Explain how an improper fraction is converted into a mixed number | Maths

Starter quiz

Which of the following are improper fractions?
- ${2} \over {8}$
- ${7} \over {4}$ ✓
- ${3} \over {9}$
- ${1} \over {10}$
- ${10} \over {9}$ ✓
Which of the following are mixed numbers?
- ${2} \over {4}$
- ${7} \over {3}$
- $1{{3} \over {5}}$ ✓
- $2{{1} \over {9}}$ ✓
- ${10} \over {9}$
Match the equation to its quotient.
- 16 ÷ 8 =
  
  ⇔
  
  2 ✓
- 24 ÷ 8 =
  
  ⇔
  
  3 ✓
- 40 ÷ 8 =
  
  ⇔
  
  5 ✓
- 56 ÷ 8 =
  
  ⇔
  
  7 ✓
- 96 ÷ 8 =
  
  ⇔
  
  12 ✓
Match the equation to its result. Remember r means a remainder.
- 17 ÷ 8 =
  
  ⇔
  
  2 r1 ✓
- 26 ÷ 8 =
  
  ⇔
  
  3 r2 ✓
- 43 ÷ 8 =
  
  ⇔
  
  5 r3 ✓
- 60 ÷ 8 =
  
  ⇔
  
  7 r4 ✓
- 99 ÷ 8 =
  
  ⇔
  
  12 r3 ✓
Match the improper fractions to their equivalent whole number.
- ${18} \over {6}$
  
  ⇔
  
  3 ✓
- ${40} \over {8}$
  
  ⇔
  
  5 ✓
- ${40} \over {10}$
  
  ⇔
  
  4 ✓
- ${50} \over {5}$
  
  ⇔
  
  10 ✓
- ${66} \over {6}$
  
  ⇔
  
  11 ✓
$Use the part-part-whole model to express <Math> {22} \over {5}</Math> as a mixed number.$

Use the part-part-whole model to express ${22} \over {5}$ as a mixed number.
- ${2} \over {5}$
- ${20} \over {5}$
- $2{{2} \over {5}}$
- $3{{2} \over {5}}$
- $4{{2} \over {5}}$ ✓

Exit quiz

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
- ninths ✓
- tenths
Complete the sentence. There are ______ ninths in one whole.
- 'nine' ✓
How many groups of nine ninths are there in 21 ninths?
- 2 ✓
- 3
- 4
- 5
- 6
How would you write 21 ninths as a mixed number?
- $1{{3} \over {9}}$
- $2{{1} \over {9}}$
- $2{{2} \over {9}}$
- $2{{3} \over {9}}$ ✓
- $2{{4} \over {9}}$
Express ${36} \over {7}$ as a mixed number.
- $4{{1} \over {7}}$
- $5{{1} \over {7}}$ ✓
- $5{{2} \over {7}}$
- $5{{3} \over {7}}$
- $5{{6} \over {7}}$
Match the improper fraction to its mixed number equivalent.
- ${29} \over {7}$
  
  ⇔
  
  $4{{1} \over {7}}$ ✓
- ${30} \over {7}$
  
  ⇔
  
  $4{{2} \over {7}}$ ✓
- ${33} \over {7}$
  
  ⇔
  
  $4{{5} \over {7}}$ ✓
- ${37} \over {7}$
  
  ⇔
  
  $5{{2} \over {7}}$ ✓
- ${39} \over {7}$
  
  ⇔
  
  $5{{4} \over {7}}$ ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

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

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).