Series route: This guide belongs to the complete PSLE Learner’s Guide volume directory. The original PSLE Learning Guide supplies the wider English, Mathematics and Science route, while PSLE Mathematics provide verified subject-specific continuation.
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This volume solves one precise learner problem: the learner sees a larger denominator and assumes the fraction must be larger, applies a same-numerator shortcut when numerators differ, or memorises the comparison without understanding that more equal parts make each part smaller. The goal is durable control, not a remembered slogan. A Primary 6 learner should be able to identify the trigger, explain the mechanism, perform the decision under time pressure and reject an attractive answer that exceeds the evidence.
- Start with the exact mistake and the evidence boundary.
- Build the mechanism before memorising a shortcut.
- Study worked contrasts and name why the near-miss fails.
- Repair misconceptions with one targeted check each.
- Attempt graded independent practice before reading the explanations.
- Return after a delay and prove that the method transfers.
- Use the parent and tutor notes after the learner has attempted the work.
The problem beneath the mistake
Compare 3/5 and 3/8. Both fractions contain three equal parts of their respective wholes, but fifths are larger than eighths. Therefore 3/5 is greater than 3/8.
A denominator tells how many equal parts make one whole. When the same whole is divided into more equal parts, each part becomes smaller. Eight equal parts are smaller than five equal parts.
The numerator tells how many of those parts are selected. When the positive numerator is fixed, the count of selected parts stays the same, so the size of each part decides the comparison.
The rule needs conditions: the fractions are positive, use the same numerator and refer to comparable wholes. It is unsafe to recite “bigger denominator means smaller fraction” without checking those conditions.
For 7/9 and 7/12, ninths are larger than twelfths, so seven ninths is larger. A number line confirms that 7/9 lies farther to the right than 7/12.
A common-denominator calculation proves the same result. Since 3/5=24/40 and 3/8=15/40, the first fraction has more fortieths. The shortcut compresses this reasoning; it does not replace it with magic.
Cross-products also work: for positive denominators, compare 3×8 with 3×5. Twenty-four is greater than fifteen, so 3/5 is greater. The shared numerator makes the pattern especially transparent.
Do not compare printed bar lengths from diagrams unless the wholes are equal and the parts are drawn to a valid scale. Fraction meaning depends on equal parts of the same-sized reference whole.
Improper fractions follow the same positive same-numerator relationship. For example, 11/4 is greater than 11/6. The fractions are above one, but quarters remain larger than sixths.
The reliable routine is check positivity, verify the numerator is identical, compare denominator size in the opposite direction, justify with piece size or an exact method, and test the result against benchmarks.
Core decision: For positive fractions with the same numerator and positive denominators, the fraction with the smaller denominator is larger. The numerator fixes the number of selected pieces; the smaller denominator makes each equal piece larger.
Fraction comparison is measurement of relative quantity, not visual comparison of two isolated digits. A dependable learner connects symbols to equal-part models, then confirms the relationship by common denominators, cross-products or number-line position.
Mechanism: why the rule works
1. Check the conditions
Confirm that both denominators are positive and the numerators are the same positive number.
A shortcut is a conditional rule; changing its conditions may reverse or destroy the conclusion.
Diagnostic check. Are the numerators identical and the quantities positive?
2. Interpret the denominator
Read the denominator as the number of equal parts in one whole.
More equal parts in the same whole means each part has smaller size.
Diagnostic check. Which partition creates larger pieces?
3. Hold the count fixed
Use the shared numerator to keep the number of selected parts unchanged.
When both fractions select the same count, only piece size controls the total selected amount.
Diagnostic check. Are we choosing the same number of pieces?
4. Reverse the denominator order
The smaller positive denominator produces the larger fraction when the numerator is fixed.
This inverse relationship is the reason the two denominator digits are not compared in the ordinary direction.
Diagnostic check. Have you reversed the comparison correctly?
5. Prove with equivalence
Convert both fractions to a common denominator.
Equal-sized units make the numerical comparison explicit and expose any mistaken shortcut.
Diagnostic check. Which fraction has more common units?
6. Check by cross-products
For a/b and a/c with positive b and c, compare ac and ab.
Multiplying by the positive common denominator bc preserves order.
Diagnostic check. Do the products confirm the piece-size argument?
7. Use benchmarks
Locate each fraction relative to zero, one half, one and other convenient values.
A benchmark can catch a reversed inequality or an implausible decimal conversion.
Diagnostic check. Does the claimed order fit the number line?
8. Protect the whole
Ensure diagrams, recipes and measures use the same reference whole or explicitly convert them.
Three pieces from a large cake need not equal three pieces from a small cake.
Diagnostic check. Are the wholes genuinely comparable?
Worked examples: make the decision visible
Pause before each answer. State the controlling evidence in one line, then complete the operation. The explanations deliberately contrast a valid route with a plausible but invalid one, because transfer grows when the learner can say why a tempting route does not apply.
Worked example 1: Fifths and eighths
Task. Compare 3/5 and 3/8.
Reasoning. The same numerator selects three pieces; fifths are larger than eighths.
Answer. 3/5 > 3/8.
Independent check. Common denominator 40 gives 24/40 > 15/40.
Contrast-and-transfer pass. Keep the governing principle from “Fifths and eighths”, but change one surface detail in the task: Compare 3/5 and 3/8. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—3/5 > 3/8.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 2: Ninths and twelfths
Task. Compare 7/9 and 7/12.
Reasoning. Ninths are larger because one whole is split into fewer parts.
Answer. 7/9 > 7/12.
Independent check. Cross-products give 7×12=84 and 7×9=63.
Contrast-and-transfer pass. Keep the governing principle from “Ninths and twelfths”, but change one surface detail in the task: Compare 7/9 and 7/12. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—7/9 > 7/12.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 3: Unit fractions
Task. Order 1/3, 1/5 and 1/10 from largest to smallest.
Reasoning. With one selected part, fewer partitions create the larger part.
Answer. 1/3 > 1/5 > 1/10.
Independent check. Decimals about 0.333, 0.2 and 0.1 confirm the order.
Contrast-and-transfer pass. Keep the governing principle from “Unit fractions”, but change one surface detail in the task: Order 1/3, 1/5 and 1/10 from largest to smallest. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—1/3 > 1/5 > 1/10.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 4: Improper fractions
Task. Compare 11/4 and 11/6.
Reasoning. The numerator remains eleven; quarters are larger than sixths.
Answer. 11/4 > 11/6.
Independent check. As mixed numbers, 2 3/4 > 1 5/6.
Contrast-and-transfer pass. Keep the governing principle from “Improper fractions”, but change one surface detail in the task: Compare 11/4 and 11/6. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—11/4 > 11/6.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 5: Same denominator distractor
Task. Compare 4/9 and 7/9.
Reasoning. This is not a same-numerator case; ninths have equal size and the numerator controls the count.
Answer. 7/9 > 4/9.
Independent check. The correct shortcut changes when the matching component changes.
Contrast-and-transfer pass. Keep the governing principle from “Same denominator distractor”, but change one surface detail in the task: Compare 4/9 and 7/9. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—7/9 > 4/9.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 6: Both parts differ
Task. Compare 3/5 and 4/7.
Reasoning. Neither numerator nor denominator is shared, so use an exact method.
Answer. 3/5 > 4/7 because 3×7=21 and 4×5=20.
Independent check. Do not use denominator size alone.
Contrast-and-transfer pass. Keep the governing principle from “Both parts differ”, but change one surface detail in the task: Compare 3/5 and 4/7. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—3/5 > 4/7 because 3×7=21 and 4×5=20.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 7: Equal fractions
Task. Compare 2/3 and 4/6.
Reasoning. The numerators are not the same, but equivalent-fraction reasoning applies.
Answer. 2/3 = 4/6.
Independent check. Cross-products are both 12.
Contrast-and-transfer pass. Keep the governing principle from “Equal fractions”, but change one surface detail in the task: Compare 2/3 and 4/6. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—2/3 = 4/6.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 8: Diagram trap
Task. Two shaded bars show three parts each, but the bars have different total lengths and no scale.
Reasoning. The drawings do not establish equal wholes.
Answer. No reliable fraction-size conclusion follows from bar length alone.
Independent check. Use the symbolic fractions or redraw equal wholes.
Contrast-and-transfer pass. Keep the governing principle from “Diagram trap”, but change one surface detail in the task: Two shaded bars show three parts each, but the bars have different total lengths and no scale. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—No reliable fraction-size conclusion follows from bar length alone.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 9: Word problem
Task. Mina drinks 5/8 L and Ravi drinks 5/6 L. Who drinks more?
Reasoning. Both amounts have numerator five and the litre is the same whole; sixths are larger than eighths.
Answer. Ravi drinks more because 5/6 > 5/8.
Independent check. The difference is 20/24−15/24=5/24 L.
Contrast-and-transfer pass. Keep the governing principle from “Word problem”, but change one surface detail in the task: Mina drinks 5/8 L and Ravi drinks 5/6 L. Who drinks more? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Ravi drinks more because 5/6 > 5/8.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
Worked example 10: Boundary case
Task. Compare 0/5 and 0/8.
Reasoning. The numerator is zero, not positive; both fractions represent zero.
Answer. 0/5 = 0/8 = 0.
Independent check. This explains why the positive-numerator condition matters.
Contrast-and-transfer pass. Keep the governing principle from “Boundary case”, but change one surface detail in the task: Compare 0/5 and 0/8. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—0/5 = 0/8 = 0.—may remain valid only if the changed detail does not alter the trigger, relationship or scope. Use the independent check again rather than trusting visual similarity. This second pass trains selection: the learner must decide whether the same method still applies, adapt one step when a condition changes, and refuse the method when its trigger disappears.
The method lab: change one condition at a time
Fold identical paper strips into 3, 4, 6 and 8 equal parts. Select the same number of parts where possible and describe how the selected length changes as the denominator grows.
Place same-numerator pairs on a number line, then verify each order with common denominators. Record any case where a careless digit comparison would reverse the truth.
Sort fraction pairs by the safest method: same numerator, same denominator, benchmark, equivalence or cross-product. Explain why one shortcut cannot govern every pile.
Create a false diagram by changing the size of the whole. Annotate exactly why the picture is not valid evidence even if the shaded piece count matches.
After a delay, derive the rule from piece size without using the memorised sentence “bigger denominator, smaller fraction”.
Common misconceptions and targeted repairs
Misconception 1: Larger denominator means larger fraction
What the learner may think. The learner compares denominator digits as ordinary whole numbers.
Why it fails. A larger denominator creates smaller equal parts of the same whole.
Targeted repair. Draw equal wholes and compare one piece.
Misconception 2: The rule works for any pair
What the learner may think. The learner ignores the shared numerator.
Why it fails. When both numerator and denominator change, either fraction may be larger.
Targeted repair. Use cross-products or common denominators.
Misconception 3: The numerator does not matter
What the learner may think. The learner transfers the same-numerator rule to same-denominator pairs.
Why it fails. With equal-sized pieces, a larger numerator selects more pieces.
Targeted repair. Name which component is fixed.
Misconception 4: Pictures always prove it
What the learner may think. The learner compares unequal bars or decorative drawings.
Why it fails. Fractions require equal parts of comparable wholes.
Targeted repair. Redraw with one common whole.
Misconception 5: Improper fractions obey a different rule
What the learner may think. The learner stops the piece-size reasoning above one.
Why it fails. Positive fractions keep the inverse denominator relationship for fixed numerator.
Targeted repair. Check with mixed numbers or cross-products.
Misconception 6: Zero follows the strict rule
What the learner may think. The learner says 0/5 is greater than 0/8.
Why it fails. Both have value zero, so there is equality.
Targeted repair. Check the positive-numerator condition.
Graded independent practice with explained answers
Attempt each item without looking ahead. Write the evidence or relationship before the final response. Early items check recognition; middle items require explanation; later items change the surface form so that copying a worked example is insufficient.
Practice 1: Direct comparison
Question. Compare 4/7 and 4/9.
Explained answer. 4/7 > 4/9.
Why this earns trust. Sevenths are larger than ninths.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “4/7 > 4/9.” from memory, but to recreate a justified answer from the new evidence.
Practice 2: Unit fractions
Question. Which is larger, 1/12 or 1/20?
Explained answer. 1/12.
Why this earns trust. Twelfths are larger pieces than twentieths.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “1/12.” from memory, but to recreate a justified answer from the new evidence.
Practice 3: Order
Question. Order 5/6, 5/8 and 5/11.
Explained answer. 5/6 > 5/8 > 5/11.
Why this earns trust. The numerator is fixed and denominator order reverses.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “5/6 > 5/8 > 5/11.” from memory, but to recreate a justified answer from the new evidence.
Practice 4: Proof
Question. Prove 2/3 > 2/5 with a common denominator.
Explained answer. 2/3=10/15 and 2/5=6/15, so 10/15>6/15.
Why this earns trust. The units are made equal.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “2/3=10/15 and 2/5=6/15, so 10/15>6/15.” from memory, but to recreate a justified answer from the new evidence.
Practice 5: Cross-product
Question. Check 9/10 and 9/13.
Explained answer. 9×13=117 exceeds 9×10=90, so 9/10>9/13.
Why this earns trust. Positive multiplication preserves order.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “9×13=117 exceeds 9×10=90, so 9/10>9/13.” from memory, but to recreate a justified answer from the new evidence.
Practice 6: Different numerator
Question. Can the shortcut compare 3/4 and 5/7 directly?
Explained answer. No.
Why this earns trust. The numerators differ; use another exact method.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “No.” from memory, but to recreate a justified answer from the new evidence.
Practice 7: Same denominator
Question. Compare 3/8 and 5/8.
Explained answer. 5/8 > 3/8.
Why this earns trust. Equal eighths make the larger piece count decisive.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “5/8 > 3/8.” from memory, but to recreate a justified answer from the new evidence.
Practice 8: Improper
Question. Compare 13/5 and 13/9.
Explained answer. 13/5 > 13/9.
Why this earns trust. Fifths are larger and thirteen are selected.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “13/5 > 13/9.” from memory, but to recreate a justified answer from the new evidence.
Practice 9: Zero
Question. Compare 0/3 and 0/100.
Explained answer. They are equal.
Why this earns trust. Both represent no selected amount.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “They are equal.” from memory, but to recreate a justified answer from the new evidence.
Practice 10: Whole condition
Question. Why must two diagrams use equal wholes?
Explained answer. Piece size depends on the size of the starting whole as well as the denominator.
Why this earns trust. Otherwise shaded lengths are not comparable.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Piece size depends on the size of the starting whole as well as the denominator.” from memory, but to recreate a justified answer from the new evidence.
Practice 11: Error repair
Question. Repair “7/12 is greater than 7/8 because 12 is greater than 8”.
Explained answer. 7/8 is greater because eighths are larger than twelfths.
Why this earns trust. The denominator describes partition size.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “7/8 is greater because eighths are larger than twelfths.” from memory, but to recreate a justified answer from the new evidence.
Practice 12: Routine
Question. State the safe sequence.
Explained answer. Check positivity and shared numerator, compare piece size, reverse denominator order, verify exactly and check the whole.
Why this earns trust. Conditions and proof are both preserved.
Transfer variation. Close the answer, wait several minutes, and rebuild the reasoning with different names, values or wording while preserving the same decision. Start by stating the evidence that activates the method; then produce the response and a separate check. If the new surface detail changes the governing condition, explain why the earlier answer pattern must not be copied. The aim is not to repeat “Check positivity and shared numerator, compare piece size, reverse denominator order, verify exactly and check the whole.” from memory, but to recreate a justified answer from the new evidence.
A four-session mastery cycle
Session 1: construct. Read the mechanism once, cover it and write a three-line model containing the trigger, the operation and the check. Add one example and one near-miss. Compare only after the model is complete. If the operation is right but the trigger is missing, the knowledge is unsafe because it may be applied in the wrong place.
Session 2: discriminate. Mix six items: two that clearly require this method, two that tempt the method but violate a condition, and two that require another skill. For every item, write “use” or “do not use” before answering. Accuracy in method selection matters more than speed at this stage.
Session 3: explain. Give a complete answer to an imagined classmate. Include the smallest sufficient evidence, the mechanism and the independent check. Remove any sentence that merely repeats the question or adds an unsupported claim. A concise causal explanation is stronger than a longer collection of familiar words.
Session 4: perform. Attempt a timed mixed set without notes. Mark uncertain decisions, but continue. During review, classify each error as trigger, evidence, operation, scope, unit or check. Reattempt one changed version after a delay. Mastery is shown when the learner chooses and adapts the method without needing the original example beside it.
Delayed transfer: prove that the learning lasts
Transfer test 1: Measurement
Compare equal numerators of litres, metres and kilograms.
Success criterion. The unit and reference whole remain consistent.
Transfer test 2: Method selection
Mix same-numerator, same-denominator and unrelated pairs.
Success criterion. The learner names the method before comparing.
Transfer test 3: Diagram critique
Judge equal and unequal whole models.
Success criterion. Only authorised equal-part evidence is used.
Transfer test 4: Delayed derivation
Rebuild the rule from partitions after one week.
Success criterion. The explanation uses piece size and conditions, not a chant.
Examination control
1. Name the target. State exactly what the question asks before selecting a rule or explanation.
2. Expose the relationship. Write the grammatical, numerical, causal or representational relationship that controls the answer.
3. Use decisive evidence. Choose the smallest fact, calculation or observation that settles the decision.
4. Check the boundary. Reject the nearest tempting claim that the evidence does not support.
5. Present precisely. Keep conditions, units, certainty and scope visible in the final response.
Under time pressure, compress the method to positive fractions → same numerator → fewer parts means larger pieces → reverse denominator order → exact check → same whole. The compressed routine is useful only after the full reasoning is understood. If it produces uncertainty, expand the step instead of guessing.
A compact error log
Use labels such as denominator direction reversed, numerator not fixed, zero boundary missed, unequal wholes compared, diagram trusted without scale or wrong shortcut selected.
Reattempt with a mixed set so the learner must decide whether the same-numerator condition is present.
Notes for parents and tutors
Use equal paper strips or food models only when the wholes are genuinely equal.
Ask “What stays the same: piece count or piece size?” before giving a rule.
Move from models to symbols and back so understanding is not tied to one representation.
Praise the learner for rejecting a shortcut when its conditions fail.
Frequently asked questions
Core rule?
With the same positive numerator, the smaller positive denominator gives the larger fraction.
Why?
The same number of larger pieces makes a larger amount.
Does it work when numerators differ?
Not as a direct shortcut.
What about zero numerators?
Both fractions equal zero.
Does it work above one?
Yes for positive same-numerator fractions.
Best proof?
Use equal-part models, common denominators or cross-products.
Why must wholes match?
Denominator alone does not set physical size when starting wholes differ.
Fastest check?
Name the shared numerator and imagine one piece from each partition.
Next routes
Return to the complete volume directory to locate the series, use the original PSLE Learning Guide for the foundation route, and continue through PSLE Mathematics for verified subject guidance. The next useful task is a mixed set in which this idea is sometimes relevant and sometimes irrelevant; that is where the learner must choose a method rather than imitate one.