Dividing Fractions — Challenge

Dividing asks how many of these fit into that, and the answer can be bigger than you started with.

What these problems cover

These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.

Problem 1

What is 12÷14?

  1. 18
  2. 12
  3. 1
  4. 2
  5. 8
Worked answer

2

The question asks how many quarters fit into a half.

Dividing by a fraction means multiplying by its reciprocal: 12·41 = 42 = 2.

Two quarters do make a half, so the answer is sensible.

Problem 2

What is 3÷15?

  1. 35
  2. 53
  3. 115
  4. 5
  5. 15
Worked answer

15

Multiply by the reciprocal of 15, which is 5: 3· 5 = 15.

This says there are 15 fifths in 3, which is right because each whole holds five of them.

Problem 3

What is 23÷ 4?

  1. 16
  2. 38
  3. 83
  4. 23
  5. 6
Worked answer

16

Dividing by 4 is multiplying by 14: 23·14 = 212.

212 reduces to 16.

Dividing by a whole number greater than 1 makes the fraction smaller, and 16 is smaller than 23.

Problem 4

A ribbon 78 of a metre long is cut into pieces each 18 of a metre long. How many pieces are there?

  1. 6
  2. 7
  3. 8
  4. 56
  5. 764
Worked answer

7

The question is how many eighths are in seven eighths, which is 78÷18.

Multiplying by the reciprocal: 78·81 = 7 pieces.

Problem 5

What is 56÷23?

  1. 59
  2. 45
  3. 54
  4. 109
  5. 34
Worked answer

54

Multiply by the reciprocal: 56·32 = 1512.

1512 reduces to 54.

The answer is greater than 1 because 56 is larger than 23.

Problem 6

How many 34-cup servings can be measured from 412 cups?

  1. 3
  2. 4
  3. 5
  4. 6
  5. 8
Worked answer

6

Write the mixed number as an improper fraction: 412 = 92.

Divide by the serving size: 92÷34 = 92·43 = 366 = 6 servings.

Problem 7

What is 910÷35?

  1. 2750
  2. 32
  3. 23
  4. 65
  5. 56
Worked answer

32

Multiply by the reciprocal: 910·53 = 4530.

4530 reduces to 32.

Multiplying the two fractions instead would give 2750, which is the trap in the options.

Problem 8

A plank 6 metres long is cut into pieces each 25 of a metre long. How many pieces are there?

  1. 12
  2. 15
  3. 18
  4. 2.4
  5. 30
Worked answer

15

Divide the length of the plank by the length of one piece: 6÷25.

Multiply by the reciprocal: 6·52 = 302 = 15 pieces.

Multiplying by 25 instead gives 2.4, which is fewer pieces than one plank could possibly make.

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