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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.
This concept is illustrated in the following examples.
Eight and 5 of the same type give 13 of that type. We have combined quantities of the same type.
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.
$8x+5x+3y=13x+5y$
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.
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, $r-2s+7s+3r-4r-5s=0$ .
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
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
$\text{15}r-6s+2r+8s-6r-7s-s-2r$
$\mid -7\mid m+\mid 6\mid m+\mid -3\mid m$
$\text{16}m$
$\mid -2\mid x+\mid -8\mid x+\mid \text{10}\mid x$
$\left(-4+1\right)k+\left(6-3\right)k+\left(\text{12}-4\right)h+\left(5+2\right)k$
$8h+7k$
$\left(-5+3\right)a-\left(2+5\right)b-\left(3+8\right)b$
$5\star +2\Delta +3\Delta -8\star$
$5\Delta -3\star$
$9\u22a0+10\u229e-11\u22a0-12\u229e$
$\text{16}x-\text{12}y+5x+7-5x-\text{16}-3y$
$\text{16}x-\text{15}y-9$
$-3y+4z-\text{11}-3z-2y+5-4\left(8-3\right)$
( [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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