Subtract a proper fraction from a mixed number crossing the whole | Maths

Starter quiz

Ten one-tenths is equivalent to ______ whole.
- 'one' ✓
${8} \over {10}$ - ${6} \over {10}$ =
- ${14} \over {10}$
- ${2} \over {10}$ ✓
- ${14} \over {20}$
- ${2} \over {0}$
- ${1} \over {10}$
Match the expressions to the difference.
- ${2} \over {4}$
  
  ⇔
  
  ${3} \over {4}$ − ${1} \over {4}$ ✓
- ${1} \over {4}$
  
  ⇔
  
  ${3} \over {4}$ − ${2} \over {4}$ ✓
- ${1} \over {5}$
  
  ⇔
  
  ${3} \over {5}$ − ${2} \over {5}$ ✓
- ${2} \over {5}$
  
  ⇔
  
  ${4} \over {5}$ − ${2} \over {5}$ ✓
- ${2} \over {8}$
  
  ⇔
  
  ${6} \over {8}$ − ${4} \over {8}$ ✓
$Use the part-part-whole model to express <Math> {15} \over {6}</Math> as a mixed number.$

Use the part-part-whole model to express ${15} \over {6}$ as a mixed number.
- ${3} \over {6}$
- ${12} \over {6}$
- $1{{9} \over {6}}$
- $2{{1} \over {6}}$
- $2{{3} \over {6}}$ ✓
Match the improper fractions to their equivalent mixed number.
- ${9} \over {5}$
  
  ⇔
  
  $1{{4} \over {5}}$ ✓
- ${18} \over {5}$
  
  ⇔
  
  $3{{3} \over {5}}$ ✓
- ${29} \over {5}$
  
  ⇔
  
  $5{{4} \over {5}}$ ✓
- ${34} \over {5}$
  
  ⇔
  
  $6{{4} \over {5}}$ ✓
- ${46} \over {5}$
  
  ⇔
  
  $9{{1} \over {5}}$ ✓
Match the mixed number to their equivalent improper fraction.
- $2{{4} \over {9}}$
  
  ⇔
  
  ${22} \over {9}$ ✓
- $3{{4} \over {5}}$
  
  ⇔
  
  ${19} \over {5}$ ✓
- $1{{6} \over {9}}$
  
  ⇔
  
  ${15} \over {9}$ ✓
- $2{{1} \over {5}}$
  
  ⇔
  
  ${11} \over {5}$ ✓
- $5{{3} \over {9}}$
  
  ⇔
  
  ${48} \over {9}$ ✓

Exit quiz

$Use the number line to calculate 6 − <Math> {3} \over {4}</Math> =$

Use the number line to calculate 6 − ${3} \over {4}$ =
- ${3} \over {4}$
- $5{{3} \over {4}}$
- $5{{2} \over {4}}$
- $5{{1} \over {4}}$ ✓
Match the expression to its difference.
- 4 − ${3} \over {4}$
  
  ⇔
  
  $3{{1} \over {4}}$ ✓
- 4 − ${3} \over {5}$
  
  ⇔
  
  $3{{2} \over {5}}$ ✓
- 4 − ${1} \over {5}$
  
  ⇔
  
  $3{{4} \over {5}}$ ✓
- 4 − ${2} \over {5}$
  
  ⇔
  
  $3{{3} \over {5}}$ ✓
- 4 − ${1} \over {4}$
  
  ⇔
  
  $3{{3} \over {4}}$ ✓
Calculate this. $5{{1} \over {4}}$ − ${3} \over {4}$ =
- $5{4} \over {4}$
- 6
- $4{{1} \over {4}}$
- $4{{2} \over {4}}$ ✓
- $4{{3} \over {4}}$
Match the expression to its difference.
- $2{{4} \over {6}}$
  
  ⇔
  
  $3{{1} \over {6}}$ − ${3} \over {6}$ ✓
- $1{{5} \over {6}}$
  
  ⇔
  
  $2{{2} \over {6}}$ − ${3} \over {6}$ ✓
- $1{{3} \over {6}}$
  
  ⇔
  
  $2{{1} \over {6}}$ − ${4} \over {6}$ ✓
- $3{{5} \over {6}}$
  
  ⇔
  
  $4{{3} \over {6}}$ − ${4} \over {6}$ ✓
Andeep has three metres of rope. He cuts off six-tenths of a metre. There is two and ______ tenths metres left.
- 'four' ✓
Izzy has four and two-tenth litres of water in a bucket. She uses six tenths of a litre to water some plants. How much water does she have left in her bucket?
- $4{{8} \over {10}}$
- $3{{5} \over {10}}$
- $3{{6} \over {10}}$ ✓
- $3{{7} \over {10}}$

Worksheet

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Lesson Details

Key learning points

Rods or number lines can be used to support subtracting fractions from whole or mixed numbers.
Mixed numbers can be expressed as improper fractions to aid subtraction.
If an answer to a calculation is an improper fraction, this should be expressed as a mixed number.
Improper fractions can be subtracted in the same way as proper fractions.

Common misconception

Children may not understand that a one can be exchanged from a whole and the fraction rewritten. E.g. four can be rewritten as three and five-fifths to add subtraction of an amount of fifths.

Use of rods or drawings will support children to understand this exchange. Four is the same as three and one; one is the same as five fifths so four is the same and three and five fifths.

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 is greater than or equal to the denominator.