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Mixed Numbers & Top Heavy Fractions (Cambridge O Level Maths)

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Mixed Numbers & Top Heavy Fractions

What are mixed numbers & top heavy fractions?

  • A mixed number has a whole number (integer) part and a fraction part

    eg. 3 3 over 4 has the whole number 3 and the fraction 3 over 4, meaning “three and three quarters”

  • A top heavy fraction – also called an improper fraction – is one with the top (numerator) bigger than the bottom (denominator)

    eg. 15 over 4 means “fifteen quarters”

Turning mixed numbers into top heavy fractions

  • Multiply the whole number by the denominator (big × bottom)
  • Add that value to the numerator
  • Write the "new" numerator over the same denominator as before 

Turning top heavy fractions into mixed numbers

  • Divide the top by the bottom (to get a whole number and a remainder)
  • The whole number is the big number
  • The fraction part is the remainder over the denominator

Examiner Tip

  • Top heavy fractions are also called "improper" fractions

Worked example

(a) Write 5 3 over 4 as an improper fraction

Multiply the whole number by the denominator, and add to the numerator.
Keep the denominator the same.

fraction numerator open parentheses 5 cross times 4 space close parentheses plus 3 over denominator 4 end fraction

Simplify

bold 23 over bold 4

(b) Write 17 over 5 as a mixed number

Divide the top by the bottom

17 ÷ 5 = 3 remainder 2

The final answer is 3, with 2 parts still left over to be divided by 5, which can be written as a mixed number

bold 3 bold 2 over bold 5

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    Mark

    Author: Mark

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.