CPM Homework Help : MC1 Problem 8-37

Simplify each of the following expressions.

Hint:

For help with parts (a), (b), and (c), refer to the lesson 6.2.4 and 6.2.6 Math Notes boxes.

$\frac { 1 } { 4 } \cdot 4$
Hint (a):
$\text{It may help to look at 4 as equal to }\frac{4}{1}.$
$\frac { 7 } { 8 } \cdot \frac { 8 } { 7 }$
Answer (b):
The answer for part (b) is $1$ .
$2 \frac { 2 } { 3 } \cdot \frac { 3 } { 8 }$
Hint (c):
You will want to convert the mixed number to a fraction before multiplying.
$\text{Can you find how many }\frac{1}{3}\text{'s are in 2?}$
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. $\frac { 2 } { 3 }$
1. $7$
1. $4 \frac { 1 } { 3 }$

Hint 1(d):

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?

Hint 2(d):

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

Answer (d):

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