Four Operations of Fractions
Multiply mixed numbers, then draw the bar that shows what is left after one part and what came before the last step.
Your child adds and subtracts mixed numbers by giving both fractions parts of the same size, and multiplies fractions, including a mixed number by a whole number. The word problems then take a fraction of a set, of the remainder or of another group, and work backwards from what is left. Each step names the whole a fraction belongs to. Read the study guide →
About this chapter
These Primary 5 fractions questions cover the four operations of fractions: adding and subtracting mixed numbers, multiplying fractions and whole numbers, and multiplying a mixed number by a whole number. The later pages use them in word problems, from a fraction of the remainder to working backwards.
Practise by question type: p5 equal fractions of two wholes questions, p5 fraction remainder questions with three parts, p5 fraction work backwards questions, p5 fraction of the remainder questions, p5 multiplying mixed numbers by whole numbers, p5 multiplying fractions questions, p5 fraction of a set questions and p5 adding and subtracting mixed numbers.
The order to learn them
Calculating with mixed numbers and fractions
4.1 to 4.3
Regroup mixed numbers when needed. Convert a mixed number to one fraction before multiplying.
Which whole does each fraction use?
4.4 to 4.7
Name the whole before calculating. A later fraction may use the remainder, one group or another part as its whole.
Working backwards from what is left
4.8
Put each fixed amount back before growing the remaining fraction to one whole.
The number tells you where a question type sits in this chapter, not what your child needs to learn first. A child who has already met a type in school can practise it without working through the ones above it.
How the end-of-year papers set these questions
Fractions appear throughout the Primary 5 papers.
The 2025 Primary 5 end-of-year papers include short mixed-number calculations and longer questions about a fraction of a set, a remainder or an unknown whole.
Longer questions change the whole between steps.
A fraction may be taken from what remains after an earlier step. Harder questions compare parts of different wholes or give only the final remainder, so every line must name the amount it is using.
The questions are modelled against top school papers.
We used the 2025 Primary 5 end-of-year papers to check the question types and the written working. Every practice question is original, and no school question is reproduced.
Everything here is modelled against top school papers. Those papers are never reproduced, and every question on this site is original.
How to set out the working clearly
These examples show Mathweave's clear, consistent layout for each method. The layout is informed by the answer keys we reviewed.
- Regroup one whole before subtracting mixed numbers When the first fraction is too small to subtract from, rewrite one whole as equal fraction parts. Keep that regrouping visible before the subtraction line.
- Convert a mixed number before multiplying Write the mixed number as an improper fraction, multiply, then return the answer to mixed-number form when the answer line asks for it.
- Name the whole used by every fraction Write the remainder before taking a fraction of it. When two fractions need one common set of parts, write lowest common multiple in full before using the common number of parts.
- Put a fixed amount back before growing the fraction Working backwards reverses one stage at a time. Add the fixed amount first, then divide to find one part and multiply to recover the whole. Write one derived value on each line.
Questions parents ask
Is this the Primary 5 syllabus?
The chapter follows the latest MOE Primary Mathematics syllabus. The syllabus defines the fraction calculations taught in Primary 5, and the papers we model against show how they are examined.
Why does the whole change in some questions?
A phrase such as a fraction of the remainder creates a new whole. The chapter teaches children to name that whole before using the fraction.
Why do some lesson pages say Primary 5 and Primary 6?
Multiplying fractions, a fraction of a set, a fraction of the remainder and equal fractions of two wholes are shared types. Each has one lesson page with the level line Primary 5 and Primary 6.
Are the questions from past papers?
We write the questions ourselves rather than copy them from papers. Each chapter is modelled on the types of question that top school papers set. A question may look like one your child has met before because it is the same type.
Primary 5 fraction word problems by question type
Primary 5 Four Operations of Fractions Study Guide
From opening a whole to subtract mixed numbers, to putting amounts back when working backwards. Six steps with bars and sets to tap, worked examples and a five-question check.
Same-size partsMixed numbersMultiplyingMixed × wholeSet and remainderEqual unitsWorking backwardsOpen the study guide →