문자와 식 전체 문제

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $n=0.75,$ evaluate

• ⓐ $\,-100(5n+1.5)$
• ⓑ $\,-100\cdot 5n+(-100)(1.5)$

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $y=-25,$ evaluate

• ⓐ $\,-(y-25)$
• ⓑ $\,-y+25$

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $w=-80,$ evaluate

• ⓐ $\,-(w-80)$
• ⓑ $\,-w+80$

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $p=0.19,$ evaluate

• ⓐ $\,-(p+0.72)$
• ⓑ $\,-p-0.72$

Evaluate Expressions Using the Distributive Property

In the following exercises, evaluate both expressions for the given value.

If $q=0.55,$ evaluate

• ⓐ $\,-(q+0.48)$
• ⓑ $\,-q-0.48$

Buying by the case Joe can buy his favorite ice tea at a convenience store for $\char36 1.99$ per bottle. At the grocery store, he can buy a case of $12$ bottles for $\char36 23.88.$

1. ⓐ Use the distributive property to find the cost of $12$ bottles bought individually at the convenience store. (Hint: notice that $\char36 1.99$ is $\char36 2-\char36 0.01.$)
2. ⓑ Is it a bargain to buy the iced tea at the grocery store by the case?

Multi-pack purchase Adele’s shampoo sells for $\char36 3.97$ per bottle at the drug store. At the warehouse store, the same shampoo is sold as a $\text{3-pack}$ for $\char36 10.49.$

1. ⓐ Show how you can use the distributive property to find the cost of $3$ bottles bought individually at the drug store.
2. ⓑ 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 $4(\char36 5.97)$ without paper or a calculator by thinking of $\char36 5.97$ as $6-0.03$ and then using the distributive property.

In the following exercises, write as the ratio of two integers.

$6$

In the following exercises, write as the ratio of two integers.

$-5$

In the following exercises, write as the ratio of two integers.

$2.9$

In the following exercises, write as the ratio of two integers.

$1.8$

In the following exercises, determine which of the numbers is rational.

$0.42,0.\overset{-}{3},2.56813\ldots$

In the following exercises, determine which of the numbers is rational.

$0.75319\ldots ,0.\overset{-}{16},1.95$

In the following exercises, identify whether each given number is rational or irrational.

ⓐ $\,\sqrt{49}$ ⓑ $\,\sqrt{55}$

In the following exercises, identify whether each given number is rational or irrational.

ⓐ $\,\sqrt{72}$ ⓑ $\,\sqrt{64}$

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$-9,0,0.361....,\frac{8}{9},\sqrt{16},9$

In the following exercises, list the ⓐ whole numbers, ⓑ integers, ⓒ rational numbers, ⓓ irrational numbers, ⓔ real numbers for each set of numbers.

$-5,\,-2\frac{1}{4},\,-\sqrt{4},\,0.\overset{-}{25},\,\frac{13}{5},\,4$

In the following exercises, use the commutative property to rewrite the given expression.

$6+4=\_\_\_\_$