Grasp Maths

Year 5

Compare and order fractions whose denominators are all multiples of the same number

Compare and order fractions by reasoning with equivalent fractions and common denominators.

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Lesson overview

Number - fractions

Fractions are easier to compare when they use a common denominator. If the denominators are multiples of the same number, we can rename the fractions in a matching form and then compare the numerators.

Make denominators match

12\frac{1}{2} and 36\frac{3}{6} are equal because 12\frac{1}{2} can be renamed as 36\frac{3}{6}.

Equivalent fractions name the same amount.

Compare sixths

46\frac{4}{6} is greater than 36\frac{3}{6} because the numerators show more equal parts.

Once the denominators match, compare the numerators.

Order a set

13\frac{1}{3}, 12\frac{1}{2} and 23\frac{2}{3} can be ordered by thinking in sixths.

Rename them as 26\frac{2}{6}, 36\frac{3}{6} and 46\frac{4}{6}.

Worked example

Which is greater: 23\frac{2}{3} or 59\frac{5}{9}?

  1. Find a common denominator of 9.
  2. 23\frac{2}{3} is the same as 69\frac{6}{9}.
  3. Compare 69\frac{6}{9} and 59\frac{5}{9}.
  4. So 23\frac{2}{3} is greater.

Round 1: Learn it

Rename the fractions when needed so the denominators match.

Finish this round to unlock Round 2: Show you know it.

Question 1

Which is greater?

Question 2

Which fraction is smallest?

Question 3

Which is equal to 12\frac{1}{2}?

Question 4

Which order is correct from least to greatest?

Question 5

Which is greater: 38\frac{3}{8} or 12\frac{1}{2}?

Common mistakes

Watch for these as you work through the lesson.

  • Comparing denominators without finding a common form.
  • Changing the denominator but not the numerator.
  • Ordering fractions by the size of the numbers alone.

Related topics

These ideas connect closely to this lesson.

  • Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths.
  • Recognise mixed numbers and improper fractions and convert from one form to the other.

Practice next

Independent practice will plug in here

This lesson teaches the pattern first. Deeper Year 5 practice can connect here later.