# 11.2 Combining like terms using addition and subtraction

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to combine like terms using addition and subtraction. By the end of the module students should be able to combine like terms in an algebraic expression.

## Section overview

• Combining Like Terms

## Combining like terms

From our examination of terms in [link] , we know that like terms are terms in which the variable parts are identical. Like terms is an appropriate name since terms with identical variable parts and different numerical coefficients represent different amounts of the same quantity. When we are dealing with quantities of the same type, we may combine them using addition and subtraction.

## Simplifying an algebraic expression

An algebraic expression may be simplified by combining like terms.

This concept is illustrated in the following examples.

1. $\text{8 records}+\text{5 records}=\text{13 records}\text{.}$

Eight and 5 of the same type give 13 of that type. We have combined quantities of the same type.

2. $\text{8 records}+\text{5 records}+\text{3 tapes}=\text{13 records}+\text{3 tapes}\text{.}$

Eight and 5 of the same type give 13 of that type. Thus, we have 13 of one type and 3 of another type. We have combined only quantities of the same type.

3. Suppose we let the letter $x$ represent "record." Then, $8x+5x=13x$ . The terms $8x$ and $5x$ are like terms. So, 8 and 5 of the same type give 13 of that type. We have combined like terms.
4. Suppose we let the letter $x$ represent "record" and $y$ represent "tape." Then,

$8x+5x+3y=13x+5y$

We have combined only the like terms.

After observing the problems in these examples, we can suggest a method for simplifying an algebraic expression by combining like terms.

## Combining like terms

Like terms may be combined by adding or subtracting their coefficients and affixing the result to the common variable.

## Sample set a

Simplify each expression by combining like terms.

$2m+6m-4m$ . All three terms are alike. Combine their coefficients and affix this result to $m$ : $2+6-4=4$ .

Thus, $2m+6m-4m=4m$ .

$5x+2y-9y\text{.}$ The terms $2y$ and $-9y$ are like terms. Combine their coefficients: $2-9=-7$ .

Thus, $5x+2y-9y=5x-7y$ .

$-3a+2b-5a+a+6b\text{.}$ The like terms are

$\underset{-7a}{\underset{-3-5+1=-7}{\underbrace{-3a,\text{}-5a,\text{}a}}}$ $\underset{8b}{\underset{2+6=8}{\underbrace{2b,\text{}6b}}}$

Thus, $-3a+2b-5a+a+6b\text{=}-7a+8b\text{.}$

$r-2s+7s+3r-4r-5s$ . The like terms are Thus, $r-2s+7s+3r-4r-5s=0$ .

## Practice set a

Simplify each expression by combining like terms.

$4x+3x+6x$

$\text{13}x$

$5a+8b+6a-2b$

$\text{11}a+6b$

$\text{10}m-6n-2n-m+n$

$9m-7n$

$\text{16}a+6m+2r-3r-\text{18}a+m-7m$

$-2a-r$

$5h-8k+2h-7h+3k+5k$

0

## Exercises

Simplify each expression by combining like terms.

$4a+7a$

$\text{11}a$

$3m+5m$

$6h-2h$

$4h$

$\text{11}k-8k$

$5m+3n-2m$

$3m+3n$

$7x-6x+3y$

$\text{14}s+3s-8r+7r$

$\text{17}s-r$

$-5m-3n+2m+6n$

$7h+3a-\text{10}k+6a-2h-5k-3k$

$5h+9a-\text{18}k$

$4x-8y-3z+x-y-z-3y-2z$

$\text{11}w+3x-6w-5w+8x-\text{11}x$

0

$\text{15}r-6s+2r+8s-6r-7s-s-2r$

$\mid -7\mid m+\mid 6\mid m+\mid -3\mid m$

$\text{16}m$

$\mid -2\mid x+\mid -8\mid x+\mid \text{10}\mid x$

$\left(-4+1\right)k+\left(6-3\right)k+\left(\text{12}-4\right)h+\left(5+2\right)k$

$8h+7k$

$\left(-5+3\right)a-\left(2+5\right)b-\left(3+8\right)b$

$5\star +2\Delta +3\Delta -8\star$

$5\Delta -3\star$

$9⊠+10⊞-11⊠-12⊞$

$\text{16}x-\text{12}y+5x+7-5x-\text{16}-3y$

$\text{16}x-\text{15}y-9$

$-3y+4z-\text{11}-3z-2y+5-4\left(8-3\right)$

## Exercises for review

( [link] ) Convert $\frac{\text{24}}{\text{11}}$ to a mixed number

$2\frac{2}{\text{11}}$

( [link] ) Determine the missing numerator: $\frac{3}{8}=\frac{?}{\text{64}}\text{.}$

( [link] ) Simplify $\frac{\frac{5}{6}-\frac{1}{4}}{\frac{1}{\text{12}}}$ .

7

( [link] ) Convert $\frac{5}{\text{16}}$ to a percent.

( [link] ) In the expression $6k$ , how many k ’s are there?

6

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Richard
Explain the following concepts using suitable exemple. 1) National budget. 2) National debt
Rosalie
other things remain constant.
explain scarcity
scarcity occurs when there are not enough resources to satisfy human's needs and wants therefore we need to allocate our resources using the price mechanism.
Isha
scarcity is when there is inadequate resources to catch the unlimited wants which would compel individual to make choice.
Prince
scarcity simply means when there's a shortages of resources to satisfy Hunan's need and wants in a particular time, which means the demand for it at the moment is higher than the supply
Abu
scarcity simply means when there's a shortages of resources to satisfy humans need and wants in a particular time, which means the demand for it at the moment is higher than it supply.
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scarcity means unlimited resources
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resources are limited but human wants can not be limited
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joint or complementary demand
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it maybe define as the amount or quantity of goods and services which a consumer is willing to buy with the ability to pay at a given price at a particular time
Habib
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why is economics a science
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Amit
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Anik
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Habib
so what is the disadvantages of mix economic system
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Ali
The question is: why is Economic a "science" and not why is economics a "social science?" Alright folks?
Xavier
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my response to the earlier question is, economics is a science but not a pure science like biology, chemistry and physics. The reason is that those pure science study inanimate object while economics study human being, their experiment are predictable.
raimi
Economics is a social science subject that shows the relationship between ends and scarce means with their alternative uses
Ajenifuja
what is Equilibrium?
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Arthur
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name the types of demand and explain any two
ALIMAMYISLA
Joint demand Composite demand Competitive demand
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Labourcan be defined as man mental and physical exertion
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Nkwenti
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Himanshu
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Rosalie
Equilibrium is a situation in which economic forces such as supply and demand balance and in the absence of extremal lnfiuences the values of economic variables will not change.
Gyamfua
what is elasticity
difference between demand and supply
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Ali
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Gyamfua
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Ajenifuja
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antony
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