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

Starter quiz

Which of the following are improper fractions?
- ${8} \over {7}$ ✓
- $1{{8} \over {9}}$
- ${7} \over {4}$ ✓
- ${3} \over {9}$
- ${1} \over {10}$
Which of the following are mixed numbers?
- $3{{2} \over {6}}$ ✓
- $1{{3} \over {9}}$ ✓
- ${7} \over {4}$
- ${10} \over {9}$
- $2{{1} \over {4}}$ ✓
Match the equation to its product.
- 2 × 8 =
  
  ⇔
  
  16 ✓
- 3 × 8 =
  
  ⇔
  
  24 ✓
- 8 × 5 =
  
  ⇔
  
  40 ✓
- 8 × 6 =
  
  ⇔
  
  48 ✓
- 11 × 8 =
  
  ⇔
  
  88 ✓
Match the calculation to its answer.
- 3 × 8 + 1 =
  
  ⇔
  
  25 ✓
- 5 × 8 + 3 =
  
  ⇔
  
  43 ✓
- 8 × 2 + 2 =
  
  ⇔
  
  18 ✓
- 8 × 5 + 4 =
  
  ⇔
  
  44 ✓
- 7 × 8 + 7 =
  
  ⇔
  
  63 ✓
Aisha has two and one-tenth of a metre of string. Which unit does she need to be thinking about?
- halves
- thirds
- quarters
- fifths
- tenths ✓
Express ${15} \over {7}$ as a mixed number.
- ${1} \over {7}$
- $1{{1} \over {7}}$
- $2{{1} \over {7}}$ ✓
- $2{{2} \over {7}}$
- $3{{1} \over {7}}$

Exit quiz

Aisha represents two and one-eighth with number rods. Which unit does she need to be thinking about?
- sixths
- sevenths
- eighths ✓
- ninths
- tenths
Complete the sentence. There are ______ eighths in one whole.
- 'eight' ✓
How many full groups of eight eighths can be made from two and one-eighth?
- 1
- 2 ✓
- 3
- 4
- 5
How would you write two and one eighth as a mixed number?
- $1{{1} \over {8}}$
- $2{{1} \over {8}}$ ✓
- ${21} \over {8}$
- $2{{2} \over {8}}$
- ${1} \over {28}$
Express $2{{1} \over {8}}$ as an improper fraction.
- ${21} \over {8}$
- ${2} \over {8}$
- ${16} \over {8}$
- ${17} \over {8}$ ✓
- ${1} \over {8}$
Match the mixed number to its improper fraction equivalent.
- $1{{2} \over {7}}$
  
  ⇔
  
  ${9} \over {7}$ ✓
- $2{{3} \over {7}}$
  
  ⇔
  
  ${17} \over {7}$ ✓
- $4{{5} \over {7}}$
  
  ⇔
  
  ${33} \over {7}$ ✓
- $4{{6} \over {7}}$
  
  ⇔
  
  ${34} \over {7}$ ✓
- $5{{1} \over {7}}$
  
  ⇔
  
  ${36} \over {7}$ ✓

Worksheet

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Lesson Details

Key learning points

Times table knowledge can help to convert a mixed number to an improper fraction.
Calculate how many of the fraction are needed to equal the value of the whole number.
Add the value of the fraction part to the numerator of the fraction equivalent to the whole number part.

Common misconception

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

First multiply the whole number by the denominator then add the numerator. Multiplying the whole number by the denominator tells us the number of parts that can be made from the whole number part then we need to add the parts shown by the numerator.

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).