PRIMARY 4 MATHEMATICS LEARNING GUIDE · BATCH 4 · GUIDE 15
Fractions can be added or subtracted only when the parts being counted are the same size. That single idea explains why common denominators matter, why equivalent fractions are useful, and why adding denominators directly usually fails.
This guide develops fraction addition and subtraction, common denominators, equivalent fractions, mixed numbers, word problems, estimation and checking. It is designed to make the unit fraction visible before the algorithm begins.
Series route: return to the Primary 4 Mathematics Learning Hub. For the broader fraction foundation, see Fractions, Decimals and Number Relationships.
1. Same Denominator Means Same-Sized Parts
3/8+2/8=5/8 because both fractions count eighths.
The denominator remains 8 because the size of the unit fraction has not changed.
Adding the denominators would change the part size and therefore change the meaning.
2. Why 1/3+1/4 Is Not 2/7
Thirds and quarters are different-sized parts. Before counting them together, express them using a common part size.
1/3=4/12.
1/4=3/12.
Therefore 1/3+1/4=7/12.
Make the units equal before adding the counts.
3. Equivalent Fractions Preserve Value
2/3=4/6=8/12.
The representation changes, but the quantity does not.
This allows fractions with different denominators to be rewritten using a shared denominator without changing their values.
4. Common Denominators and Common Multiples
To add 1/4 and 1/6, choose a denominator that is a multiple of both 4 and 6.
12 works:
1/4=3/12 and 1/6=2/12.
Total=5/12.
Factors and multiples therefore connect directly to fraction arithmetic.
5. A Common Denominator Need Not Be the Smallest
For 1/4+1/6, denominator 24 also works:
1/4=6/24, 1/6=4/24, total=10/24=5/12.
A smaller common denominator often reduces work, but any valid common denominator can produce the correct result when simplified properly.
6. Adding Two Fractions
Calculate 2/5+1/3.
Common denominator 15:
2/5=6/15.
1/3=5/15.
Total=11/15.
7. Subtracting Two Fractions
Calculate 5/6−1/4.
Common denominator 12:
5/6=10/12.
1/4=3/12.
Difference=7/12.
8. Estimate Fraction Size First
5/6 is close to 1. One quarter is 0.25. So 5/6−1/4 should be a little above one half.
7/12 is about 0.58, which is plausible.
Magnitude checks help catch denominator and conversion errors.
9. Improper Answers Can Be Valid
3/4+2/3 uses denominator 12:
9/12+8/12=17/12.
17/12=1 5/12.
A fraction sum can exceed one. Do not force the numerator to stay smaller than the denominator.
10. Mixed-Number Addition
1 2/3+2 1/6.
2/3=4/6.
Fraction parts: 4/6+1/6=5/6.
Whole parts: 1+2=3.
Total=3 5/6.
11. Mixed-Number Addition With Regrouping
2 3/4+1 2/3.
3/4=9/12 and 2/3=8/12.
Fraction sum=17/12=1 5/12.
Whole sum=3, plus the regrouped whole gives 4 5/12.
The fraction part can create another whole.
12. Mixed-Number Subtraction Without Regrouping
4 5/6−2 1/3.
1/3=2/6.
5/6−2/6=3/6=1/2.
Whole-number difference=2.
Answer=2 1/2.
13. Mixed-Number Subtraction With Regrouping
4 1/3−1 5/6.
1/3=2/6, so 4 2/6−1 5/6 cannot subtract the fraction parts directly.
Regroup one whole: 3 8/6−1 5/6.
Answer=2 3/6=2 1/2.
One whole has been exchanged for six sixths.
14. Fraction Word Problem With Same Whole
A student reads 2/5 of a book on Monday and 1/4 of the same book on Tuesday. What fraction is read altogether?
2/5=8/20.
1/4=5/20.
Total=13/20.
Both fractions refer to the same original book, so addition is valid after equalising part sizes.
15. Finding the Fraction Remaining
If 13/20 is read, the amount remaining is:
20/20−13/20=7/20.
“Remaining” often means subtracting a known part from one whole.
16. Fractions With Different Reference Wholes Cannot Be Added Blindly
If a child uses 1/3 of the original amount and then 1/4 of the remaining amount, the two fractions do not refer to the same whole.
You cannot simply add 1/3+1/4 and claim 7/12 of the original was used.
First calculate the remaining amount, then apply the second fraction to that new reference whole.
17. A Changing-Whole Example
A tank contains 72 L. First 1/3 is used. Then 1/4 of the remaining water is used.
First use=24 L. Remaining=48 L.
Second use=1/4 of48=12 L.
Total used=36 L; final remaining=36 L.
The second fraction acts on 48, not 72.
18. Fraction Difference Problems
3/4 of a number is 18 more than 1/2 of the same number.
1/2=2/4.
The difference is 1/4 of the number.
1/4=18, so the whole=72.
Common denominators expose the difference in equal units.
19. Fraction Total Problems
A receives 2/5 of a total and B receives the rest. If B receives 36, find the total.
B receives 3/5.
3 units=36, one unit=12.
Whole=60.
Fraction arithmetic and bar-model unit reasoning meet naturally here.
20. Simplify When It Helps
6/8 and 3/4 have the same value.
Simplifying can make a final answer easier to read and compare, but simplification should preserve value exactly.
Use common factors to divide numerator and denominator by the same non-zero whole number.
21. Common Errors
| Error | Weak link | Repair question |
|---|---|---|
| 1/3+1/4=2/7 | Part sizes differ | What common-sized part can represent both? |
| Denominator changed but numerator not | Equivalent fraction not preserved | What multiplication was applied to numerator and denominator? |
| Improper sum rejected | Fraction assumed always below one | Can several fractional parts make more than one whole? |
| Changing reference wholes added directly | Whole not tracked | Fraction of what? |
| Mixed subtraction fails | Regrouping not understood | Can one whole be exchanged for denominator-sized parts? |
22. Practice Laboratory
- Calculate 3/8+2/8.
- Calculate 1/3+1/4.
- Calculate 2/5+1/3.
- Calculate 5/6−1/4.
- Calculate 3/4+2/3.
- Calculate 1 2/3+2 1/6.
- Calculate 2 3/4+1 2/3.
- Calculate 4 5/6−2 1/3.
- Calculate 4 1/3−1 5/6.
- A child reads 3/8 of a book then 1/4 of the same book. What fraction is read?
- What fraction remains?
- A tank has 60 L. 1/3 is used, then 1/4 of the remaining amount is used. How much remains?
- 3/4 of a number is 15 more than 1/2. Find the number.
- A gets 3/8 of a total; B gets the rest and receives 35. Find total.
- Simplify 12/18.
23. Explained Answers
1. 5/8.
2. 7/12.
3. 11/15.
4. 7/12.
5. 1 5/12.
6. 3 5/6.
7. 4 5/12.
8. 2 1/2.
9. 2 1/2.
10. 3/8+2/8=5/8.
11. 3/8.
12. First use20, remain40; second use10; final=30 L.
13. Difference is1/4; whole=60.
14. B=5/8; five units35, one7, total=56.
15. 2/3.
24. Teaching Routine: Name the Unit Fraction
Before adding or subtracting, ask the learner to say what one part represents: thirds, fourths, sixths, twelfths. If the part sizes differ, create a common denominator. If a mixed-number subtraction is blocked, regroup one whole into denominator-sized parts.
The reusable route is: name whole → name part size → equalise units → calculate → simplify → estimate/check.
25. Why This Matters Later
Ratio, percentage and algebra all require students to transform representations while preserving value. Fraction addition trains exactly that discipline: change form without changing meaning.
Continue to Nets, 2D Representations and 3D Spatial Reasoning →
Sources and Boundaries
Curriculum scope is aligned with the MOE Primary Mathematics Syllabus, updated October 2025. All examples and teaching routines are independently written by eduKate Publishing.
Editorial control: Wintour House V1.0 · CivDJ · eduKate Publishing.
