Singapore Mathematics | International Edition: Ratio

Singapore Math ratio guide for families and teachers outside Singapore. What Primary 6 students learn about ratio, how Singapore teaches it with units and models, and how to practise it at home.

A ratio compares quantities by equal parts.

That single idea carries a great deal of later Mathematics.

In Singapore Mathematics, ratio is a Primary 6 topic in the current primary syllabus. Students learn to write ratios, find equivalent ratios, simplify them and use them to share a quantity. They also learn how a ratio connects to a fraction.

Ratio then returns in Secondary 1 and grows into map scales, proportion and similar figures.

This guide is useful for families and teachers who want to:

• understand what Singapore expects at Primary 6;
• teach ratio at home in a clear sequence;
• prepare a child who is moving into a Singapore school; or
• support a student using Singapore Math materials in another country.

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What Ratio Means in Singapore Mathematics

A ratio such as 3 : 4 says that for every 3 parts of one quantity, there are 4 parts of another.

The parts are equal in size. The ratio tells us how many parts each quantity has, not how big each part is.

That is why Singapore students often describe a ratio in units. If boys and girls are in the ratio 3 : 4, the boys have 3 units, the girls have 4 units and the whole group has 7 units.

Once one unit is known, everything else follows.

This way of thinking connects directly to the bar model, where each unit is drawn as an equal bar. The Singapore Math Bar Model guide explains the drawing method itself.

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Where Ratio Sits in the Singapore Syllabus

In the current primary syllabus, ratio appears only at Primary 6. It is not part of Primary 5 Standard Mathematics, and it does not appear in Foundation Mathematics.

At Primary 6, students learn:

• ratio notation a : b and a : b : c, where a, b and c are whole numbers;
• equivalent ratios;
• writing a ratio in its simplest form;
• dividing a quantity in a given ratio;
• finding the ratio of two or three given quantities;
• finding the missing term in a pair of equivalent ratios; and
• the relationship between fraction and ratio.

Ratios involving fractions or decimals are excluded at Primary 6.

Level	What students do with ratio
Primary 6	Whole-number ratios, equivalent ratios, simplest form, sharing a quantity, missing terms, ratio and fraction
Secondary 1	Ratios involving rational numbers, including fractions and decimals
Secondary 2	Map scales, and direct and inverse proportion

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How Singapore Teaches Ratio

1. Start with parts, not numbers

Students first compare small collections they can see: 2 red beads for every 3 blue beads. The ratio is read in order, so red to blue is 2 : 3.

2. Build equivalent ratios

If the pattern repeats, 2 : 3 becomes 4 : 6, then 6 : 9. Multiplying both terms by the same number keeps the comparison the same.

3. Simplify

Dividing both terms by a common factor gives the simplest form. 12 : 18 becomes 2 : 3. This links back to Factors and Multiples.

4. Use units to share a quantity

Add the terms to find the total number of units. Divide the quantity by that total to find one unit.

5. Connect ratio and fraction

If A : B = 2 : 3, then A is 2/5 of the total and B is 3/5 of the total. A is also 2/3 of B. Students learn to say which whole each fraction refers to.

6. Move to three quantities

The same unit method works for a : b : c.

The order of these steps matters. Children who jump straight to “share in the ratio” without seeing equal parts often learn a procedure they cannot adapt.

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A Worked Example

A drawn model helps here. Draw 3 equal bars for Mei and 4 equal bars of the same length for Tom, then label the whole as $84.

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Common Mistakes

• Reading the order wrongly. Boys to girls 2 : 3 is not the same as girls to boys. Fix: write the names above the numbers before working.
• Using a ratio term as a fraction of the whole. In 3 : 4, the first quantity is 3/7 of the whole, not 3/4. Fix: find the total units first.
• Stopping before the simplest form. Simplifying 18 : 24 to 9 : 12 is not finished. Fix: divide by the highest common factor, 6, to get 3 : 4.
• Mixing units of measure. 50 cm to 2 m is not 50 : 2. Fix: convert first, so 50 cm : 200 cm = 1 : 4.
• Changing both quantities when only one changes. In before-and-after problems, one quantity often stays the same. Fix: mark the unchanged quantity and make its units match in both ratios.
• Adding to both terms. Adding the same number to both terms does not give an equivalent ratio. Fix: only multiply or divide both terms by the same number.

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Teaching Ratio Outside Singapore

Singapore Math materials use the same ratio notation found in most English-language curricula: a colon between the terms.

A few points are worth knowing when you use Singapore materials elsewhere.

• The word “unit”. Singapore working often says “1 unit = $12”. Here a unit means one equal part, not a unit of measurement.
• Timing. In Singapore’s current syllabus, ratio is a Primary 6 topic. Your local curriculum may introduce it at a different stage, so decide by readiness rather than age. The Singapore Math Grade Levels guide explains why direct conversions are unreliable.
• Prerequisites. Ratio depends on multiplication facts, factors and fractions. If those are weak, repair them first.
• Working without a calculator. PSLE Paper 1 does not allow calculators, so students need mental and written methods as well as calculator skills.
• HCF. Singapore says “highest common factor” (HCF). Some curricula call it the greatest common factor (GCF).

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How to Practise Ratio at Home

A short, regular routine works better than one long weekend session.

1. Begin with real objects such as beads, coins or blocks. Make “2 for every 3” patterns and say them aloud.
2. Write the ratio, then build two equivalent ratios from it.
3. Simplify three ratios a day using the highest common factor.
4. Solve one sharing problem with a drawn model.
5. Ask one fraction question about the same model: what fraction of the whole is the first quantity?
6. Once a week, mix ratio with earlier topics so the child must decide which method to use.

Ten to fifteen minutes is enough when the work is focused.

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Try These

1. Write 18 : 24 in its simplest form.
2. Find the missing number: 5 : 8 = 20 : ?
3. $150 is shared among Ann, Ben and Cal in the ratio 2 : 3 : 5. How much does Cal receive?
4. The ratio of red beads to blue beads is 4 : 5. What fraction of all the beads are blue?

Answers

1. 3 : 4, by dividing both terms by 6.
2. 32, because both terms are multiplied by 4.
3. $75. There are 10 units, so 1 unit = $15, and Cal has 5 units.
4. 5/9. Blue has 5 units out of 4 + 5 = 9 units.

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What Comes Next

Ratio is a bridge topic.

• In Secondary 1, ratios can involve fractions and decimals.
• In Secondary 2, ratio leads to Map Scales and Direct and Inverse Proportion.
• In Congruence and Similarity, the corresponding sides of similar figures are in proportion.

A student who understands ratio as equal parts usually finds these later topics easier to learn.

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Frequently Asked Questions

When do Singapore students learn ratio?

In the current primary syllabus, ratio is taught in Primary 6. It continues in Secondary 1 and Secondary 2.

Is a ratio the same as a fraction?

No, but they are closely linked. A ratio compares parts with parts. A fraction compares a part with a whole. If A : B = 2 : 3, then A is 2/5 of the total.

Do Primary 6 ratios include decimals or fractions?

No. At Primary 6 the terms are whole numbers. Ratios involving fractions and decimals come in Secondary 1.

Is ratio part of Foundation Mathematics?

No. Ratio does not appear in the Primary 5 or Primary 6 Foundation Mathematics content.

Should my child always draw a model?

Draw one when the relationship is unclear. As confidence grows, many students write the units directly without drawing.

My child knows the steps but gets before-and-after questions wrong. Why?

These questions usually depend on spotting which quantity stays the same. Practise naming the unchanged quantity before calculating.

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Helpful Reading

• Singapore Mathematics | International Edition: Fractions and Division
• Singapore Mathematics | International Edition: Rate
• Singapore Mathematics | International Edition: Direct and Inverse Proportion
• Singapore Math Bar Model | A Guide to Model Drawing
• Why Are Ratio, Rate and Percentage So Easy to Confuse?
• Ratio, Rate and Proportion | Mathematics Knowledge Object
• MOE Primary Mathematics Syllabus
• SEAB PSLE Formats Examined in 2026

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Ratio in Singapore Mathematics

Equal parts first.

Order matters.

Find one unit, then the rest.

Know which whole a fraction belongs to.

Taught this way, ratio stops being a trick for word problems.

It becomes a way of seeing how quantities relate.

That habit carries a student from Primary 6 into proportion, scale and similarity.

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Ask Bukit Timah Tutor

Bukit Timah Tutor teaches Mathematics in small groups of three students in Singapore.

If your child is learning Singapore Mathematics at home, in an international school or in a Singapore school, and you are unsure where to begin with this topic, send us a short message with the student’s level and one example of the work.

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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.

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