Which is larger: 5/6 or 7/9? A learner may choose seven ninths because seven is bigger than five, while another may choose five sixths but cannot explain why. For Lorong Chuan families comparing weekday and weekend Primary 4 Mathematics tuition, this is a useful diagnostic because it checks whether fractions are being compared as quantities of the same whole, rather than as two pairs of whole-number digits.
The correct comparison is 5/6 > 7/9. Divide the common-sized whole into eighteen equal pieces: five sixths becomes fifteen eighteenths, while seven ninths becomes fourteen eighteenths. One extra eighteenth makes five sixths larger.
The Singapore Primary 4 syllabus includes equivalent fractions and comparing unlike fractions. A tutor should help the pupil understand the choice of a common unit, verify the result and later reason about a fresh fraction pair. The best weekly timetable supports that explanation rather than simply increasing question volume.
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What to check before teaching · Worked Mathematics example · When weekday or weekend fits · Three-pupil tutorial evidence · An independent transfer check · Questions parents ask · What to arrange next
Check the common whole before choosing a comparison method
Draw two rectangles with exactly the same length and width. Label the first rectangle five sixths and the second seven ninths. Make clear that the rectangles represent the same-sized whole; without that condition, comparing the shaded areas by fractions alone would be misleading.
Partition the first rectangle into six equal strips and shade five. Then partition the second rectangle into nine equal strips and shade seven. The strips have different widths, which is why counting only the selected strips cannot establish which fraction is larger.
Ask the child whether having seven shaded strips must mean a larger shaded area. It does not, because the nine parts in the second rectangle are individually smaller than the six parts in the first. The denominator changes the size of each fractional unit.
Next ask what would make the two drawings directly comparable. We can redraw both using equal-sized fractional pieces, so the same number of parts would make one whole in each rectangle. That motivates finding a common denominator.
The pupil may recall that eighteen is a common multiple of six and nine. Six equal pieces can each be subdivided into three, and nine equal pieces can each be subdivided into two, producing eighteen equal pieces in either rectangle.
The crucial idea is that subdividing an existing piece does not change the shaded quantity. It changes only how finely the whole is partitioned. A child who believes equivalent fractions require new shading needs that misconception addressed before a numerical conversion rule is taught.
Retain the pupil’s first sketch. Equal-whole modelling is often the earliest point of difficulty, and identifying that fact helps a tutor avoid prescribing drills for the wrong reason.
Convert 5/6 and 7/9 into eighteenths, then compare
Find a common denominator for six and nine. Eighteen is a shared multiple: 6 × 3 = 18 and 9 × 2 = 18. We can now express both fractions using eighteenths of an equally sized whole.
For five sixths, multiply numerator and denominator by three: 5/6 = 15/18. Each original sixth is divided into three smaller pieces, so five selected sixths become fifteen selected eighteenths.
For seven ninths, multiply numerator and denominator by two: 7/9 = 14/18. Each original ninth becomes two smaller pieces, so seven selected ninths become fourteen selected eighteenths.
Compare the equal units: 15/18 > 14/18. Therefore 5/6 > 7/9. The difference is one eighteenth of the same-sized whole, since 15/18 − 14/18 = 1/18.
A useful independent check compares what is missing from one whole. Five sixths is missing one sixth; seven ninths is missing two ninths. Express these missing amounts in eighteenths: 1/6 = 3/18 and 2/9 = 4/18. The fraction missing less is closer to one, so five sixths is larger.
This second argument is not a new rule to memorise; it is another way of viewing the same diagram. Both shaded quantities lie below one, and a smaller unshaded remainder means a larger shaded share of the common whole.
A common error is to compare only the numerators seven and five. Ask what each selected piece represents. A ninth is smaller than a sixth when the wholes are equal, so counting unequal pieces without converting their sizes is not a valid comparison.
Another error is multiplying only the denominator to obtain 5/18 instead of 15/18. That shrinks the value rather than preserving it. Ask the child to subdivide each of the five selected sixths into three and count the resulting selected smaller parts.
The result should be expressed in a complete sentence: “Five sixths is larger than seven ninths because fifteen eighteenths is larger than fourteen eighteenths.” That explanation connects the mathematical notation to a consistent unit of comparison.
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Choose tuition timing for the concentration required by equivalence
A weekday Primary 4 Mathematics tutorial may work well when a child has encountered unlike fractions in school and brings an original exercise showing the first mistake. If the error was choosing a denominator without preserving the numerator, the tutor can identify the exact missing idea while the lesson remains familiar.
However, reducing a comparison to a rushed multiplication procedure can make an uncertain learner more dependent on memorised steps. Lorong Chuan families should check the actual travel time to the centre, food, homework and concentration after school rather than assuming an available weekday hour is automatically effective.
A weekend tutorial may provide enough space for drawing equivalent strips, discussing why eighteenth-sized units are useful, and comparing the result with a complementary missing-fraction check. Such careful conversation is valuable for children who can compute products but cannot justify the equivalence.
Yet a long Saturday session is not necessarily a better teaching window. If the child has already attended sport, another enrichment class and family events, a shorter settled weekday session may permit more accurate reasoning.
Parents should ask what the child can do independently after instruction: can the pupil recognise the need for a common-sized whole, find a common denominator and compare two new fractions without the original answer on the page?
A few minutes of delayed review with different denominators often provides more information than repeating 5/6 and 7/9 immediately. The timetable should leave space for that independent revisit and for ordinary family life.
| What to compare | Weekday option | Weekend option |
|---|---|---|
| Support for the original school misconception | Prompt feedback on a recently taught equivalent-fraction question | Space to draw and compare different fraction representations |
| Actual learning window | Check tiredness, food, schoolwork and door-to-door travel | Check weekend commitments, recovery time and class suitability |
| Evidence of transfer | Fresh unlike-fraction comparison on a later day | Fresh weekday school-style problem without the first diagram |
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Teach from the first mistake rather than giving every pupil the same rule
In a small three-pupil class, one learner may compare seven to five and ignore denominators. Another may recognise eighteen as the correct common denominator but write 5/18 instead of 15/18. A third may convert both fractions correctly yet reverse the greater-than sign in the final answer.
Those are different starting points. The first child needs a same-sized whole and an explanation of piece sizes. The second needs equivalent-fraction drawings that link each multiplication on top to the same multiplication on the bottom. The third needs a comparison sentence that matches the common-denominator values.
An effective tutor asks each learner to explain how the denominator and numerator changed. “I divided every original sixth into three equal smaller pieces, so five selected sixths became fifteen eighteenths.” A student who can show this on a model is less likely to forget why the written algorithm works.
Discuss the second missing-parts check only when pupils can identify the whole confidently. That method is particularly illuminating when both fractions are close to one, but it should not distract from a learner who still confuses the reference whole.
A useful accuracy check is estimating the fractions as sizes rather than converting to long decimals. Five sixths is a large share, missing only one sixth; seven ninths is also large but missing two ninths. The comparison through eighteenths makes the slight difference exact.
A tutor should tell the parent which concept required a hint and show one new pair of fractions at the next session. Finishing ten similar conversions under constant prompting does not prove the pupil can independently choose a common unit.
For related explanations, see How to Study Primary 4 Mathematics Equivalent Fractions, the established Primary 4 Mathematics Tuition | Lorong Chuan guide and the wider eduKate Mathematics learning hub.
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Compare 7/8 with 5/6 in a fresh independent task
Several days later, write 7/8 and 5/6 on a clean page. Ask which is larger and let the learner choose a strategy without mentioning eighteenths or showing the previous worked example.
A common denominator is twenty-four. Multiply the first fraction’s numerator and denominator by three to get 7/8 = 21/24. Multiply the second’s numerator and denominator by four to get 5/6 = 20/24.
Since 21/24 > 20/24, we conclude 7/8 > 5/6. Their difference is one twenty-fourth. The two original denominators, eight and six, are different, but equivalent fractions let us compare equal-sized units.
Ask for an alternative check. Seven eighths is missing one eighth from one whole, while five sixths is missing one sixth. One eighth is smaller than one sixth when the wholes are equal, so seven eighths is closer to one.
If the pupil gets the right answer by comparing the numerators seven and five, ask whether that method would always work. It would not, as different denominators make the pieces different sizes. The learner needs an explanation that remains valid when the two numerators and denominators change.
If the child writes 7/24 rather than 21/24, ask how each selected eighth becomes three smaller pieces. The drawn model should show seven groups of three selected pieces, not seven single pieces.
For an additional challenge, ask the student to place both fractions on a fraction strip between zero and one. Both are near one; seven eighths is slightly farther right. A number-line check can reinforce the magnitude rather than treating fraction conversion as a paper-only exercise.
Save the first answer and the first prompt needed. Independent use of a different common denominator and a valid second reason shows more robust understanding than reproducing the original fifteen-eighteenths calculation.
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Questions Lorong Chuan parents ask
Why is 5/6 greater than 7/9 even though five is smaller than seven?
The selected pieces have different sizes. With equal-sized wholes, 5/6 is 15/18 while 7/9 is 14/18, so 5/6 is larger.
Is multiplying both numerator and denominator necessary?
Yes when changing an equivalent fraction by a factor. Multiplying only one of them changes the fraction’s value rather than just its representation.
Can I compare how much is missing from one whole?
Yes, particularly when both fractions are close to one. For 5/6 and 7/9, the missing amounts are 3/18 and 4/18, so the first fraction is larger.
Should I choose a weekday or weekend Primary 4 tutorial?
Choose the slot where the child can reason with a common whole, explain a valid equivalence and later compare a new pair independently. Timetable convenience alone is not a teaching method.
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Use the first attempt to plan a suitable lesson
Before choosing a slot, bring one recent school problem, the child’s original calculation before correction and a note of the first prompt required. The eduKate Mathematics learning hub and Singapore Mathematics tuition by area index connect this topic to wider study routes. The MOE Primary Mathematics syllabus, updated October 2025, remains the authoritative reference for learning objectives; the worked task here is a diagnostic example, not an exhaustive syllabus assessment.
Lorong Chuan names the residential area addressed, not a guaranteed eduKate lesson venue beside the MRT station or elsewhere on a named road. Confirm the real teaching address, current fees, tutor, 3-pax placement, exact available lesson times and door-to-door travel before selecting a weekday or weekend. The Education and Tuition | Lorong Chuan article and Learning Lorong Chuan family guide provide further neighbourhood context.
To discuss a class, use the parent–student consultation route, sharing the student’s current level, independent learning difficulty and a realistic family timetable. Ask what successful transfer to a new example will look like after a few sessions; page counts and speed alone are incomplete evidence.
For connected lower-primary guides, see Primary 1 Mathematics | Lorong Chuan, weekday versus weekend and Primary 2 Mathematics | Lorong Chuan, weekday versus weekend. These pages address different learning questions within the same local decision series.
Continue across primary levels: Primary 3 Mathematics | Lorong Chuan. These related guides examine different learning needs and help parents see how a manageable weekly tutorial can change with the child’s stage.
Continue into upper-primary Lorong Chuan Mathematics: Primary 5 mixed-number fractions · Primary 6 successive percentage changes · PSLE fixed-total ratio transfers · Primary Mathematics examination preparation.