Primary 6 · Chapter 1
Start with the order of the quantities, then use equal units to solve sharing and changing-ratio problems. Try the questions before opening the working.
Self-paced lessons · Modelled on top school exam questions · No sign-up for the samples
The Ratio chapter
Watch · The introduction
Watch the explanation, then try a question for yourself.
Try · Modelled on top school exam questions
Try each question yourself first, then check your answer or compare it with the solution. These questions are written by Mathweave, not copied from school papers. No sign-up is needed.
Question 1 of 3
Try solving it yourself before opening the solution.
The number of apples to oranges to pears in a basket is in the ratio 2 : 3 : 4. What fraction of the fruit in the basket are pears?
Ans: 4/9
Question 2 of 3
Try solving it yourself before opening the solution.
In a store, the number of large boxes to the number of small boxes is 2 : 3. Each large box holds 10 tiles and each small box holds 5 tiles. There are 210 tiles altogether. How many small boxes are there?
Ans: 18
Question 3 of 3
Try solving it yourself before opening the solution.
A community centre collected vouchers worth $2, $5 and $10. There were as many $10 vouchers as $5 vouchers. The number of $2 vouchers to the number of $10 vouchers was 4 : 3. The vouchers were worth $424 altogether. What was the total value of the $2 vouchers?
Ans: $64
Follow a lesson link beside a question, or browse the chapter below.
The chapter · Ten question types
A linked row opens a published lesson with its own film. Explore the explanation and available practice on that page.
Mixed practice, where the types return unannounced and unlabelled, is a chapter-level activity. It has no lesson page of its own.
For a before-and-after question, check what changes before choosing a method.
Depth · One question type, all the way up
These eight Ratio questions show the full progression, from a direct calculation to mixed concepts, an unfamiliar challenge and a Paper 2 question.
Basic
Read one share straight from the unit.
Priya and Samuel share 45 beads in the ratio 2 : 3. How many beads does Samuel get?
Intermediate
The whole is not given. You work back to it from one share.
A prize is shared between Wei Jie and Hui Min in the ratio 4 : 5. Wei Jie receives $28. How much is the prize altogether?
All concepts combined
The chapter's question types come back together, and nothing tells you which is which.
The number of marbles Chloe and Marcus had was in the ratio 7 : 3. Chloe then gave Marcus 24 marbles, and they had the same number each. How many marbles did Chloe have at first?
The ratio of comic books to storybooks on a shelf was 2 : 5. After 18 more comic books were added, the ratio became 4 : 5. How many storybooks are on the shelf?
The number of Adam's bottle caps to Grace's is in the ratio 3 : 5. What fraction of all the caps are Adam's?
More than one concept
One question combines two question types. Identifying both is part of the skill, so neither is labelled.
A bakery sold 630 loaves and rolls altogether one morning. The number of loaves to the number of rolls was 4 : 5. Loaves are sold in packs of 7 for $9 and rolls are sold in packs of 5 for $14. How much money did the bakery take that morning?
Harder questions
A harder question: the ratio counts boxes, the total counts tiles, and the divisor is not given.
In a store, the number of large boxes to the number of small boxes is 2 : 3. Each large box holds 10 tiles and each small box holds 5 tiles. There are 210 tiles altogether. How many small boxes are there?
Exam-style questions
Children practise choosing and setting out the methods needed for multi-step Paper 2 questions that combine question types. Worked solutions show how to set out the method.
A shop stocked plain T-shirts and printed T-shirts. 25% of the T-shirts were printed. The shop then sold 30 printed T-shirts and 30 plain T-shirts. After that, 20% of the T-shirts left were printed. How many T-shirts did the shop stock at first?
The order · Three groups
The building blocks
1.1 to 1.4
What a ratio says, and how to handle one before any word problem starts. Notation, equivalence, sharing, and the same bar read as a fraction.
Before and after
1.5 to 1.7, then 1.11
Start by identifying what stays unchanged: the total, the difference or one quantity. The final type has no unchanged quantity.
The two types the papers set most
1.9 and 1.10
These are the two ratio forms that appear most often in the papers we model against.
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.
The papers · Modelled against top school papers
Paper 1 has 30 questions for 50 marks: 18 multiple-choice questions and 12 short-answer questions. Paper 2 has 15 questions for 50 marks: 5 short-answer questions and 10 structured or long-answer questions.
A Paper 1 ratio question is usually notation or one equivalence step; the four- and five-mark items appear in Paper 2, and they are almost always a before-after question or a ratio set against a money total.
Close to half of Paper 2 questions combine two or more topics and account for a larger share of the marks. Practice questions are not labelled by type, so children must choose the methods they need.
Everything here is modelled against top school papers. Those papers are never reproduced, and every question on this site is original.
Written working · Clear methods, line by line
These examples show Mathweave's clear, consistent layout for each method. The layout is informed by the answer keys we reviewed.
Parents · Asked and answered
The question types follow the latest MOE Primary Mathematics syllabus. The syllabus defines what is taught; the papers we model against show how it is examined.
The order above is the order the chapter teaches, but no lesson here is locked behind another. A child who has met a type in school can practise it straight away.
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.
Practice uses different numbers for each question type, points out the common mistake when your child makes it and records which types your child can complete independently.