Below are the solutions and answers to the Week 4 Practice Problems and Solutions.

Practice Exercises 1

Note: In multiplying fractions, we multiply the numerator by the numerator of the other fraction, and then multiply the denominator by the denominator of the other fraction. For whole numbers, we can put 1 as the denominator. All fractions must be in lowest terms.

A. 1/2 × 1/3 = 1/6
B. 2/3 × 4/5 = 8/15
C. 8/1 × 5/6 = 40/6 = 6 4/6 or 6 2/3
D. 2 5/8 × 3 = 21/8 × 3/1 = 63/8 = 7 7/8
E. 3 1/8 × 4/5 = 25/8 × 4/5 = 100/40 = 2 20/40 or 2 1/2
F. 1 2/3 × 2 3/4 = 5/3 × 11/4 = 55/12 = 4 7/12

Practice Exercises 2

A. When dividing fractions you get the reciprocal of the divisor, and then multiply. In 1/5÷ 3/10, the divisor 3/10 and the reciprocal of 3/10 is 10/3. So, 1/5 × 10/3 = 10/15 or 2/3

B. 1/2 ÷ 3/8 = 1/2 × 8/3 = 8/6 = 1 2/6 or 1 1/3

C. 9 ÷ 3/7 = 9 × 7/3 = 63/3 or 21

D. 2 5/8 ÷ 2

First, we convert 2 5/8 to improper fraction as follows. That is $2\frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{21}{8}$. Don’t forget that the denominator of the mixed fraction is the same as the denominator of the improper fractions.

Here, the reciprocal of 2 is 1/2. So, 21/8 × 1/2 = 21/16 = 1 5/16

E. 3 1/8 ÷ 3/5 = 25/8 × 5/3 = 125/24 = 5 5/24

F. 2 3/4 ÷ 1 1/8 = 11/4 ÷ 9/8 = 11/4 × 8/9 = 88/36 = 2 16/36 or 2 4/9

Practice Problems

Note: In multiplication and division of fractions, all mixed fractions must be converted to improper fractions (see Practice Problem 2D above).

1.) 2/3 × 1/4 = 2/12 or 1/6

2.) 3/5 × 35/1=105/5 = 21 (women)
2/5 × 35/1 = 70/5 = 14 (men)

3.) 2 3/4 × 7 = (11/4) ×  7 = 77/4 = 19 1/4

4.) A = L × W
A = (35 1/4) × (20 1/2) = (141/4) × (41/2)
= 5781/8= 722 5/8

5.) 2 4/5 × 5/1= 14/5 × 5/1 = 14

6.) 1 1/2 L juice is to be shared equally by 6 friends, so 1 1/2 ÷ 6.

The mixed fraction  1 1/2 is 3/2 in improper form.

Dividing by 6 is the same as multiplying by 1/6, so 3/2 × 1/6 = 3/12

3/12 is not yet in its lowest term. So get its lowest term, divide the numerator and denominator by their GCF which is 3.  So, 3/12 will become 1/4.

The final answer is 1/4 L.

7.) 8 ÷ 2/5 = 8 × 5/2 = 8/1 × 5/2 = 40/2 = 20.

8.) Bookshelf length divided by book’s thickness = number of books that will fit in the bookshelf

5 1/4 feet ÷ 1 1/2 inches = ?

Notice that the units are in feet and inches. We cannot proceed until the units are the same, so we need  to convert feet into inches. (1 ft = 12 in) So 5 ft × 12 in per ft = 60 in. We still have 1/4 ft, so 1/4 of 12 which is 3 in. All in all, we have 63 in. Now our equation is

63  ÷ 3/2 = 63/1 × 2/3

= 126/3 = 42.