Fractions: Equivalence, Ordering and Calculation
Fractions: Equivalence, Ordering and Calculation covers finding equivalent fractions, simplifying a fraction to its lowest terms, comparing and ordering fractions with different denominators, and adding and subtracting fractions (including mixed numbers) by first finding a common denominator.
Before you start
Make sure you're comfortable with these topics first:
Method
- To find an equivalent fraction, multiply (or divide) the numerator and the denominator by the same number.
- To simplify a fraction, divide the numerator and the denominator by their highest common factor.
- To compare or order fractions with different denominators, convert them to a common denominator first so they can be compared directly.
- To add or subtract fractions with different denominators, find a common denominator, convert both fractions, then add or subtract only the numerators.
- For mixed numbers, either convert both to improper fractions first, or add or subtract the whole number and fraction parts separately, regrouping if the fraction part becomes more than one whole.
- Always check whether the final answer can be simplified further.
Worked example
Work out 2 3/4 + 1 5/6, giving your answer as a mixed number in its simplest form.
- Convert both mixed numbers to improper fractions: 2 3/4 = 11/4, and 1 5/6 = 11/6.
- Find a common denominator for 4 and 6: the lowest common multiple is 12.
- Convert both fractions: 11/4 = 33/12, and 11/6 = 22/12.
- Add the numerators: 33/12 + 22/12 = 55/12.
- Convert back to a mixed number: 55 divided by 12 = 4 remainder 7, so the answer is 4 7/12.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Write 3/5 as an equivalent fraction with a denominator of 20.Show answer
Answer: 12/20
Q2Simplify 18/24.Show answer
Answer: 3/4
Q3Which is larger, 5/8 or 2/3?Show answer
Answer: 2/3 (5/8 = 0.625, 2/3 = 0.667 to 3 d.p.)
Q4Work out 1/3 + 1/4.Show answer
Answer: 7/12
Q5Work out 5/6 - 1/2.Show answer
Answer: 1/3
Q6Work out 2 1/2 + 1 3/4, giving your answer as a mixed number.Show answer
Answer: 4 1/4
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Put these fractions in order, starting with the smallest: 3/4, 5/8, 7/12.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
Work out 3 1/5 - 1 7/10. Give your answer as a mixed number in its simplest form.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the fractions: equivalence, ordering and calculation worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on fractions: equivalence, ordering and calculation, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.