Fractions: Comparing, Adding and Subtracting
Comparing, adding and subtracting fractions is the Year 5 topic that covers comparing and ordering fractions whose denominators are multiples of the same number, and adding or subtracting fractions where one denominator is a multiple of the other.
Before you start
Make sure you're comfortable with these topics first:
Method
- To compare fractions with different denominators, first find a common denominator (a number both denominators divide into exactly), then convert each fraction so they share that denominator.
- Once fractions share a denominator, compare or order them just by comparing their numerators - the fraction with the bigger numerator is the bigger fraction.
- To add or subtract fractions that already share a denominator, add or subtract the numerators only and keep the denominator the same.
- To add or subtract fractions with different denominators, convert them to a common denominator first (multiply the numerator and denominator of each fraction by whatever makes the denominators match), then add or subtract the numerators.
- If the answer is an improper fraction, convert it to a mixed number by dividing the numerator by the denominator; the whole number is the answer to the division and the remainder becomes the new numerator.
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and put the result over the same denominator.
- Always check whether the final fraction can be simplified, by dividing the numerator and denominator by their highest common factor.
Worked example
Work out 2/3 + 5/6, giving your answer as a mixed number in its simplest form.
- The denominators are 3 and 6; since 6 is a multiple of 3, 6 can be used as the common denominator.
- Convert 2/3 to sixths by multiplying the numerator and denominator by 2: 2/3 = 4/6.
- Add the numerators, keeping the denominator the same: 4/6 + 5/6 = 9/6.
- 9/6 is an improper fraction; dividing 9 by 6 gives 1 remainder 3, so 9/6 = 1 and 3/6.
- Simplify 3/6 by dividing the numerator and denominator by their highest common factor, 3: 3/6 = 1/2. So 2/3 + 5/6 = 1 and 1/2.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Which is greater, 3/4 or 5/8?Show answer
Answer: 3/4, because 3/4 = 6/8, and 6/8 is greater than 5/8
Q2Work out 3/5 + 1/5.Show answer
Answer: 4/5
Q3Work out 7/10 - 3/10, giving your answer in its simplest form.Show answer
Answer: 4/10, which simplifies to 2/5
Q4Work out 1/4 + 5/12, giving your answer in its simplest form.Show answer
Answer: 3/12 + 5/12 = 8/12, which simplifies to 2/3
Q5Convert the improper fraction 11/4 to a mixed number.Show answer
Answer: 2 and 3/4
Q6Convert the mixed number 3 and 2/5 to an improper fraction.Show answer
Answer: 17/5
Q7Order these fractions from smallest to largest: 1/2, 5/8, 3/8.Show answer
Answer: 3/8, 1/2, 5/8
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Freya says that 5/6 + 1/3 = 6/9. Explain why Freya is wrong, then work out the correct 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 - 2 available
A ribbon is 7/8 m long. Priya cuts off a piece 1/4 m long to use for a bow. How much ribbon is left? Give your answer as a fraction of a metre in its simplest form.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
Tom eats 2/5 of a pizza. Ben eats 1/4 of the same pizza. What fraction of the pizza is left?
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: comparing, adding and subtracting worksheet pack - 6 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: comparing, adding and subtracting, 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.