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Fractions Toolkit

Number

Recognising each form

  • A mixed number is written as a whole number beside a proper fraction
    • 4 2/9 means four wholes together with two ninths
  • Any value above 1 can be written either as a mixed number or as an equivalent improper fraction

Converting a mixed number to an improper fraction

  • Multiply the whole number by the denominator, then add the numerator
  • Write the result over the original denominator
    • For 4 2/9: 4 × 9 = 36, and 36 + 2 = 38, giving 38/9

Converting an improper fraction to a mixed number

  • Work out how many whole denominators fit inside the numerator
  • That count becomes the whole part, and whatever is left over sits above the original denominator
    • For 29/6: 29 ÷ 6 = 4 remainder 5, giving 4 5/6
Worked example

Converting both ways

Write 4 3/5 as an improper fraction, and write 47/6 as a mixed number.

Solution:

  • For the mixed number, multiply the whole part by the denominator and add the numerator
  • 4 × 5 = 20, then 20 + 3 = 23
  • The denominator does not change, so 4 3/5 = 23/5
  • For the improper fraction, divide the numerator by the denominator
  • 47 ÷ 6 = 7 remainder 5
  • The whole part is the 7 and the remainder becomes the new numerator, so 47/6 = 7 5/6
  • Check by reversing: 7 × 6 = 42, and 42 + 5 = 47