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Year 4

Explain how an improper fraction is converted into a mixed number

I can explain how an improper fraction is converted into a mixed number.

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New
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Year 4

Explain how an improper fraction is converted into a mixed number

I can explain how an improper fraction is converted into a mixed number.

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Share activities with pupils
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Lesson details

Key learning points

  1. Times table knowledge can help to convert an improper fraction to a mixed number.
  2. Work out how many wholes can be made from the numerator of the improper fraction.
  3. Any fractions left over form the fraction part of the mixed number.

Keywords

  • Mixed number - A mixed number is a whole number and a fraction combined.

  • Improper fraction - An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).

Common misconception

Children may make mistakes when using the generalisation if they are unaware of the structure behind it and the reason that we divide.

Find how many groups of the denominator can be made from the numerator by dividing. This tells us how many full groups we can make, which gives us the whole number part of the mixed number. The remainder tells us the fractional part.

This lesson extends generalisations developed in Lesson 1 and 2 of this unit. Take time to make connections with prior learning and support pupils to generalise about how to convert between mixed numbers and improper fractions.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of the following are improper fractions?
$$ {2} \over {8}$$
Correct answer: $$ {7} \over {4}$$
$$ {3} \over {9}$$
$$ {1} \over {10}$$
Correct answer: $$ {10} \over {9}$$
Q2.
Which of the following are mixed numbers?
$$ {2} \over {4}$$
$$ {7} \over {3}$$
Correct answer: $$1{{3} \over {5}}$$
Correct answer: $$ 2{{1} \over {9}}$$
$$ {10} \over {9}$$
Q3.
Match the equation to its quotient.
Correct Answer:16 ÷ 8 =,2

2

Correct Answer:24 ÷ 8 =,3

3

Correct Answer:40 ÷ 8 =,5

5

Correct Answer:56 ÷ 8 =,7

7

Correct Answer:96 ÷ 8 =,12

12

Q4.
Match the equation to its result. Remember r means a remainder.
Correct Answer:17 ÷ 8 =,2 r1

2 r1

Correct Answer:26 ÷ 8 =,3 r2

3 r2

Correct Answer:43 ÷ 8 =,5 r3

5 r3

Correct Answer:60 ÷ 8 =,7 r4

7 r4

Correct Answer:99 ÷ 8 =,12 r3

12 r3

Q5.
Match the improper fractions to their equivalent whole number.
Correct Answer:$$ {18} \over {6}$$,3

3

Correct Answer:$$ {40} \over {8}$$,5

5

Correct Answer:$$ {40} \over {10}$$,4

4

Correct Answer:$$ {50} \over {5}$$,10

10

Correct Answer:$$ {66} \over {6}$$,11

11

Q6.
Use the part-part-whole model to express $$ {22} \over {5}$$ as a mixed number.
An image in a quiz
$$ {2} \over {5}$$
$$ {20} \over {5}$$
$$2{{2} \over {5}}$$
$$3{{2} \over {5}}$$
Correct answer: $$4{{2} \over {5}}$$

Exit quiz

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6 Questions

Q1.
Aisha has 21 counters. Each counter has $$ {3} \over {9}$$ written on it. Which unit does she need to be thinking about?
sixths
sevenths
eighths
Correct answer: ninths
tenths
Q2.
Complete the sentence. There are ninths in one whole.
Correct Answer: nine, 9
Q3.
How many groups of nine ninths are there in 21 ninths?
Correct answer: 2
3
4
5
6
Q4.
How would you write 21 ninths as a mixed number?
$$ 1{{3} \over {9}}$$
$$ 2{{1} \over {9}}$$
$$ 2{{2} \over {9}}$$
Correct answer: $$ 2{{3} \over {9}}$$
$$ 2{{4} \over {9}}$$
Q5.
Express $$ {36} \over {7}$$ as a mixed number.
$$ 4{{1} \over {7}}$$
Correct answer: $$ 5{{1} \over {7}}$$
$$ 5{{2} \over {7}}$$
$$ 5{{3} \over {7}}$$
$$ 5{{6} \over {7}}$$
Q6.
Match the improper fraction to its mixed number equivalent.
Correct Answer:$$ {29} \over {7}$$,$$ 4{{1} \over {7}}$$

$$ 4{{1} \over {7}}$$

Correct Answer:$$ {30} \over {7}$$,$$ 4{{2} \over {7}}$$

$$ 4{{2} \over {7}}$$

Correct Answer:$$ {33} \over {7}$$,$$ 4{{5} \over {7}}$$

$$ 4{{5} \over {7}}$$

Correct Answer:$$ {37} \over {7}$$,$$ 5{{2} \over {7}}$$

$$ 5{{2} \over {7}}$$

Correct Answer:$$ {39} \over {7}$$,$$ 5{{4} \over {7}}$$

$$ 5{{4} \over {7}}$$