#### Solved Examples and Worksheet for Dividing Fractions with/without Models

Q1Find the quotient:
67 ÷ 34

A. 1828
B. 78
C. 87
D. 228

Step: 1
67 ÷ 34
[Original expression.]
Step: 2
= 67 × 43
[Multiply 67 by 43, the reciprocal of 34.]
Step: 3
= 27 × 41
[Cancel 6 with 3.]
Step: 4
= 2 × 47 × 1
[Multiply the numerators and the denominators separately.]
Step: 5
= 87
[Simplify.]
Q2Find the quotient:
3 ÷ 23

A. 412
B. 29
C. 323
D. 2

Step: 1
3 ÷ 23
[Original expression.]
Step: 2
= 31 ÷ 23
[Write the whole number 3 as a fraction with denominator of 1.]
Step: 3
= 31 × 32
[Multiply 31 by the reciprocal of 23.]
Step: 4
= 3 × 31 × 2
[Multiply the numerators and the denominators.]
Step: 5
= 92 = 412
[Convert improper fraction into mixed number.]
Q32 honeybees can suck 34 of nectar from a flower. What fraction of nectar can one honeybee suck?
A. 223
B. 118
C. 38
D. 12

Step: 1
2 = 21
[Rewrite the whole number 2 as a fraction, with denominator 1.]
Step: 2
34 ÷ 2 = 34 ÷ 21
[Divide 34 by 2.]
Step: 3
34 ÷ 21 = 34 x 12
[Multiply 34 by the reciprocal of 21.]
Step: 4
= 3x14x2
[Multiply the numerators and the denominators.]
Step: 5
= 38
[Simplify.]
Step: 6
Each honeybee can suck 38 part of nectar from a flower.
Q4How many 14 in. are there in 14 ft?
A. 14
B. 11
C. 13
D. 12

Step: 1
14 ft = 14 ft × 121in.ft = 3 in.
[1 ft = 12 in. Convert ft into in.]
Step: 2
Number of 14 inches in 14 ft = 3 ÷ 14
Step: 3
3 ÷ 14
[Divide 3 by 14.]
Step: 4
= 31 ÷ 14
[Rewrite the whole number 3 as a fraction, with the denominator 1.]
Step: 5
= 31 × 41
[Multiply 31 with the reciprocal of 14.]
Step: 6
= 3 × 41 × 1
[Multiply the numerators and the denominators.]
Step: 7
= 12
[Simplify.]
Step: 8
Number of 14 inches in 14 ft = 12
Q5How many 110 oz are there in 12 lb?

A. 90
B. 70
C. 80
D. 100

Step: 1
12 lb = 162 oz = 8 oz
[Since 1 lb = 16 oz.]
Step: 2
8 ÷ 110
[Divide 8 by 110.]
Step: 3
= 81 ÷ 110
[Rewrite the whole number 8 as a fraction, with the denominator 1.]
Step: 4
= 81 × 101
[Multiply 81 with the reciprocal of 110.]
Step: 5
= 8 × 101 × 1
[Multiply the numerators and denominators.]
Step: 6
= 80
[Simplify.]
Step: 7
There are 80, 110 oz in 12 lb.
Q66 people ate 511of the food ordered. How much food did each person eat?
A. 566
B. 3011
C. 665
D. 667

Step: 1
511 ÷ 6
[Write the expression.]
Step: 2
= 511 ÷ 61
[Write the whole number as a fraction.]
Step: 3
= 511 × 16
[Multiply by the reciprocal of 61, which is 16.]
Step: 4
= 5 × 111 × 6
[Multiply numerators and denominators separately.]
Step: 5
= 566
[Simplify.]
Step: 6
So, each person ate 566 of the food ordered.
Q7Mike distributes 46 of a cake to 20 students in his class on his birthday. What fraction of cake does each student get?

A. 130
B. 120
C. 30
D. 530

Step: 1
46 ÷ 20
[Write the expression.]
Step: 2
= 46 ÷ 201
[Write the whole number as a fraction.]
Step: 3
= 46 × 120
[Multiply by the reciprocal of 201, which is 120.]
Step: 4
= 16 × 15
[Cancel 20 with 4.]
Step: 5
= 1 × 16 × 5
[Multiply numerators and denominators separately.]
Step: 6
= 130
[Simplify.]
Step: 7
So, each student gets 130 of the cake.
Q813 of the guests got 19 of a cake in a party. How many guests are needed to share 1 cake?
A. 5
B. 7
C. 3
D. 4

Step: 1
13 ÷ 19
[Write the expression.]
Step: 2
= 13 x 91
[Multiply by the reciprocal of 19, which is 91.]
Step: 3
= 11 x 31
[Cancel 9 with 3.]
Step: 4
= 3
[Simplify.]
Step: 5
So, 3 guests got 1 cake.
Q915 customers bought 1213of the bags in a shop. What fraction of bags does each person buy?
A. 165
B. 465
C. 565
D. 54

Step: 1
1213 ÷ 15
[Write the equation.]
Step: 2
= 1213 ÷ 151
[Write the whole number as a fraction.]
Step: 3
= 1213 x 115
[Multiply by the reciprocal of 151, which is 115.]
Step: 4
= 413 x 15
[Cancel 15 and 12 with 3.]
Step: 5
= 4x113x5
[Multiply numerators and denominators separately.]
Step: 6
= 465
[Simplify.]
Step: 7
So, the fraction of bags each customer got is 465.
Q1049 of the food is sufficient to feed 32 animals in a zoo. What fraction of food is required to feed one animal?

A. 174
B. 472
C. 172
D. 474

Step: 1
49 ÷ 32
[Write the expression.]
Step: 2
49 ÷ 321
[Write the whole number as a fraction.]
Step: 3
49 x 132
[Multiply by the reciprocal of 321, which is 132.]
Step: 4
19 x 18
[Cancel 32 with 4.]
Step: 5
1x19x8
[Multiply numerators and denominators separately.]
Step: 6
= 172
[Simplify.]
Step: 7
So, 172 of the food is sufficient to feed one animal.