### Home > MC1 > Chapter 8 > Lesson 8.2.2 > Problem8-37

8-37.

Simplify each of the following expressions.

1. $\frac { 1 } { 4 } \cdot 4$

2. $\frac { 7 } { 8 } \cdot \frac { 8 } { 7 }$

3. $2 \frac { 2 } { 3 } \cdot \frac { 3 } { 8 }$

4. When two numbers have a product of one, they are called reciprocals or multiplicative inverses. What is the reciprocal or multiplicative inverse of each of these numbers?

1. $\frac { 2 } { 3 }$

2. 7

3. $4 \frac { 1 } { 3 }$

For help with parts (a), (b), and (c), refer to the Math Notes boxes below.

$\text{It may help to look at 4 as equal to }\frac{4}{1}.$

The answer for part (b) is 1.

You will want to convert the mixed number to a fraction before multiplying.
$\text{Can you find how many }\frac{1}{3}\text{'s are in 2?}$

For part (d), it may help to look back at part (b) of this problem.
Do you notice a way to apply that expression and solution to this question?

It may also help to turn parts (ii) and (iii) into fractions.
$\text{ If 7 equals }\frac{7}{1} \text{ and }4\frac{1}{3} \text{ equals }\frac{13}{3},\text{ can you find their reciprocals?}$

$\text{The reciprocal of (i) is }\frac{3}{2} \text{ and the answer to (iii) is }\frac{3}{13}.$
Did you find the answer to (ii)?