PSLE Mathematics Learning Guide · Guide 41
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Equivalent fractions are different names for the same quantity. One half, two quarters and four eighths do not describe three different sizes when they refer to the same whole. They describe the same point on the number line using different-sized parts.
This guide develops one habit: change numerator and denominator by the same non-zero factor so that the value stays fixed; simplify only by removing a common factor from both parts; and check that the new fraction still represents the same quantity.
Guide 18 covers fraction addition, subtraction and multiplication. Guide 27 covers comparing and ordering fractions. This page owns the more foundational job of recognising, generating and simplifying equivalent forms before those later operations are used.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context. All examples below are original eduKate teaching material.
Equivalent fractions occupy the same position
Imagine one strip divided into 2 equal parts and one half shaded. Now divide each half again into 2 equal parts. Two of the four smaller parts are shaded.
So 1/2 = 2/4.
Divide every quarter into 2 again and four of eight parts are shaded: 1/2 = 2/4 = 4/8.
The number of pieces changed. The shaded amount did not.
Generate an equivalent fraction by multiplying both parts
To express 3/5 with denominator 20, ask what multiplies 5 to 20. The factor is 4.
Multiply the numerator by the same factor:
3/5 = (3×4)/(5×4) = 12/20.
Multiplying only the denominator would change the size of each piece without changing how many pieces are taken. That changes the value.
Simplify by dividing numerator and denominator by the same common factor
18/24 has numerator and denominator both divisible by 6.
18÷6 = 3 and 24÷6 = 4.
So 18/24 = 3/4.
The fraction is in simplest form when numerator and denominator have no common factor greater than 1.
Simplifying in stages is valid
24/36 can be simplified by dividing both parts by 2:
24/36 = 12/18.
Then divide both by 6:
12/18 = 2/3.
You could also divide 24 and 36 by their greatest common factor 12 in one step. Both routes preserve value.
Simplifying is not subtraction
A learner writes 8/12 = 4/8 by subtracting 4 from numerator and denominator. This is wrong.
8/12 = 2/3 because both numerator and denominator can be divided by 4.
Subtracting the same number from numerator and denominator does not generally preserve a fraction’s value.
The factor must match
For 5/7, multiplying the numerator by 3 and denominator by 2 gives 15/14. That is not equivalent.
Equivalent scaling uses the same multiplication or division factor on both numerator and denominator.
Find the missing number from the scaling relationship
3/4 = ?/20.
4 × 5 = 20, so 3 × 5 = 15.
Answer: 15.
For ?/18 = 2/3, 3 × 6 = 18, so 2 × 6 = 12. Answer: 12.
Cross-products can verify equivalence
Are 6/8 and 9/12 equivalent?
6×12 = 72 and 8×9 = 72.
The cross-products are equal, so the fractions are equivalent.
This works because both fractions can be rewritten over a common product denominator. It is a check, not a replacement for understanding what equivalence means.
Improper fractions simplify by the same rule
21/15 has common factor 3.
21/15 = 7/5 = 1 2/5.
Simplifying and changing between improper and mixed-number form are separate steps. The value must stay constant through both.
Mixed-number fractional parts may also simplify
2 6/8 = 2 3/4.
The whole-number part stays 2. Only the fractional part is rewritten in an equivalent simplest form.
Equivalent fractions share one point on a number line
0 — 1/4 — 2/4 — 3/4 — 1
The point 2/4 is also 1/2.
On an eighths number line, 4/8 lands at the same point. A number line makes equivalence visible as a location, not merely an algorithm.
Equivalent fractions build common denominators
To add 1/3 + 1/4, thirds and quarters need a common part size.
1/3 = 4/12 and 1/4 = 3/12.
The equivalent fractions make addition possible because both are now counted in twelfths.
Use Guide 18 for the full operation.
Equivalent forms also support comparison
Compare 5/6 and 7/9.
5/6 = 15/18.
7/9 = 14/18.
Therefore 5/6 > 7/9.
Use Guide 27 for a wider comparison toolkit.
Main worked workshop: sixteen original tasks
1.
Write an equivalent fraction to 1/3 with denominator 12.
Answer: 4/12.
2.
Write an equivalent fraction to 5/8 with denominator 40.
Answer: 25/40.
3.
Complete 7/9 = ?/36.
Answer: 28.
4.
Complete ?/25 = 3/5.
Answer: 15.
5.
Simplify 12/18.
Answer: 2/3.
6.
Simplify 28/42.
Answer: 2/3.
7.
Simplify 45/60.
Answer: 3/4.
8.
Simplify 36/54.
Answer: 2/3.
9.
Are 4/6 and 10/15 equivalent?
Answer: yes; both simplify to 2/3.
10.
Are 3/8 and 9/20 equivalent?
Answer: no.
11.
Write 18/12 in simplest improper form and mixed form.
Answer: 3/2 = 1 1/2.
12.
Simplify 3 8/12.
Answer: 3 2/3.
13.
A learner writes 6/10 = 3/8 by subtracting 3 from numerator and 2 from denominator.
Repair: divide both by 2: 6/10 = 3/5.
14.
A learner changes 4/7 to 8/21.
Repair: numerator multiplied by 2 but denominator by 3, so value changed. Correct examples include 8/14 or 12/21.
15.
Find a fraction equivalent to 11/15 with numerator 44.
Answer: 44/60.
16.
Find the simplest form of 84/126.
Answer: 2/3.
How to know simplification is finished
Check whether numerator and denominator still share a factor greater than 1.
For 12/20, dividing by 2 gives 6/10. But both still share factor 2. Divide again to get 3/5.
3 and 5 share no factor above 1, so 3/5 is simplest.
Common equivalence errors
Error 1: multiply numerator and denominator by different factors.
Error 2: simplify by subtracting.
Error 3: stop simplifying too early.
Error 4: change only the denominator to reach a requested denominator.
Error 5: treat two fractions with different appearances as automatically different values.
Independent transfer check
- Complete 2/7 = ?/35.
- Complete ?/24 = 5/6.
- Simplify 16/28.
- Simplify 42/63.
- Are 15/20 and 6/8 equivalent?
- Write 24/18 in simplest improper form and mixed form.
- Explain why multiplying numerator and denominator by 5 preserves a fraction’s value.
- Explain why subtracting the same number from numerator and denominator does not generally preserve value.
Independent-check answers
1. 10.
2. 20.
3. 4/7.
4. 2/3.
5. Yes; both simplify to 3/4.
6. 4/3 = 1 1/3.
7. Both the number of parts taken and the total number of equal parts scale by the same factor, leaving the ratio unchanged.
8. Subtraction changes numerator and denominator by different relative proportions, so the ratio usually changes.
Parent and tutor guide
Use fraction strips or folded paper first when the learner thinks equivalent fractions should look different in size. Then move to multiplicative scaling.
Ask “What factor changed the denominator?” before allowing a missing-numerator calculation. For simplification, ask “What common factor can be removed from both?”
After success, reverse the direction: give an equivalent fraction and ask for the original, or ask the learner to prove two fractions are equal in two different ways.
The learner’s final card
Did numerator and denominator change by the same factor? Does the value stay at the same number-line point? Can both parts still be divided by a common factor? Have I reached simplest form without changing the quantity?
Continue through Batch 11
Continue with Guide 42: Compare and Order Decimals, Guide 43: Length Problems in Mixed Units, and Guide 44: Mass Problems in Kilograms and Grams.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All examples and solutions are original eduKate teaching material. This guide treats fraction equivalence and simplest form as cumulative Primary Mathematics knowledge relevant to PSLE preparation.