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 . 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.

Answer: 20 cakes

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.

Answer: 42 books

9.) 5 pumpkin pies are to be shared equally among 12 persons, equals 5/12.

10.) We have 8 3/4 hectares ÷ 4 children

35/4 ÷ 4 =35/4 × 1/4 = 35/16

Converting 35/16 to mixed fraction, we have 2 3/16.