaurant was closed .
• The company's owner is Alice Brown , whom I respect very much .

Now that you understand this, we can look at the four different sentence structures.

Structure #1: Simple Sentences

A simple sentence is one independent clause . A clause is a group of words that contain a subject and a verb, and an independent clause it a group of words that form a complete thought when you put them together. Here are some examples:

• She ate lunch. (Independent clause)
• The car drove on the road.  (Independent clause)
• On Tuesday, I had my test. (Independent clause)

Again, all of these sentences are complete thoughts .

Structure #2: Compound Sentences

A compound sentence is made of two independent clauses joined by a coordinating conjunction .

Although the most commonly used coordinating conjunctions are but , and , so , and or, there are  seven coordinating conjunctions in English:

The above sentences are all independent clauses joined by a coordinating conjunction, so they are all compound sentences.

Structure #3: Complex Sentences

A complex sentence has a dependent clause and an independent clause. The dependent clause can come at the beginning of the sentence or at the end. Here are some examples:

• She fell asleep because she was tired .
• Because she was tired , she fell asleep.
• I'll call you if I go .
• If I go , I'll call you.

(Note: When a dependent clause starts a sentence, you should put a comma at its end to show where the clause ends.)

An adjective clause (also known as a relative clause) is also considered a dependent clause as well. E.g.:

• This is the store where I bought my hat.
• Vancouver, which is in western Canada , is a beautiful city.

Structure #4: Compound-Complex

A compound-complex sentence has the following:

• two independent clauses joined a coordinating conjunction
• a dependent clause

The dependent clause can be anywhere in the sentence. Here are some examples:

• She took out her umbrella because it was raining , and then she walked home.
• I don't like exercising, but I'll do it if I have to .
• The man who was on the other side of the street waved, so I looked at him.

Question: What about Compound-Compound? Complex-Complex?

Technically, you can make more complicated types of of sentence structures, for example:

• She arrived and then he arrived and then I arrived so we were all there.

Is this Compound-Compound-Compound sentence? No. It's still just called a Compound sentence. Also, it's a badly written sentence.

• Before she went home , she cleaned up the area where she had worked .

Is this a Complex-Complex sentence? No. It's still called a complex sentence, even though there are two dependent clauses.

Why is all this important? What sentence structures should I use?

Spoken English tends to mainly use simple and compound sentences, but higher-level writing (e.g. academic and business communications) should use some complex structures. A complex sentence can be more efficient because it can contain several ideas in the same sentence. Also, using conjunctions such although or because  helps the reader understand how ideas relate to each other, which makes your writing more cohesive . 

Still, w riting well doesn't mean only using long and complicated sentences. Writing is most effective when it's clear. This can be achieved by using short, simple sentences, such as this one. I n short, writing effectively and efficiently means using a variety of sentence structures.

^ By the way, the above two paragraphs contained the following:

• Spoken English tends to mainly use simple and compound sentences, but higher-level writing (e.g. academic and business communications) should use a variety of structures (i.e. simple, compound, and complex).
• A complex sentence can be more efficient because it can contain several ideas in the same sentence.
• Also, using conjunctions such ' although ' or ' because ' helps the reader understand how ideas relate to each other , which makes your writing more cohesive .
• Writing is most effective when it's clear.
• Still, writing well doesn't mean only using long and complicated sentences. 
• This can be achieved by using short, simple sentences, such as this one.
• I n short, writing effectively and efficiently means using a variety of sentence structures.
• Compound-complex : 0

Do you think you understand? Try our exercises below!

Exercises #1: Identifying Sentence Structures

• The man smiled and laughed.  Simple Compound Complex Compound-Complex
• The man smiled, but I did not know why.  Simple Compound Complex Compound-Complex
• When the cat is away, the mice will play.  Simple Compound Complex Compound-Complex
• The answer is not known.  Simple Compound Complex Compound-Complex
• If people would like to apply, they can call 1-800-493-222 or they can e-mail [email protected] .  Simple Compound Complex Compound-Complex
• He asked me a question so I answered.  Simple Compound Complex Compound-Complex
• I e-mailed the company, and they responded immediately, which surprised me. Simple Compound Complex Compound-Complex
• Simple (Independent clause) Note: "and laughed" is not a clause because it does not contain another subject and verb. Therefore, this sentence only has one clause
• Compound (Independent clause + coordinating conjunction + Independent clause)
• Complex (Dependent clause + Independent clause)
• Simple (Independent clause)
• Compound-complex (Dependent clause, independent clause + coordinating conjunction + independent clause)
• Compound-complex (Independent clause, coordinating conjunction, independent clause, dependent clause)

Exercises #2: Identifying Sentence Structures

• The train station was still closed but a few coffee shops were open.  Simple Compound Complex Compound-Complex
• If you have further questions, please do not hesitate to ask.  Simple Compound Complex Compound-Complex
• Some people only need a computer to do their jobs, so they can easily work from home. Simple Compound Complex Compound-Complex
• On the second weekend of July last year, I went camping. Simple Compound Complex Compound-Complex
• As population increases, food shortages become more common and quality of life can decrease.  Simple Compound Complex Compound-Complex
• The price of the service increased by 20%, but because the company did not inform its customers, many people demanded an explanation.  Simple Compound Complex Compound-Complex
• Many students didn't understand, so their teacher explained the answer very clearly and slowly.  Simple Compound Complex Compound-Complex
• Simple (Independent clause) Note: "On the second weekend of July last year" is a prepositional phrase, not a clause because there is no subject or verb.
• Compound-Complex (Dependent clause, Independent clause + coordinating conjunction Independent clause)
• Compound-Complex (Independent clause, coordinating conjunction, dependent clause, independent clause)
• Compound (Independent clause, coordinating conjunction, Independent clause)

If you have any questions about sentence structures, please leave a comment below or visit our forums .

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32 comments on “ Four Sentence Structures: Simple, Compound, Complex, & Compound-Complex ”

Thank you so much for my preparation for my Half- yearly exams

Yes it true I like it but the activity was hard

THANK YOU FROM MONGOLIA

thank you very much .A clear explanation.

I’ve really understood the lesson it was very superb, and easy to understood, really preciate your efforts, and your helping Thank u so much.

I think it is very useful for me to study.

It is very important.

I think this way is good for my study.

Thanks a lot for the notes, the clarifications, the remakes, and the exercises. But I also heard there are somewhere that there are “compound-complex-complex” sentences with more than two independent, and more than two dependent clauses in them. What do you take of this? Regards.

thanks a lot for the notes but i understood this lesson.

thanks , i liked this alot!

when you call to your U.S. bank you may fine yourself speaking to a customer service representative who is sitting in the Philippines or Puerto Rico and when you need technical support for your home computer you will probably get help from a programmer in New Delhi where’s the independent clause an the dependent clause?

What do you think? Read the above page and give it a try.

ty very much for this

Understood and this section was very interesting.

Thanks teacher

Thanks this really helps.

It was really informative

I find it difficult, some people understand, some people don’t. But I’ll try harder.

Thank you so much as I learned a lot about sentence structure which will help me in my future English speaking test. I am so happy with this

this page is amazing. thank you.

THANK YOU FROM ROME HABITANT ICI BEASTIA

Thank you so much

Thank you. It was very helpful

Love this wow

Thank you . It was really very helpful.

In some compound sentences, I didnt find a comma. I was figuring out , if we write a compound sentence without putting a comma, is it OK?

Hello. Some English teachers would say that you should have a comma before the coordinating conjunction (FANBOYS) in a compound sentence. However, it’s not really needed, and if you don’t put one, it’s not a mistake.

Wow，that’s helpful!especially for non-language learner.

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3.2: Representation of Chemical Compounds

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Learning Objectives

• Symbolize the composition of molecules using molecular formulas and empirical formulas
• Represent the bonding arrangement of atoms within molecules using structural formulas

A molecular formula is a representation of a molecule that uses chemical symbols to indicate the types of atoms followed by subscripts to show the number of atoms of each type in the molecule. (A subscript is used only when more than one atom of a given type is present.) Molecular formulas are also used as abbreviations for the names of compounds.

The structural formula for a compound gives the same information as its molecular formula (the types and numbers of atoms in the molecule) but also shows how the atoms are connected in the molecule. The structural formula for methane contains symbols for one C atom and four H atoms, indicating the number of atoms in the molecule (Figure \(\PageIndex{1}\)). The lines represent bonds that hold the atoms together. (A chemical bond is an attraction between atoms or ions that holds them together in a molecule or a crystal.) We will discuss chemical bonds and see how to predict the arrangement of atoms in a molecule later. For now, simply know that the lines are an indication of how the atoms are connected in a molecule. A ball-and-stick model shows the geometric arrangement of the atoms with atomic sizes not to scale, and a space-filling model shows the relative sizes of the atoms.

Although many elements consist of discrete, individual atoms, some exist as molecules made up of two or more atoms of the element chemically bonded together. For example, most samples of the elements hydrogen, oxygen, and nitrogen are composed of molecules that contain two atoms each (called diatomic molecules) and thus have the molecular formulas H 2 , O 2 , and N 2 , respectively. Other elements commonly found as diatomic molecules are fluorine (F 2 ), chlorine (Cl 2 ), bromine (Br 2 ), and iodine (I 2 ). The most common form of the element sulfur is composed of molecules that consist of eight atoms of sulfur; its molecular formula is S 8 (Figure \(\PageIndex{2}\)).

It is important to note that a subscript following a symbol and a number in front of a symbol do not represent the same thing; for example, H 2 and 2H represent distinctly different species. H 2 is a molecular formula; it represents a diatomic molecule of hydrogen, consisting of two atoms of the element that are chemically bonded together. The expression 2H, on the other hand, indicates two separate hydrogen atoms that are not combined as a unit. The expression 2H 2 represents two molecules of diatomic hydrogen (Figure \(\PageIndex{3}\)).

Compounds are formed when two or more elements chemically combine, resulting in the formation of bonds. For example, hydrogen and oxygen can react to form water, and sodium and chlorine can react to form table salt. We sometimes describe the composition of these compounds with an empirical formula , which indicates the types of atoms present and the simplest whole-number ratio of the number of atoms (or ions) in the compound . For example, titanium dioxide (used as pigment in white paint and in the thick, white, blocking type of sunscreen) has an empirical formula of TiO 2 . This identifies the elements titanium (Ti) and oxygen (O) as the constituents of titanium dioxide, and indicates the presence of twice as many atoms of the element oxygen as atoms of the element titanium (Figure \(\PageIndex{4}\)).

As discussed previously, we can describe a compound with a molecular formula, in which the subscripts indicate the actual numbers of atoms of each element in a molecule of the compound. In many cases, the molecular formula of a substance is derived from experimental determination of both its empirical formula and its molecular mass (the sum of atomic masses for all atoms composing the molecule). For example, it can be determined experimentally that benzene contains two elements, carbon (C) and hydrogen (H), and that for every carbon atom in benzene, there is one hydrogen atom. Thus, the empirical formula is CH. An experimental determination of the molecular mass reveals that a molecule of benzene contains six carbon atoms and six hydrogen atoms, so the molecular formula for benzene is C 6 H 6 (Figure \(\PageIndex{5}\)).

If we know a compound’s formula, we can easily determine the empirical formula. (This is somewhat of an academic exercise; the reverse chronology is generally followed in actual practice.) For example, the molecular formula for acetic acid, the component that gives vinegar its sharp taste, is C 2 H 4 O 2 . This formula indicates that a molecule of acetic acid (Figure \(\PageIndex{6}\)) contains two carbon atoms, four hydrogen atoms, and two oxygen atoms. The ratio of atoms is 2:4:2. Dividing by the lowest common denominator (2) gives the simplest, whole-number ratio of atoms, 1:2:1, so the empirical formula is CH 2 O. Note that a molecular formula is always a whole-number multiple of an empirical formula.

Example \(\PageIndex{1}\): Empirical and Molecular Formulas

Molecules of glucose (blood sugar) contain 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. What are the molecular and empirical formulas of glucose?

The molecular formula is C 6 H 12 O 6 because one molecule actually contains 6 C, 12 H, and 6 O atoms. The simplest whole-number ratio of C to H to O atoms in glucose is 1:2:1, so the empirical formula is CH 2 O.

Exercise \(\PageIndex{1}\)

A molecule of metaldehyde (a pesticide used for snails and slugs) contains 8 carbon atoms, 16 hydrogen atoms, and 4 oxygen atoms. What are the molecular and empirical formulas of metaldehyde?

Molecular formula, C 8 H 16 O 4 ; empirical formula, C 2 H 4 O

It is important to be aware that it may be possible for the same atoms to be arranged in different ways: Compounds with the same molecular formula may have different atom-to-atom bonding and therefore different structures. For example, could there be another compound with the same formula as acetic acid, C 2 H 4 O 2 ? And if so, what would be the structure of its molecules?

If you predict that another compound with the formula C 2 H 4 O 2 could exist, then you demonstrated good chemical insight and are correct. Two C atoms, four H atoms, and two O atoms can also be arranged to form methyl formate, which is used in manufacturing, as an insecticide, and for quick-drying finishes. Methyl formate molecules have one of the oxygen atoms between the two carbon atoms, differing from the arrangement in acetic acid molecules. Acetic acid and methyl formate are examples of isomers —compounds with the same chemical formula but different molecular structures (Figure \(\PageIndex{7}\)). Note that this small difference in the arrangement of the atoms has a major effect on their respective chemical properties. You would certainly not want to use a solution of methyl formate as a substitute for a solution of acetic acid (vinegar) when you make salad dressing.

Many types of isomers exist (Figure \(\PageIndex{8}\)). Acetic acid and methyl formate are structural isomers , compounds in which the molecules differ in how the atoms are connected to each other. There are also various types of spatial isomers , in which the relative orientations of the atoms in space can be different. For example, the compound carvone (found in caraway seeds, spearmint, and mandarin orange peels) consists of two isomers that are mirror images of each other. S -(+)-carvone smells like caraway, and R -(−)-carvone smells like spearmint.

A molecular formula uses chemical symbols and subscripts to indicate the exact numbers of different atoms in a molecule or compound. An empirical formula gives the simplest, whole-number ratio of atoms in a compound. A structural formula indicates the bonding arrangement of the atoms in the molecule. Ball-and-stick and space-filling models show the geometric arrangement of atoms in a molecule. Isomers are compounds with the same molecular formula but different arrangements of atoms.

Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors.  Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] ).

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Simple, Compound, Complex, and Compound-Complex Sentences - PowerPoint PPT Presentation

Simple, Compound, Complex, and Compound-Complex Sentences

Simple, compound, complex, and compound-complex sentences once a writer knows the difference between the three sentence types (simple, compound, and complex), it is ... – powerpoint ppt presentation.

• A simple sentence contains a subject and verb.
• It expresses a single complete thought.
• A simple sentence is a single independent clause.
• The cat crept through the dark house.
• The wary mouse watched from underneath an upturned cereal box.
• The predatory cat stopped and surveyed his surroundings.
• The mouse darted for the safety of the nearly invisible hole under the cabinet.
• A compound sentence contains two independent clauses.
• Conjunctions (for, and, nor, but, or, and yet, so) join these independent clauses. (Hint The conjunctions spell FANBOYS.)
• The conjunction used can impact the meaning of the sentence.
• The cat was unsuccessful in his attempt to catch the mouse, and the mouse was equally as unlucky in his attempt to get the cheese.
• The dog had watched all of this, but he had refused to become involved.
• The mouse could wait until dark, or he could risk a daylight raid on the pantry.
• The cat usually slept during the day, yet curiosity held him at the corner of the kitchen.
• A complex sentence is an independent clause joined by one or more dependent clauses.
• A subordinating conjunction begins the dependent clauses.
• A dependent clause that begins a sentence must be followed by comma.
• A dependent clause has a subject and a verb, but it does not make sense on its own.
• after how until
• although if unless
• as in as much   as if
• in order that when as long as
• at least whenever as much as
• now that whereas soon
• wherever as though since
• while because so that
• before even if that
• even though   though
• After he gave it some thought, the mouse decided to wait until later for his trek.
• The cat fell asleep on the warm kitchen because he was deprived of sleep the night before.
• When the mouse heard the soft snoring of his sleeping nemesis, he scurried to the pantry and grabbed enough food for a week.
• The dedicated, feline sleuth keeps his nightly vigil even though the foresighted mouse will not be venturing out this week.
• A compound-complex sentence is a sentence that has at least two independent clauses and at least one dependent clause.
• The same subordinating conjunctions are used to introduce the dependent clauses.
• The same coordinating conjunctions (FANBOYS) are used for joining the independent clauses.
• After the two adversaries had spent years playing this cat and mouse game, they were joined by their children, and the fun continued.
• Even though it seems the two were bent on the others destruction, the cat and mouse were rather fond of one another, and neither wanted the others defeat.
• This game was begun thousands of years ago, and it will continue far into the future as other cats and mice revel in hide-and-seek.
• 1. The teacher walked into the classroom, greeted the students, and took attendance.
• 2. Juan played football while Jane went shopping.
• 3. Juan played football, yet Jim went shopping.
• 4. Although Mexico has a better team, they lost the tournament, and their more aggressive style did not pay off.
• 5. The island was filled with many trails winding through the thick underbrush, a small lake, and dangerous wild animals.
• 6. Naoki passed the test because he studied hard, but Stacy did not understand the material.

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