Singapore Math equivalent fractions guide for families and teachers outside Singapore. What Primary 3 students learn about equivalent fractions and simplest form, how Singapore teaches them, and how to practise at home.
1/2, 2/4 and 4/8 look different.
They name exactly the same amount.
In Singapore Mathematics, equivalent fractions are a Primary 3 topic in the current primary syllabus. Students find equivalent fractions, write fractions in simplest form, compare unlike fractions and add or subtract two related fractions within one whole.
These skills carry every later fraction topic, from adding with different denominators in Primary 4 to ratio in Primary 6.
This guide is useful for families and teachers who want to:
- understand what Singapore expects at Primary 3;
- explain why equivalent fractions work, not only how;
- prepare a child who is moving into a Singapore school; or
- support a student using Singapore Math materials in another country.
Quick facts
Level: Primary 3 (common to all students), revisited in Primary 5 Foundation
Strand: Number and Algebra
Official source: MOE Primary Mathematics Syllabus, the 2021 syllabus first examined at PSLE in 2026
Comes after: Introducing Fractions and Multiplication Tables
Leads to: Adding and Subtracting Fractions and Ratio
What Equivalent Fractions Mean in Singapore Mathematics
Two fractions are equivalent when they name the same part of the same whole.
Fold a strip in half and shade one half. Fold it again: the shaded part is now 2/4. Fold once more: it is 4/8. The shaded amount never changed. Only the number of equal parts did.
That picture gives the rule. Multiplying the numerator and denominator by the same number gives an equivalent fraction. So does dividing both by the same number.
A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. 8/12 in simplest form is 2/3.
Equivalent fractions let students compare and add fractions that start with different denominators.
Where Equivalent Fractions Sit in the Singapore Syllabus
In the current primary syllabus, equivalent fractions are taught in Primary 3.
At Primary 3, students learn:
- equivalent fractions and the simplest form;
- comparing and ordering unlike fractions, with denominators not exceeding 12;
- finding an equivalent fraction given the denominator or the numerator; and
- adding and subtracting two related fractions within one whole, with denominators not exceeding 12.
The syllabus calls these “related fractions”. The usual meaning is that one denominator is a multiple of the other, as with 1/2 and 3/8.
Equivalent fractions and simplest form appear again in Primary 5 Foundation Mathematics.
| Level | What students do |
|---|---|
| Primary 2 | Compare unit fractions and like fractions only |
| Primary 3 | Equivalent fractions, simplest form, comparing unlike fractions, adding and subtracting two related fractions |
| Primary 4 | Add and subtract with up to two different denominators, not exceeding 12 |
| Primary 6 | Equivalent ratios, using the same idea |
How Singapore Teaches Equivalent Fractions
1. Fold and compare
Fold strips into halves, quarters and eighths, and line them up. Children see that 1/2, 2/4 and 4/8 cover the same length.
2. Use a fraction wall
Rows of strips cut into halves, thirds, quarters and so on make many equivalences visible at once.
3. Find the multiplier
From 3/4 to ?/12, the denominator is multiplied by 3, so the numerator must be too: 9/12.
4. Simplify by dividing
8/12: both terms divide by 4, giving 2/3. Children may divide in two steps, first by 2 and then by 2 again.
5. Compare unlike fractions
Rename both fractions with the same denominator, then compare numerators.
6. Add two related fractions
Rename one fraction so the denominators match, then add as like fractions.
The strip picture should come before the rule. A child who has seen 1/2 and 4/8 match is far less likely to add 1 to the top and bottom.
Worked Examples
Finding and simplifying equivalent fractions
Question: Find the missing numerator in 3/4 = ?/12. Then write 8/12 in its simplest form.
Step 1. 4 × 3 = 12, so the denominator has been multiplied by 3.
Step 2. Multiply the numerator by 3 as well: 3 × 3 = 9. So 3/4 = 9/12.
Step 3. For 8/12, the largest number that divides both 8 and 12 is 4.
Step 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, so 8/12 = 2/3.
Check: 2/3 cannot be simplified further, because 2 and 3 share no factor other than 1.
Comparing and adding with equivalent fractions
Question: Which is greater, 3/4 or 5/6? Then find 1/2 + 3/8.
Step 1. 12 is a multiple of both 4 and 6. Rename: 3/4 = 9/12 and 5/6 = 10/12.
Step 2. 10/12 is greater than 9/12, so 5/6 is greater.
Step 3. For 1/2 + 3/8, rename 1/2 as 4/8.
Step 4. 4/8 + 3/8 = 7/8.
Check: 7/8 is less than 1 whole, as the Primary 3 limit expects, and 7 and 8 share no common factor.
Common Mistakes
- Adding the same number to top and bottom. 2/3 becomes 3/4. Fix: only multiply or divide both terms by the same number. A strip picture shows that 3/4 is larger than 2/3.
- Changing only one term. 3/4 becomes 3/12. Fix: whatever happens to the denominator must happen to the numerator.
- Stopping before the simplest form. 8/12 becomes 4/6 and the child stops. Fix: check whether the new numerator and denominator still share a factor.
- Comparing denominators only. A child says 5/6 is smaller than 3/4 because 6 parts are smaller than 4 parts. Fix: rename both fractions with the same denominator first.
- Thinking simplifying changes the value. Some children think 2/3 is “less” than 8/12 because the numbers are smaller. Fix: show both on strips of the same length.
Teaching Equivalent Fractions Outside Singapore
The idea is universal. A few details help when using Singapore materials.
- Simplest form. Singapore says “simplest form”. Some materials say “lowest terms”. They mean the same thing.
- Related fractions. This Singapore syllabus term is less common elsewhere. At Primary 3 it limits adding and subtracting to pairs such as halves and eighths.
- Timing. In Singapore’s current syllabus, this is a Primary 3 topic. Decide by readiness, and see the Singapore Math Grade Levels guide for why grade conversions are unreliable.
- Prerequisites. Equivalent fractions depend on multiplication tables. In Singapore, the tables of 6, 7, 8 and 9 are also Primary 3 content, so the two topics support each other.
- Factors. Common factors are formally taught in Primary 4. At Primary 3, children can simplify by trying small divisors such as 2, 3 and 5.
How to Practise Equivalent Fractions at Home
Short sessions with strips and drawings work well.
- Make a paper fraction wall with halves, thirds, quarters, sixths, eighths and twelfths.
- Find three fractions equivalent to 1/2 and three equivalent to 1/3.
- Fill two missing numerators or denominators, such as 2/5 = ?/10.
- Simplify three fractions and check each one on the wall.
- Compare one pair of unlike fractions by renaming.
- Add one pair of related fractions, such as 1/4 + 3/8.
Ten minutes is enough when the child explains each step.
Try These
- Find the missing number: 2/5 = ?/10.
- Write 9/12 in its simplest form.
- Which is greater, 3/4 or 7/12?
- Find 3/10 + 1/2. Give your answer in simplest form.
Answers
- 4. The denominator is multiplied by 2, so the numerator is too.
- 3/4. Both 9 and 12 divide by 3.
- 3/4. It equals 9/12, which is greater than 7/12.
- 4/5. 1/2 = 5/10, so 3/10 + 5/10 = 8/10, which simplifies to 4/5.
What Comes Next
Equivalent fractions open the way to most later fraction work.
- Adding and Subtracting Fractions uses renaming to add fractions with different denominators.
- Mixed Numbers and Improper Fractions needs renaming to compare and simplify.
- In Primary 6, Ratio uses the same idea in equivalent ratios.
A student who can explain why 3/4 = 9/12 has the core idea for all three.
Frequently Asked Questions
When do Singapore students learn equivalent fractions?
In the current primary syllabus, equivalent fractions and simplest form are taught in Primary 3.
What does “simplest form” mean?
The numerator and denominator share no common factor other than 1. For example, 6/8 in simplest form is 3/4.
What are related fractions?
The syllabus uses the term for the Primary 3 adding and subtracting work. The usual meaning is that one denominator is a multiple of the other, such as 1/3 and 5/6.
Is it wrong to simplify in two steps?
No. Dividing 8/12 by 2 and then by 2 again is correct. Dividing by the largest common factor is just quicker.
Why do denominators stay at 12 or below?
The Primary 2 to Primary 4 content sets this limit for comparing, adding and subtracting fractions. Small denominators keep attention on the idea rather than on large numbers.
My child knows the rule but still makes errors. Why?
The rule is often applied without the picture. Go back to strips for a week, then return to written work.
Helpful Reading
- Singapore Mathematics | International Edition: Introducing Fractions
- Singapore Mathematics | International Edition: Adding and Subtracting Fractions
- Singapore Mathematics | International Edition: Factors and Multiples
- Primary Mathematics: Fractions of a Quantity, Equivalence and Operations
- Fractions, Decimals and Percentages | Mathematics Knowledge Object
- Fractions and Ratio to Functions | Mathematics Dependency Corridor
- MOE Primary Mathematics Syllabus
Equivalent Fractions in Singapore Mathematics
Same amount, different names.
Multiply both terms, or divide both terms.
Never add to both.
Simplify until no common factor is left.
Taught this way, equivalent fractions are not a trick for exams.
They are the reason fractions can be compared, added and turned into ratios.
That one idea supports years of later Mathematics.
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.
Bukit Timah Tutor
8 Fourth Avenue, Singapore 268674
Near Sixth Avenue MRT
Three-student Mathematics tutorials
By appointment
Properly taught kids shine a bright light into the future.
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.
← Previous: Singapore Mathematics | International Edition: Introducing Fractions
Next: Singapore Mathematics | International Edition: Adding and Subtracting Fractions →
All 100 topics in the International Edition