Solved Examples and Worksheet for Dividing Fractions with/without Models

Q1Find the quotient:
67 ÷ 34

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

Solutions
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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.]
Correct Answer is :   87
Q2Find the quotient:
3 ÷ 23
A. 412
B. 29
C. 323
D. 2

Solutions
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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.]
Correct Answer is :   412
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

Solutions
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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.
Correct Answer is :   38
Q4How many 14 in. are there in 14 ft?
A. 14
B. 11
C. 13
D. 12

Solutions
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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
Correct Answer is :   12
Q5How many 110 oz are there in 12 lb?

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

Solutions
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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.
Correct Answer is :   80
Q66 people ate 511of the food ordered. How much food did each person eat?
A. 566
B. 3011
C. 665
D. 667

Solutions
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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.
Correct Answer is :   566
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

Solutions
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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.
Correct Answer is :   130
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

Solutions
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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.
Correct Answer is :   3
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

Solutions
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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.
Correct Answer 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

Solutions
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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.
Correct Answer is :   172

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