PSLE Mathematics Learning Guide · Guide 18
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Fractions become difficult when the learner treats numerators and denominators as independent whole numbers. They are not. A fraction is one quantity built from a numerator–denominator relationship.
Adding 1/3 and 1/4 does not give 2/7 because thirds and quarters are different-sized parts. Multiplying 2/3 by 3/5 does not require common denominators because multiplication asks for a fraction of another fraction. Mixed numbers also need careful interpretation before they enter an operation.
This guide uses one working habit: identify the whole, make part sizes compatible for addition or subtraction, multiply numerators and denominators only when multiplication is the actual relationship, convert mixed numbers when needed, and simplify without changing the quantity.
The MOE Primary Mathematics syllabus updated October 2025 provides the curriculum context, while the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples here are original eduKate teaching material.
Fractions must belong to a common whole before they can be combined meaningfully
One half of a small pizza and one half of a large pizza are both 1/2, but they are not necessarily the same physical amount. Fraction notation gives a relationship to a whole.
Within one fixed whole, equivalent fractions name the same amount:
1/2 = 2/4 = 3/6 = 50/100.
Equivalent forms are useful because they let differently named parts be rewritten with the same part size.
Add like fractions by combining equal-sized parts
3/8 + 2/8 = 5/8.
The denominator remains 8 because the pieces are still eighths. Only the number of eighths changes.
The same idea explains subtraction:
7/10 − 3/10 = 4/10 = 2/5.
Unlike denominators need a common part size
Calculate 1/3 + 1/4.
A common denominator is 12:
1/3 = 4/12 and 1/4 = 3/12.
So 1/3 + 1/4 = 7/12.
The common denominator is not chosen because “fractions must always have the same denominator”. It is chosen because addition requires the parts being counted to have the same size.
Subtraction uses the same compatibility rule
5/6 − 1/4.
Common denominator 12:
5/6 = 10/12 and 1/4 = 3/12.
Difference = 7/12.
Estimate as a sense check: 5/6 is a little less than 1, and 1/4 is 0.25, so an answer a little above 1/2 is plausible. 7/12 ≈ 0.583 fits.
Improper fractions and mixed numbers are different forms of the same quantity
7/4 = 1 3/4.
The improper fraction is often easier for multiplication because it keeps the quantity in one fraction. Mixed-number form can be easier to interpret in a final answer.
Convert 2 1/3 to an improper fraction:
2 wholes = 6/3, so 2 1/3 = 7/3.
Mixed-number addition can be done in more than one valid way
Calculate 2 1/4 + 1 2/3.
Method 1: add wholes and fractions.
2 + 1 = 3.
1/4 + 2/3 = 3/12 + 8/12 = 11/12.
Answer = 3 11/12.
Method 2: convert both to improper fractions:
9/4 + 5/3 = 27/12 + 20/12 = 47/12 = 3 11/12.
Mixed-number subtraction may require regrouping
Calculate 4 1/5 − 2 3/5.
Because 1/5 is smaller than 3/5, regroup one whole:
4 1/5 = 3 6/5.
Then:
3 6/5 − 2 3/5 = 1 3/5.
Improper-fraction method:
21/5 − 13/5 = 8/5 = 1 3/5.
Multiplying fractions asks for a fraction of a fraction
2/3 × 3/5 means two thirds of three fifths, or three fifths of two thirds.
2/3 × 3/5 = 6/15 = 2/5.
Unlike addition, multiplication does not require a common denominator because no same-sized parts are being directly combined.
Simplify before or after multiplication
4/9 × 3/8.
You can multiply directly:
12/72 = 1/6.
Or simplify cross-factors first:
4 and 8 reduce to 1 and 2; 3 and 9 reduce to 1 and 3.
Result = 1/(3×2) = 1/6.
Cross-cancellation is valid because factors in a product are being reduced; it is not valid across addition.
A whole number can be written as a fraction over 1
3 × 2/5 = 3/1 × 2/5 = 6/5 = 1 1/5.
In a word problem, “3 groups of 2/5 kg” is exactly this multiplication.
Use multiplication to find a fraction of a quantity
Find 3/8 of 64.
3/8 × 64 = 3 × 8 = 24, because 64 ÷ 8 = 8.
A learner can divide by the denominator first and multiply by the numerator, or multiply by the fraction directly. Both express the same relationship.
Main worked workshop: sixteen original fraction tasks
1.
3/7 + 2/7.
Answer: 5/7.
2.
9/10 − 4/10.
Answer: 1/2.
3.
1/2 + 1/3.
Answer: 5/6.
4.
7/8 − 1/6.
Answer: 21/24 − 4/24 = 17/24.
5.
2 1/5 + 3 2/5.
Answer: 5 3/5.
6.
5 1/4 − 2 3/4.
Answer: 2 1/2.
7.
3/4 × 2/5.
Answer: 3/10.
8.
5/6 × 3/10.
Answer: 1/4.
9.
4 × 3/7.
Answer: 12/7 = 1 5/7.
10.
2/3 of 45.
Answer: 30.
11.
5/8 of 72.
Answer: 45.
12.
1/3 + 2/5 + 1/15.
Answer: 5/15 + 6/15 + 1/15 = 12/15 = 4/5.
13.
3 1/2 × 2/7.
Reasoning: 7/2 × 2/7 = 1.
14.
A tank is 3/5 full. Half of the water is used. What fraction of full capacity remains?
Answer: Half of 3/5 remains = 3/10 of full capacity.
15.
A learner writes 2/3 + 1/4 = 3/7.
Repair: Rewrite using twelfths: 8/12 + 3/12 = 11/12.
16.
A learner writes 2/3 × 3/4 = 5/7.
Repair: Multiplication multiplies numerators and denominators: 6/12 = 1/2.
The reference whole still matters in word problems
Suppose a pupil spends 1/3 of the original amount of money, then 1/4 of what remains. The fractions do not share the same reference whole. Guide 1 covers this in detail: Find the Reference Whole Before You Use a Fraction or Percentage.
Fraction arithmetic can be flawless while the wrong quantity is being operated on. Always connect the calculation back to the noun and time state in the problem.
Use size to reject impossible products
If two positive proper fractions are multiplied, the product must be smaller than either factor.
Example: 3/4 × 2/3 = 1/2. A result such as 5/4 would be impossible.
If a fraction greater than 1 is multiplied by another quantity, the product can grow. The direction depends on the size of the multiplier.
Common fraction-operation errors
Error 1: Add numerators and denominators.
Error 2: Use a common denominator for multiplication even when unnecessary.
Error 3: Cross-cancel across addition.
Error 4: Convert a mixed number incorrectly.
Error 5: Use the correct arithmetic on the wrong reference whole.
Error 6: Leave an answer unsimplified when the task expects simplest form.
Independent transfer check
- 2/5 + 1/10
- 7/9 − 1/6
- 1 3/4 + 2 2/3
- 4 1/6 − 1 5/6
- 3/5 × 10/21
- 4/7 of 63
- Explain why a common denominator is needed for 1/3 + 1/4 but not for 1/3 × 1/4.
- Explain why 2/3 × 3/5 should be less than 2/3.
Independent-check answers
1. 1/2.
2. 14/18 − 3/18 = 11/18.
3. 4 5/12.
4. 2 1/3.
5. 2/7.
6. 36.
7. Addition combines equal-sized parts, so the part size must match; multiplication forms a fraction of another fraction and does not require matching denominators.
8. Multiplying by 3/5, a number below 1, reduces the positive quantity.
Parent and tutor guide
Use fraction strips or bar diagrams when denominator meaning is unstable. Ask what one denominator unit means before teaching the algorithm.
If mixed-number subtraction fails, compare the mixed and improper-fraction methods. If multiplication errors persist, ask the learner to say “fraction of fraction” aloud and predict whether the result should grow or shrink.
Separate arithmetic failure from reference-whole failure. They need different repairs.
The learner’s final card
What whole does the fraction belong to? For addition or subtraction, are the part sizes the same? For multiplication, what fraction of what is being taken? Is the final size sensible? Can I simplify without changing the value?
Continue through the PSLE Mathematics Learning Guide
Return to Guide 17: Whole-Number Place Value. Continue with Guide 19: Decimal Operations and Guide 20: Rate and the Unitary Method.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and suggested solutions are original eduKate teaching material. Equivalent correct fraction methods may exist.