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 knows that 1/n becomes smaller as n increases but assumes the decrease is a fixed step, overlooking that consecutive unit fractions get progressively closer together. 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
A unit fraction has numerator 1. Examples include 1/2, 1/3, 1/4 and 1/10. As the denominator grows, the same whole is divided into more equal parts, so one part becomes smaller.
The change is not a constant subtraction. The gap from 1/2 to 1/3 is 1/6, while the gap from 1/3 to 1/4 is 1/12. The second gap is only half as large.
For consecutive positive denominators n and n+1, the gap is 1/n − 1/(n+1). Converting to a common denominator gives exactly 1/[n(n+1)].
As n increases, the product n(n+1) increases, so the unit-fraction gap becomes smaller. This is a mechanism, not a pattern guessed from a few decimal approximations.
On a number line, the points 1/2, 1/3, 1/4 and so on crowd closer to 0. They never become negative and no positive unit fraction equals 0.
The order must remain clear: 1/2 is greater than 1/3, so the positive gap is 1/2−1/3. Reversing the subtraction gives a negative change rather than the distance between the values.
A common denominator reveals both order and distance. For example, 1/5=6/30 and 1/6=5/30, so their gap is 1/30.
The shrinking-gap idea helps estimate differences, place fractions accurately and reject equally spaced drawings that misrepresent unit fractions.
It also prevents a language trap: the denominators rise by 1 each time, but the fraction values do not fall by the same amount. Equal changes in a denominator produce unequal changes in value.
The safe routine is order, common scale, subtract, generalise: identify the larger unit fraction, express both on one denominator, find the exact positive gap and compare its denominator with nearby gaps.
Core decision: For positive n, 1/n is greater than 1/(n+1), and their exact gap is 1/[n(n+1)]. Because n(n+1) grows as n grows, consecutive unit fractions become closer together while approaching 0.
A denominator tells how many equal parts form a whole. Increasing that count makes each part smaller, but the relationship is reciprocal rather than linear. Exact fraction subtraction exposes the changing spacing.
Mechanism: why the rule works
1. Read the denominator as partition count
One nth is one part when a whole is split into n equal parts. More equal parts mean a smaller single part.
This comparison assumes the same whole. Different-sized wholes cannot be compared from denominators alone.
Diagnostic check. Are both fractions portions of the same whole?
2. Put neighbours on a common scale
For 1/n and 1/(n+1), use the common denominator n(n+1). The numerators become n+1 and n.
The two converted numerators differ by exactly 1, making the gap visible.
Diagnostic check. Can you reconstruct both original fractions after conversion?
3. Derive the gap
Subtract the smaller value from the larger: (n+1)/[n(n+1)]−n/[n(n+1)]=1/[n(n+1)].
The result is a unit fraction whose denominator is the product of the two neighbouring denominators.
Diagnostic check. Did you subtract in the order that gives a positive distance?
4. Compare adjacent gaps
The gap between 1/n and 1/(n+1) is 1/[n(n+1)], while the next is 1/[(n+1)(n+2)].
The second denominator is larger, so the second positive unit-fraction gap is smaller.
Diagnostic check. Which product denominator is larger?
5. Separate denominator steps from value steps
The denominator increases by a constant 1, but reciprocal values respond nonlinearly.
Equal horizontal steps in denominator space are not equal vertical steps in fraction value.
Diagnostic check. Are you comparing labels or actual quantities?
6. Use the number-line limit carefully
The sequence 1/n approaches 0 as n grows because the parts can become arbitrarily small.
Approaches does not mean reaches. For every positive whole n, 1/n remains positive.
Diagnostic check. Can any finite positive denominator make the numerator 1 produce zero?
7. Check with decimals without depending on them
Decimals such as 0.5, 0.333… and 0.25 can confirm direction, but exact fractions give the precise gap.
Rounded decimals can hide small differences or create false equality.
Diagnostic check. Does the exact subtraction support the decimal impression?
8. Apply only to unit fractions
The rule concerns numerator 1 and consecutive positive denominators. Fractions with other numerators require their own comparison.
For example, 3/5 and 3/6 have a related same-numerator pattern but a different gap formula.
Diagnostic check. Have you checked the numerator and denominator conditions?
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: First gap
Task. Find the gap between 1/2 and 1/3.
Reasoning. Use sixths: 1/2=3/6 and 1/3=2/6.
Answer. The gap is 1/6.
Independent check. The formula gives 1/(2×3)=1/6.
Contrast-and-transfer pass. Keep the governing principle from “First gap”, but change one surface detail in the task: Find the gap between 1/2 and 1/3. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The gap is 1/6.—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 2: Next gap
Task. Find the gap between 1/3 and 1/4.
Reasoning. Use twelfths: 4/12−3/12.
Answer. The gap is 1/12.
Independent check. It is smaller than 1/6, showing that spacing shrinks.
Contrast-and-transfer pass. Keep the governing principle from “Next gap”, but change one surface detail in the task: Find the gap between 1/3 and 1/4. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The gap is 1/12.—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: Fifths and sixths
Task. Find 1/5−1/6.
Reasoning. Use denominator 30: 6/30−5/30.
Answer. The gap is 1/30.
Independent check. The neighbouring-denominator product is 5×6.
Contrast-and-transfer pass. Keep the governing principle from “Fifths and sixths”, but change one surface detail in the task: Find 1/5−1/6. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The gap is 1/30.—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: Tenths and elevenths
Task. Find the exact gap between 1/10 and 1/11.
Reasoning. Use denominator 110: 11/110−10/110.
Answer. The gap is 1/110.
Independent check. Do not round both fractions too early.
Contrast-and-transfer pass. Keep the governing principle from “Tenths and elevenths”, but change one surface detail in the task: Find the exact gap between 1/10 and 1/11. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The gap is 1/110.—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: Compare gaps
Task. Which is larger: the gap from 1/4 to 1/5 or from 1/5 to 1/6?
Reasoning. The gaps are 1/20 and 1/30. With positive unit fractions, the smaller denominator gives the larger value.
Answer. The 1/4-to-1/5 gap is larger.
Independent check. Both are written as exact distances.
Contrast-and-transfer pass. Keep the governing principle from “Compare gaps”, but change one surface detail in the task: Which is larger: the gap from 1/4 to 1/5 or from 1/5 to 1/6? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The 1/4-to-1/5 gap is larger.—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: Number-line drawing
Task. Should 1/2,1/3,1/4 and1/5 be equally spaced?
Reasoning. Their gaps are 1/6,1/12 and1/20, which are unequal and decreasing.
Answer. No; the points crowd closer toward 0.
Independent check. A labelled diagram should reflect quantity, not denominator rhythm.
Contrast-and-transfer pass. Keep the governing principle from “Number-line drawing”, but change one surface detail in the task: Should 1/2,1/3,1/4 and1/5 be equally spaced? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—No; the points crowd closer toward 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.
Worked example 7: Approach not arrival
Task. Does 1/1,000 equal 0 because it is very small?
Reasoning. Its numerator is positive and denominator finite, so the fraction is positive.
Answer. No. It equals 0.001.
Independent check. Small is not identical to zero.
Contrast-and-transfer pass. Keep the governing principle from “Approach not arrival”, but change one surface detail in the task: Does 1/1,000 equal 0 because it is very small? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—No. It equals 0.001.—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: Reverse subtraction
Task. A pupil writes 1/6−1/5=1/30 as the gap.
Reasoning. That subtraction order is negative: 1/6−1/5=−1/30. The distance uses larger minus smaller.
Answer. The positive gap is 1/5−1/6=1/30.
Independent check. Order and absolute distance are separated.
Contrast-and-transfer pass. Keep the governing principle from “Reverse subtraction”, but change one surface detail in the task: A pupil writes 1/6−1/5=1/30 as the gap. Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The positive gap is 1/5−1/6=1/30.—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: General proof
Task. Show the gap between 1/n and1/(n+1).
Reasoning. Use the common denominator n(n+1), giving numerators n+1 and n.
Answer. The gap is 1/[n(n+1)].
Independent check. Substitution with n=4 restores 1/20.
Contrast-and-transfer pass. Keep the governing principle from “General proof”, but change one surface detail in the task: Show the gap between 1/n and1/(n+1). Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—The gap is 1/[n(n+1)].—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: Condition check
Task. Can the same formula be used for 2/5 and2/6?
Reasoning. No. These are not unit fractions; direct subtraction gives 12/30−10/30=2/30=1/15.
Answer. Use the formula only when the numerator is 1.
Independent check. Check conditions before importing a pattern.
Contrast-and-transfer pass. Keep the governing principle from “Condition check”, but change one surface detail in the task: Can the same formula be used for 2/5 and2/6? Before recalculating or rewriting, name which evidence remains controlling and which detail has changed. The original conclusion—Use the formula only when the numerator is 1.—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
Make a table for n=2 through 10 with columns 1/n, 1/(n+1), exact gap and decimal gap. Use the exact column to explain why rounding is only a check.
Draw a number line from 0 to 1/2 and place six unit fractions using a consistent scale. Compare the visual gaps with 1/[n(n+1)].
Hold the denominator step at +1 and record the value change. Then hold a value step approximately constant and see that denominator changes cannot remain constant.
Create three near-miss claims: equally spaced, reaches zero, and formula works for every same-numerator pair. Disprove each with an exact calculation or condition check.
Common misconceptions and targeted repairs
Misconception 1: Denominator plus one means value minus a constant
What the learner may think. The learner expects equal fraction gaps.
Why it fails. Reciprocal values change by 1/[n(n+1)], which depends on n.
Targeted repair. Calculate two adjacent gaps and compare.
Misconception 2: Larger denominator means larger fraction
What the learner may think. The learner follows the numeral rather than partition size.
Why it fails. For positive unit fractions of the same whole, more parts make each part smaller.
Targeted repair. Sketch equal wholes divided into n and n+1 parts.
Misconception 3: Very small equals zero
What the learner may think. The learner replaces approach with arrival.
Why it fails. Every finite positive unit fraction remains greater than zero.
Targeted repair. Write an exact decimal or inequality.
Misconception 4: Dots on a sketch may be equally spaced
What the learner may think. The learner trusts a rough illustration.
Why it fails. A not-to-scale drawing cannot override exact values.
Targeted repair. Use computed gaps to place points.
Misconception 5: Rounded decimals are exact
What the learner may think. The learner reports two rounded values as equal.
Why it fails. Rounding can erase a real difference.
Targeted repair. Return to fraction subtraction.
Misconception 6: Formula has no conditions
What the learner may think. The learner applies 1/[n(n+1)] to non-unit or nonconsecutive fractions.
Why it fails. The derivation used numerator 1 and denominators n,n+1.
Targeted repair. State conditions before using the result.
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: Order
Question. Which is greater,1/7 or1/8?
Explained answer. 1/7 is greater.
Why this earns trust. One seventh is a larger part of the same whole.
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 “1/7 is greater.” from memory, but to recreate a justified answer from the new evidence.
Practice 2: Gap
Question. Find 1/7−1/8.
Explained answer. 1/56.
Why this earns trust. The common denominator is 7×8.
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 “1/56.” from memory, but to recreate a justified answer from the new evidence.
Practice 3: Next gap
Question. Find 1/8−1/9.
Explained answer. 1/72.
Why this earns trust. The converted numerators differ by one.
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 “1/72.” from memory, but to recreate a justified answer from the new evidence.
Practice 4: Comparison
Question. Which gap is larger,1/7−1/8 or1/8−1/9?
Explained answer. 1/56 is larger than1/72.
Why this earns trust. Positive unit fractions with smaller denominators are larger.
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 “1/56 is larger than1/72.” from memory, but to recreate a justified answer from the new evidence.
Practice 5: Formula
Question. State the gap between1/n and1/(n+1).
Explained answer. 1/[n(n+1)].
Why this earns trust. The expression comes from exact subtraction.
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/[n(n+1)].” from memory, but to recreate a justified answer from the new evidence.
Practice 6: Substitution
Question. Use n=12.
Explained answer. The gap between1/12 and1/13 is1/156.
Why this earns trust. Twelve times thirteen is 156.
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 “The gap between1/12 and1/13 is1/156.” from memory, but to recreate a justified answer from the new evidence.
Practice 7: Number line
Question. Do consecutive unit fractions remain equally spaced?
Explained answer. No. Their gaps shrink as denominators increase.
Why this earns trust. The gap denominator product grows.
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. Their gaps shrink as denominators increase.” from memory, but to recreate a justified answer from the new evidence.
Practice 8: Limit language
Question. Does1/n become zero for some positive whole n?
Explained answer. No. It remains positive for every finite n.
Why this earns trust. Approaching zero is not reaching zero.
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. It remains positive for every finite n.” from memory, but to recreate a justified answer from the new evidence.
Practice 9: Reverse order
Question. Evaluate1/9−1/8.
Explained answer. −1/72.
Why this earns trust. The first fraction is smaller.
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 “−1/72.” from memory, but to recreate a justified answer from the new evidence.
Practice 10: Condition
Question. Does the formula directly apply to2/7 and2/8?
Explained answer. No. They are not unit fractions; subtract directly.
Why this earns trust. The numerator condition is checked.
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. They are not unit fractions; subtract directly.” from memory, but to recreate a justified answer from the new evidence.
Practice 11: Diagram audit
Question. A sketch places1/2,1/3,1/4 equally. What is wrong?
Explained answer. The exact gaps are1/6 and1/12, so equal spacing is inaccurate.
Why this earns trust. Computed quantities control the drawing.
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 “The exact gaps are1/6 and1/12, so equal spacing is inaccurate.” from memory, but to recreate a justified answer from the new evidence.
Practice 12: Routine
Question. State the safe method.
Explained answer. Identify the larger unit fraction, use a common denominator, subtract exactly and compare product denominators.
Why this earns trust. Order, calculation and generalisation are visible.
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 “Identify the larger unit fraction, use a common denominator, subtract exactly and compare product denominators.” 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: Gap table
After two days, rebuild five consecutive gaps without notes.
Success criterion. Every gap follows from common-denominator subtraction.
Transfer test 2: Number-line transfer
Place1/6 through1/12 accurately enough to show crowding.
Success criterion. Relative gaps match their exact order.
Transfer test 3: Condition challenge
Sort examples into unit-consecutive, unit-nonconsecutive and non-unit cases.
Success criterion. The formula is used only in its valid domain.
Transfer test 4: Blank-page proof
Derive1/[n(n+1)] and explain why it shrinks.
Success criterion. The proof includes common numerators and a growing product denominator.
Examination control
1. Check the same whole. Denominator comparison assumes a common whole.
2. Order before subtracting. Use larger minus smaller for a positive gap.
3. Create one scale. Common denominators reveal exact distance.
4. State the conditions. Unit fractions and consecutive positive denominators matter.
5. Keep exact form. Use decimals only as a secondary check.
Under time pressure, compress the method to same whole → order → common denominator → exact gap → compare products. 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
Label mistakes as whole changed, order reversed, common denominator wrong, equal-step assumption, zero claimed, rounding trusted or formula overextended.
Retest with larger denominators after a delay. The learner should predict a smaller gap before calculating it.
Notes for parents and tutors
Use identical paper strips to show that one part shrinks as the partition count grows.
Ask for two exact gaps before discussing the general formula.
Treat a calculator decimal as a check, not the source of proof.
Let the learner correct an equally spaced number line using exact fraction distances.
Frequently asked questions
What is a unit fraction?
A fraction with numerator 1 and a positive denominator.
Why does it shrink when the denominator grows?
The same whole is divided into more equal parts.
What is the gap between1/n and1/(n+1)?
It is1/[n(n+1)].
Why do gaps shrink?
The product n(n+1) grows, making its unit fraction smaller.
Do the values reach zero?
No finite positive unit fraction equals zero, though the values approach it.
Can I use decimals?
Yes as a check, but exact fractions preserve the real gap.
Does the formula work for2/n?
Not directly; derive that case separately.
What is the quickest check?
Convert neighbouring unit fractions to the product denominator; their numerators differ by one.
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.