Mathematics Tutor Singapore | Primary 4 Maths fractions often become difficult when the fractions have different denominators. A pupil may add one-third and one-quarter and write two-sevenths, following the tempting but incorrect rule of adding every visible number. The first useful question is simpler: are we counting the same-sized parts?
Did you know that one-third and one-quarter of the same whole can be redrawn as four-twelfths and three-twelfths? Once the parts have the same size, adding them is just counting seven twelfths. A visual bar or folded paper makes that decision understandable instead of mysterious.
This Singapore Primary 4 Mathematics learning guide teaches addition and subtraction of unlike fractions, common denominators, mixed numbers, regrouping, story problems and independent checks. It respects the October 2025 MOE Primary Mathematics scope, which limits the given denominators and number of distinct denominators in this strand. The goal is confidence with equivalent units, not unnecessary acceleration.
Explore the Primary 4 unlike-fractions lessons
- Fractions name equal parts of one whole
- Adding fractions with the same denominator
- Why unlike denominators need a common unit
- Worked example: one-third plus one-quarter
- How to choose a suitable common denominator
- Worked subtraction: five-sixths minus one-quarter
- Mixed numbers: separate whole numbers and fractions
- Subtract mixed numbers by regrouping a whole
- Check if a sum is above or below one
- Use a bar model when the story changes its whole
- Worked ribbon problem: add two unlike fractions
- Worked remaining quantity after two uses
- Nine mistakes a P4 tutor should diagnose
- Sixteen original P4 fraction questions and answers
- A realistic ten-session learning sequence
- Questions about Primary 4 fraction tuition
- MOE syllabus and Mathematics learning route
Fractions name equal parts of one whole
A denominator describes how many equal parts form a whole. A numerator describes how many of those parts are selected. For 3/4, a whole has been partitioned into four equal parts and three are selected. This only works as a fraction model when the parts are equal relative to the same whole.
The word same is important. Half a small pizza and half a much larger pizza are both fractions of one-half, but the actual quantities of food differ. Before adding fractions from a story, a student must identify whether the fractions refer to one common reference whole.
If a number-line question places 3/4 between zero and one, each quarter interval is the same length. That visual meaning also underpins fraction addition: first agree on the size of the counted unit, then count how many units there are.
- Name the whole to which each fraction refers.
- Identify the size of each unit part using its denominator.
- Use an equivalent fraction to change the unit without changing the quantity.
- Add or subtract only after the denominators match.
- Simplify the result when suitable and decide whether it exceeds one.
- Check the answer with a visual size estimate or inverse operation.
Adding fractions with the same denominator
If two fractions describe pieces of equal size, addition is straightforward. Two-fifths plus one-fifth is three-fifths, because we have two of the same fifth-size pieces and add one more. The denominator stays five; it does not become ten.
| Question | Count equal pieces | Answer |
|---|---|---|
| 2/5 + 1/5 | 2 fifths + 1 fifth | 3/5 |
| 3/8 + 2/8 | 3 eighths + 2 eighths | 5/8 |
| 7/12 − 2/12 | 7 twelfths − 2 twelfths | 5/12 |
| 9/10 − 3/10 | 9 tenths − 3 tenths | 6/10 = 3/5 |
A learner who changes 2/5+1/5 into 3/10 has confused adding fractions with multiplying fractions. I ask them to draw five equal blocks and shade three after combining, then compare the drawing with three-tenths. The mismatch is visible.
Why unlike denominators need a common unit
The pieces in 1/3 and 1/4 are not the same size: a third is bigger than a quarter of the same whole. Counting “one plus one” does not tell us how large the resulting piece is. We first subdivide the whole into parts that can represent both fractions exactly.
For thirds and quarters, twelve equal parts are convenient. One-third equals four-twelfths because each third can be divided into four equal smaller parts. One-quarter equals three-twelfths because each quarter can be divided into three smaller parts. The value of each fraction is conserved.
An equivalent fraction such as 1/3=4/12 does not mean we added four parts to the original amount; it means we described the same area using a smaller unit. This equivalence is the mathematical foundation of the common-denominator procedure.
Worked example: one-third plus one-quarter
Compute 1/3+1/4. Use denominator twelve. The first fraction becomes 4/12 and the second 3/12. Add their numerators: 4/12+3/12=7/12.
| Stage | Working | Reason |
|---|---|---|
| Original | 1/3 + 1/4 | Different unit fractions |
| Rewrite thirds | 1/3 = 4/12 | Equivalent fraction |
| Rewrite quarters | 1/4 = 3/12 | Same unit size |
| Add | 4/12 + 3/12 | 7/12 |
| Check | 7/12≈0.583 | Between 1/2 and 1 |
A useful estimate is that 1/3 is about 0.333 and 1/4 is 0.25, so the sum should be near 0.583, not 2/7≈0.286. Even without decimals, we know the sum exceeds one-half because one-third plus one-quarter is slightly greater than one-quarter plus one-quarter.
Choose a suitable common denominator
A common denominator is a positive number divisible by both original denominators. For 1/3 and 1/4, twelve works. For 1/4 and 1/6, twelve also works. For 1/6 and 3/8, twenty-four is a useful common denominator.
| Original denominators | Suitable common denominator | Reason |
|---|---|---|
| 3 and 4 | 12 | Both divide 12 |
| 4 and 6 | 12 | Both divide 12 |
| 6 and 8 | 24 | Both divide 24 |
| 5 and 10 | 10 | Both divide 10 |
| 8 and 12 | 24 | Both divide 24 |
Using the product of the denominators always gives a common denominator for positive whole denominators, but it may produce larger numbers than necessary. For 1/4+1/6, using denominator twenty-four is valid, giving 6/24+4/24=10/24, then 5/12. Using twelve gives 3/12+2/12=5/12 immediately.
The efficient choice is helpful, but understanding equivalence comes first. A pupil should be able to explain why multiplying numerator and denominator by the same nonzero integer leaves the fraction unchanged.
Worked subtraction: five-sixths minus one-quarter
Calculate 5/6−1/4. The least common denominator is twelve. Five-sixths is 10/12 and one-quarter is 3/12. Subtract the numerators to get 7/12.
Check: 1/4+7/12 = 3/12+7/12 =10/12=5/6, reconstructing the original amount. The result must be less than 5/6 and greater than zero, which it is.
| Move | Working | Value |
|---|---|---|
| Convert first fraction | 5/6 ×2/2 | 10/12 |
| Convert second fraction | 1/4 ×3/3 | 3/12 |
| Subtract | 10/12−3/12 | 7/12 |
| Check by addition | 7/12+3/12 | 10/12=5/6 |
Mixed numbers: whole parts and fractional parts
A mixed number combines a whole number with a proper fraction. For example 2 1/3 represents two wholes plus one-third, and 1 1/4 represents one whole plus one-quarter. We can add their whole parts and fractional parts separately as long as we preserve the correct equivalent units.
Compute 2 1/3+1 1/4. The whole-number parts add to three. The fraction parts 1/3+1/4 equal 7/12. Therefore the sum is 3 7/12.
Alternatively, convert to improper fractions: 2 1/3=7/3=28/12 and 1 1/4=5/4=15/12. Their sum is 43/12, equivalent to 3 7/12. Both methods describe the same quantity.
| Method | Working | Answer |
|---|---|---|
| Whole and fraction parts | (2+1)+(1/3+1/4) | 3 7/12 |
| Improper fractions | 7/3+5/4=28/12+15/12 | 43/12=3 7/12 |
Subtract mixed numbers by regrouping one whole
Now calculate 3 1/4−1 2/3. The fractional part one-quarter is smaller than two-thirds, so subtracting fractional parts directly would give a negative fraction even though the full mixed-number difference is positive.
Regroup one whole from the three. Write 3 1/4 as 2+1+1/4 =2+5/4 =2+15/12. Write 1 2/3 as 1+8/12. Subtract: (2−1)+(15/12−8/12)=1 7/12.
| Representation | Whole part | Fraction part |
|---|---|---|
| 3 1/4 originally | 3 | 1/4 |
| After regrouping one whole | 2 | 5/4=15/12 |
| Subtract 1 2/3 | −1 | −8/12 |
| Answer | 1 | 7/12 |
Check by adding 1 7/12+1 2/3 = 2+(7/12+8/12) =2+15/12 =3 1/4. The recovered starting amount confirms the subtraction.
Another method uses improper fractions throughout: 3 1/4=13/4=39/12, 1 2/3=5/3=20/12, and difference is 19/12=1 7/12. A pupil need not use both during every question, but comparing them is valuable for understanding.
Check whether a sum should exceed one
If we add 5/6 and 3/8, both fractions are positive, with the first greater than one-half and the second just under one-half. Their sum should exceed one. Using common denominator twenty-four gives 20/24+9/24=29/24=1 5/24.
A result smaller than 5/6 would be impossible because we have added a positive fraction. Similarly, a subtraction 5/6−1/4 should be smaller than 5/6. These size checks catch incorrect denominator operations even before exact computation is finished.
| Problem | Expected size | Exact answer |
|---|---|---|
| 1/3+1/4 | Between 1/2 and 1 | 7/12 |
| 5/6−1/4 | Positive, below 5/6 | 7/12 |
| 5/6+3/8 | Greater than 1 | 1 5/24 |
| 3 1/4−1 2/3 | Between 1 and 2 | 1 7/12 |
A bar model reveals the reference whole
Suppose two children use ribbons measured from the same original one-metre length. One uses one-third of a metre and another one-quarter of a metre. Since both fractions describe the same one-metre unit, we can add them as 7/12 of a metre.
But if a story says one child uses one-third of a ribbon and the second uses one-quarter of what remains, the reference has changed. After using one-third, two-thirds remain; one-quarter of those two-thirds is one-sixth of the original. The total used is one-third plus one-sixth, equal to one-half. This is a distinct two-stage interpretation.
I keep this distinction explicit because advanced PSLE problem sums often test the changing whole. First teach straightforward addition of fractions of the same unit; only then introduce fractions of a changing remainder as enrichment.
Worked ribbon problem: add two unlike fractions
A craft club uses 2/5 m of blue ribbon and 3/10 m of gold ribbon. Find the total ribbon length, assuming both lengths are measured in metres. Convert 2/5 to 4/10; then 4/10+3/10=7/10 m.
If the club began with one metre of ribbon in a simplified story, the amount remaining would be 1−7/10=3/10 m. But if these are two physically separate colours cut from different reels, asking for “the amount left from one metre” requires extra information. The story, not merely the symbols, determines which whole is relevant.
Worked remaining quantity after two uses
A one-metre tape is cut by 1/3 m and then by 1/4 m. Since both lengths are absolute fractions of a metre, combined cut length is 7/12 m and remaining length is 1−7/12=5/12 m.
Compare this with cutting one-third of the whole tape first, then one-quarter of the remaining length. The second cut is 1/4×2/3=1/6 of the original, so the remainder is 1−1/3−1/6=1/2 of the original metre. The answers differ because the wording differs.
The multiplication of two fractions in the second variation is an advanced bridge to the following Primary Five learning. It is not the starting procedure for the P4 addition/subtraction syllabus point.
Nine mistakes a P4 tutor should diagnose
| Wrong attempt | Underlying issue | Next diagnostic |
|---|---|---|
| 1/3+1/4=2/7 | Denominators incorrectly added | Draw same whole in twelfths |
| 2/5+1/5=3/10 | Like units not understood | Count fifth-size pieces |
| 5/6−1/4=4/2 | Numerators and denominators treated separately | Convert to twelfths |
| Changes denominator but not numerator | Equivalence not preserved | Multiply top and bottom by same factor |
| 3 1/4−1 2/3=2 −5/12 | Mixed-number regrouping incomplete | Exchange one whole for twelfths |
| Cancels across fraction addition | Factors confused with sum terms | Check if expression is one product |
| Adds a fraction of remainder to one of original directly | Reference whole changed | Name each stage’s whole |
| Gives 29/24 as 1 5/12 | Improper conversion wrong | Divide 29 by 24 |
| Reports a subtraction bigger than starting fraction | Size check absent | Estimate before calculating |
A pupil who makes accurate equivalent fractions but misreads “of the remainder” needs word-problem modelling. Another who knows the reference whole but cannot find a common denominator needs unit-equivalence practice. Good tutoring distinguishes the causes.
Sixteen original Primary Four fraction questions
1. Same denominator addition
2/7+3/7=5/7.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
2. Same denominator subtraction
9/10−3/10=6/10=3/5.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
3. Simple unlike addition
1/3+1/4=7/12.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
4. Another unlike addition
1/4+1/6=3/12+2/12=5/12.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
5. Unlike subtraction
5/6−1/4=10/12−3/12=7/12.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
6. Fraction addition to one
2/3+1/3=1.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
7. An improper answer
5/6+3/8=29/24=1 5/24.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
8. Unlike subtraction to a positive fraction
7/8−1/3=21/24−8/24=13/24.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
9. Add mixed numbers
2 1/3+1 1/4=3 7/12.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
10. Subtract mixed numbers with regrouping
3 1/4−1 2/3=1 7/12.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
11. Whole-number plus fraction
2+3/5=2 3/5.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
12. Improper to mixed
29/24=1 5/24.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
13. Add ribbon lengths
2/5 m +3/10 m=7/10 m.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
14. Remaining ribbon
One metre minus 1/3 m minus 1/4 m leaves 5/12 m.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
15. Fraction of changing remainder extension
After 1/3 of a whole is used, 1/4 of what remains is 1/6 of the original.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
16. Inverse check
For 5/6−1/4=7/12, adding back 1/4 yields 7/12+3/12=5/6.
Identify whether both fractions use the same whole, find a common unit and check the final size. A revised question after a short gap tests whether the pupil understands rather than copying a sample.
A realistic Primary 4 revision sequence
| Session | Learning focus | Evidence of understanding |
|---|---|---|
| 1 | Read denominator as unit size | Labels equal parts |
| 2 | Equivalent fractions from a bar | Conserves amount |
| 3 | Add like denominators | Keeps denominator fixed |
| 4 | Find common denominators | Chooses convenient multiple |
| 5 | Add unlike fractions | Explains conversion |
| 6 | Subtract unlike fractions | Checks by addition |
| 7 | Improper answers and mixed numbers | Regroups beyond one |
| 8 | Borrow one whole in subtraction | Explains regrouping |
| 9 | Read short fraction word problems | Identifies reference whole |
| 10 | Mixed delayed test | Explains without teacher cues |
A meaningful home activity is to fold identical paper strips into thirds, quarters and twelfths and compare their sizes. The learner should explain how many twelfths make one-third or one-quarter. The objective is independent transfer to new numbers, not a race to more advanced worksheets.
Frequently asked questions about P4 fractions
Why can’t I add denominators?
Denominators name unit size. You must first express the fractions in the same-sized unit before adding the counts of those units.
What is a common denominator?
A number divisible by the original denominators so each fraction can be written in equivalent parts of the same size.
Do I always need the least common denominator?
It is often efficient, but any valid common denominator gives an equivalent result when used correctly.
Why can adding proper fractions produce an improper fraction?
Two positive shares can combine to exceed one whole, as 5/6+3/8 does.
How do I subtract when the first mixed number has a smaller fractional part?
Regroup one whole into suitable fractional parts, or use improper fractions.
When should I simplify a fraction?
When an equivalent simpler fraction or a mixed-number answer is appropriate to the question’s instructions.
How are fractions of a remainder different?
The reference whole changes after the first stage; a fraction of the remainder is not automatically a fraction of the original.
Is this part of the Primary 4 MOE curriculum?
Yes, P4 includes adding and subtracting fractions with given denominators not exceeding 12 and at most two distinct denominators, together with mixed-number foundations.
Does mastering fractions guarantee PSLE marks?
No. It is an important foundation, but later performance depends on many topics and conditions.
MOE syllabus and connected Mathematics routes
The MOE Primary Mathematics syllabus updated October 2025 identifies P4 mixed and improper fractions, fractional part of a set and addition/subtraction with the denominators of given fractions no greater than 12 and not more than two different denominators. A common denominator derived while solving may exceed twelve; the syllabus condition concerns the denominators of the given fractions.
Continue through the Mathematics Learning Hub. Review Primary 3 Equivalent Fractions and Primary 4 Fractions on Number Lines. For the next operation, use Primary 5 Multiplying Fractions. For changing reference wholes, see PSLE Reference-Whole Problems.
The original Secondary 1 Mathematics Tutor Clementi small-group teaching reference remains unchanged. For a specific learning gap, arrange an eduKate Singapore consultation with an equivalent-fraction question and one failed mixed-number example so the tutor can find the first misunderstanding.