11.1 Algebraic expressions

${\displaystyle 9m-2n,}$ if ${\displaystyle m=-2}$ and ${\displaystyle n=5}$

${\displaystyle -3x-5y+2z}$ , if ${\displaystyle x=-4}$ , ${\displaystyle y=3}$ , ${\displaystyle z=0}$

${\displaystyle \frac{\text{10}a}{\mathrm{3b}}+\frac{\mathrm{4b}}{2}}$ , if ${\displaystyle a=-6}$ , and ${\displaystyle b=2}$

${\displaystyle 8\left(3m-5n\right)}$ , if ${\displaystyle m=-4}$ and ${\displaystyle n=-5}$

${\displaystyle 3\left[-\text{40}-2\left(4a-3b\right)\right]}$ , if ${\displaystyle a=-6}$ and ${\displaystyle b=0}$

${\displaystyle {5y}^2+6y-\text{11}}$ , if ${\displaystyle y=-1}$

${\displaystyle -x^2+2x+7}$ , if ${\displaystyle x=4}$

${\displaystyle {\left(-x\right)}^2+2x+7}$ , if ${\displaystyle x=4}$

In an algebraic expression, terms are separated by signs and factors are separated by signs.

${\displaystyle 3m+7n}$

${\displaystyle 5x+\text{18}y}$

${\displaystyle 4a-6b+c}$

${\displaystyle 8s+2r-7t}$

${\displaystyle m-3n-4a+7b}$

${\displaystyle 7a-2b-3c-4d}$

${\displaystyle -6a-5b}$

${\displaystyle -x-y}$

What is the function of a numerical coefficient?

Write ${\displaystyle 1m}$ in a simpler way.

Write 1 s in a simpler way.

In the expression 5 a , how many a ’s are indicated?

In the expression –7 c , how many c ’s are indicated?

${\displaystyle 2m-6n}$ , if ${\displaystyle m=-3}$ and ${\displaystyle n=4}$

${\displaystyle 5a+6b}$ , if ${\displaystyle a=-6}$ and ${\displaystyle b=5}$

${\displaystyle 2x-3y+4z}$ , if ${\displaystyle x=1}$ , ${\displaystyle y=-1}$ , and ${\displaystyle z=-2}$

${\displaystyle 9a+6b-8x+4y}$ , if ${\displaystyle a=-2}$ , ${\displaystyle b=-1}$ , ${\displaystyle x=-2}$ , and ${\displaystyle y=0}$

${\displaystyle \frac{8x}{3y}+\frac{\text{18}y}{2x},}$ if ${\displaystyle x=9}$ and ${\displaystyle y=-2}$

${\displaystyle \frac{-3m}{2n}-\frac{-6n}{m},}$ if ${\displaystyle m=-6}$ and ${\displaystyle n=3}$

${\displaystyle 4\left(3r+2s\right)}$ , if ${\displaystyle r=4}$ and ${\displaystyle s=1}$

${\displaystyle 3\left(9a-6b\right)}$ , if ${\displaystyle a=-1}$ and ${\displaystyle b=-2}$

${\displaystyle -8\left(5m+8n\right)}$ , if ${\displaystyle m=0}$ and ${\displaystyle n=-1}$

${\displaystyle -2\left(-6x+y-2z\right)}$ , if ${\displaystyle x=1}$ , ${\displaystyle y=1}$ , and ${\displaystyle z=2}$

${\displaystyle -\left(\text{10}x-2y+5z\right)}$ if ${\displaystyle x=2}$ , ${\displaystyle y=8}$ , and ${\displaystyle z=-1}$

${\displaystyle -\left(a-3b+2c-d\right)}$ , if ${\displaystyle a=-5}$ , ${\displaystyle b=2}$ , ${\displaystyle c=0}$ , and ${\displaystyle d=-1}$

${\displaystyle 3\left[\text{16}-3\left(a+3b\right)\right]}$ , if ${\displaystyle a=3}$ and ${\displaystyle b=-2}$

${\displaystyle -2\left[5a+2b\left(b-6\right)\right]}$ , if ${\displaystyle a=-2}$ and ${\displaystyle b=3}$

${\displaystyle -\left\{6x+3y\left[-2\left(x+4y\right)\right]\right\}}$ , if ${\displaystyle x=0}$ and ${\displaystyle y=1}$

${\displaystyle -2\left\{\text{19}-6\left[4-2\left(a-b-7\right)\right]\right\}}$ , if ${\displaystyle a=\text{10}}$ and ${\displaystyle b=3}$

${\displaystyle x^2+3x-1}$ , if ${\displaystyle x=5}$

${\displaystyle m^2-2m+6}$ , if ${\displaystyle m=3}$

${\displaystyle {6a}^2+2a-\text{15}}$ , if ${\displaystyle a=-2}$

${\displaystyle {5s}^2+6s+\text{10},}$ if ${\displaystyle x=-1}$

${\displaystyle \text{16}{x}^2+8x-7}$ , if ${\displaystyle x=0}$

${\displaystyle -{8y}^2+6y+\text{11},}$ if ${\displaystyle y=0}$

${\displaystyle {\left(y-6\right)}^2+3\left(y-5\right)+4}$ , if ${\displaystyle y=5}$

${\displaystyle {\left(x+8\right)}^2+4\left(x+9\right)+\mathrm{1,}}$ if ${\displaystyle x=-6}$

( [link] ) Perform the addition: ${\displaystyle 5\frac{3}{8}+2\frac{1}{6}}$ .

( [link] ) Arrange the numbers in order from smallest to largest: ${\displaystyle \frac{\text{11}}{\text{32}},\frac{\text{15}}{\text{48}}\text{, and}\frac{7}{\text{16}}}$

( [link] ) Find the value of ${\displaystyle {\left(\frac{2}{3}\right)}^2+\frac{8}{\text{27}}}$

( [link] ) Write the proportion in fractional form: “9 is to 8 as x is to 7.”

( [link] ) Find the value of ${\displaystyle -3\left(2-6\right)-\text{12}}$