7.3 Distributive property  (Page 2/2)

$4(x+8)$

$3(a+9)$

$8(4y+9)$

$9(3w+7)$

$6(c-13)$

$7(y-13)$

$7(3p-8)$

$5(7u-4)$

$\frac{1}{2}(n+8)$

$\frac{1}{3}(u+9)$

$\frac{1}{4}(3q+12)$

$\frac{1}{5}(4m+20)$

$9\left(\frac{5}{9}y-\frac{1}{3}\right)$

$10\left(\frac{3}{10}x-\frac{2}{5}\right)$

$12\left(\frac{1}{4}+\frac{2}{3}r\right)$

$12\left(\frac{1}{6}+\frac{3}{4}s\right)$

$r(s-18)$

$u(v-10)$

$(y+4)p$

$(a+7)x$

$\mathrm{-2}(y+13)$

$\mathrm{-3}(a+11)$

$\mathrm{-7}(4p+1)$

$\mathrm{-9}(9a+4)$

$\mathrm{-3}(x-6)$

$\mathrm{-4}(q-7)$

$\mathrm{-9}(3a-7)$

$\mathrm{-6}(7x-8)$

$-(r+7)$

$-(q+11)$

$-(3x-7)$

$-(5p-4)$

$5+9(n-6)$

$12+8(u-1)$

$16-3(y+8)$

$18-4(x+2)$

$4-11(3c-2)$

$9-6(7n-5)$

$22-(a+3)$

$8-(r-7)$

$\mathrm{-12}-(u+10)$

$\mathrm{-4}-(c-10)$

$(5m-3)-(m+7)$

$(4y-1)-(y-2)$

$5(2n+9)+12(n-3)$

$9(5u+8)+2(u-6)$

$9(8x-3)-(\mathrm{-2})$

$4(6x-1)-(\mathrm{-8})$

$14(c-1)-8(c-6)$

$11(n-7)-5(n-1)$

$6(7y+8)-(30y-15)$

$7(3n+9)-(4n-13)$

If $v=\mathrm{-2},$ evaluate

1. ⓐ $6(4v+7)$
2. ⓑ $6·4v+6·7$

If $u=\mathrm{-1},$ evaluate

1. ⓐ $8(5u+12)$
2. ⓑ $8·5u+8·12$

If $n=\frac{2}{3},$ evaluate

1. ⓐ $3(n+\frac{5}{6})$
2. ⓑ $3·n+3·\frac{5}{6}$

If $y=\frac{3}{4},$ evaluate

1. ⓐ $4(y+\frac{3}{8})$
2. ⓑ $4·y+4·\frac{3}{8}$

If $y=\frac{7}{12},$ evaluate

1. ⓐ $\mathrm{-3}(4y+15)$
2. ⓑ $3·4y+(\mathrm{-3})·15$

If $p=\frac{23}{30},$ evaluate

1. ⓐ $\mathrm{-6}(5p+11)$
2. ⓑ $\mathrm{-6}·5p+(\mathrm{-6})·11$

If $m=0.4,$ evaluate

1. ⓐ $\mathrm{-10}(3m-0.9)$
2. ⓑ $\mathrm{-10}·3m-(\mathrm{-10})(0.9)$

If $n=0.75,$ evaluate

1. ⓐ $\mathrm{-100}(5n+1.5)$
2. ⓑ $\mathrm{-100}·5n+(\mathrm{-100})(1.5)$

If $y=\mathrm{-25},$ evaluate

1. ⓐ $-(y-25)$
2. ⓑ $-y+25$

If $w=\mathrm{-80},$ evaluate

1. ⓐ $-(w-80)$
2. ⓑ $-w+80$

If $p=0.19,$ evaluate

1. ⓐ $-(p+0.72)$
2. ⓑ $-p-0.72$

If $q=0.55,$ evaluate

1. ⓐ $-(q+0.48)$
2. ⓑ $-q-0.48$

Buying by the case Joe can buy his favorite ice tea at a convenience store for $\text{\$1.99}$ per bottle. At the grocery store, he can buy a case of $12$ bottles for $\text{\$23.88}.$

ⓐ Use the distributive property to find the cost of $12$ bottles bought individually at the convenience store. (Hint: notice that $\text{\$1.99}$ is $\text{\$2}-\text{\$0.01}.$ )

ⓑ Is it a bargain to buy the iced tea at the grocery store by the case?

Multi-pack purchase Adele’s shampoo sells for $\text{\$3.97}$ per bottle at the drug store. At the warehouse store, the same shampoo is sold as a $\text{3-pack}$ for $\text{\$10.49}.$

ⓐ Show how you can use the distributive property to find the cost of $3$ bottles bought individually at the drug store.

ⓑ How much would Adele save by buying the $\text{3-pack}$ at the warehouse store?

Simplify $8\left(x-\frac{1}{4}\right)$ using the distributive property and explain each step.

Explain how you can multiply $4(\text{\$5.97})$ without paper or a calculator by thinking of $\text{\$5.97}$ as $6-0.03$ and then using the distributive property.