Did you know that adding the denominators changes the size of the parts? In 2/7 + 3/7, both fractions already count sevenths, so the total is 5/7, not 5/14. The numerators count parts; the shared denominator names the size of each part.
For Bukit Timah parents checking Primary Mathematics tuition, draw two identical bars divided into sevenths. Shade two parts, then three more. Ask the child to name the unit before calculating: “How many sevenths altogether?” If the denominators differ, first rename both quantities using equal-sized parts.
Keep the child’s first answer and explanation. Then use one same-denominator example, one unlike-denominator example and one simple estimate. A useful tuition check is whether the child can explain why a common denominator is needed and reject an impossible answer, not merely repeat a rule.
eduKateSG · Bukit Timah · Practical learning guide
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SECTION 1 OF 5
Separate the number of parts from the size of each part
A fraction such as 3/7 means three parts when one whole has been divided into seven equal parts. The numerator tells how many selected parts there are; the denominator identifies the unit fraction.
Adding 2/7 and 3/7 combines two sevenths and three sevenths. Because the parts are the same size, the counts can be combined directly.
Ask the child to say the unit aloud. “Two sevenths plus three sevenths equals five sevenths” makes the structure audible.
SECTION 2 OF 5
Use a picture to expose the denominator error
Draw one whole divided into seven equal sections. Shade two sections in one colour and three in another. There are five shaded sevenths, while the whole still contains seven sevenths.
If the child writes 5/14, ask what a fourteenth would look like. Fourteenths are smaller pieces; no step in the picture divided every seventh again.
This is a correction by meaning, not by warning. The learner sees why the tempting operation changes the unit.
SECTION 3 OF 5
Rename unlike fractions before adding
In 1/2 + 1/3, halves and thirds are different-sized units. They cannot be counted together until both fractions are expressed with a common denominator.
Using sixths gives 1/2 = 3/6 and 1/3 = 2/6, so the sum is 5/6. Multiplying a numerator and denominator by the same non-zero number preserves the fraction’s value while changing its name.
Have the child show the equivalence with a bar model or number line before relying only on a procedure.
SECTION 4 OF 5
Estimate before accepting the answer
For positive fractions, 1/2 + 1/3 must be greater than 1/2 and less than 1. The incorrect answer 2/5 is smaller than 1/2, so estimation catches it quickly.
Use benchmarks such as 0, 1/2 and 1. The goal is not a perfect decimal estimate; it is a sensible range that tests the final fraction.
A tutor can record whether the error comes from fraction meaning, equivalent fractions, multiplication facts or rushed notation. Those need different repairs.
SECTION 5 OF 5
Check transfer with a fresh representation
After a worked example, give a new task with different denominators and no model already drawn. Ask the child to choose a representation, find a common unit and explain each renaming.
Include a same-denominator question nearby. The learner must decide when a common-denominator step is already complete and when it is still needed.
Progress is visible when the child preserves the unit, estimates the result and can explain the method on a new example without a cue.
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Bring one useful example to a consultation
Bring the child’s original attempt, the exact task and any help already used. Ask which idea or decision needs teaching, how a fresh independent attempt will be checked, and whether a suitable 3-pax placement and subject arrangement are available.
Continue with the closest question
- Why a bigger denominator does not automatically mean a bigger fraction
- Primary 3 fractions and division foundations
- Why a child chooses the wrong operation in Maths word problems
Match support to the actual course
The examples are original teaching illustrations. The routines are practical educational guidance, not measured outcomes, grade promises or universal marking rules. Match every task to what has been taught and to the school’s instructions.
Source check: 11 October 2026. For examination preparation, confirm the actual subject, level, candidate type, examination year and syllabus before choosing materials.