PSLE Mathematics Learning Guide · Guide 63 · Wintour V1.0 Companion to Guide 3
Return to the PSLE Learning Guide · Parent guide: Ratio Units and Actual Quantities
An equivalent-ratio question looks small: 3:5 = 12:?. But the important idea is not the missing box. It is the same multiplicative scale.
3 becomes 12 by multiplying by 4. The corresponding 5 must also be multiplied by 4. So the missing term is 20.
Equivalent ratios preserve a relationship by multiplying or dividing every corresponding term by the same non-zero factor.
This guide isolates the current Primary 6 skill of finding a missing term in a pair of equivalent ratios. The parent ratio guide explains equivalence, ratio-unit value, totals and differences more broadly. This page goes deeper into the diagnostic errors that happen when a learner scales one term but not its partner, matches the wrong positions, or uses additive rather than multiplicative change.
The same scale factor must act on corresponding terms
2:7 = 6:?
2→6 is ×3.
So 7→21 is also ×3.
Missing term: 21.
If the second term were multiplied by 4 instead, the relationship would change.
Keep first term with first term, second with second
A:B = 4:9 = 20:?
A terms: 4 and20.
B terms: 9 and?.
Scale factor=5.
B=45.
A common error is to compare4 with9 because they are next to each other. Those are different groups inside the same ratio, not corresponding terms across equivalent ratios.
Simplify first when the scale factor is hidden
18:30 = 3:?
Simplify18:30 by6 →3:5.
So the missing term is 5.
This is often easier than trying to find the direct division factor from30 while holding the relationship mentally.
Equivalent ratios can scale down as well as up
24:36 = ?:9.
36→9 is ÷4.
24÷4=6.
Equivalent ratio:6:9, which simplifies to2:3, just like24:36.
One-unit reasoning gives another route
5:8 = 15:?
If5 ratio units become15 actual units, one original ratio unit corresponds to3 actual units in the scaled pair.
8 units correspond to24.
Missing term=24.
This is the same scale-factor idea interpreted through ratio units.
Equivalent ratios behave like equivalent fractions
3:5 = 12:20 can be compared with:
3/5 = 12/20.
Both numerator and denominator scale by4.
This does not mean every ratio should be treated as a fraction of a whole. It means the multiplicative equivalence structure is shared.
Cross-products can verify a completed two-term ratio
Is4:7 equivalent to20:35?
4×35=140.
7×20=140.
The cross-products agree, so the ratios are equivalent.
For4:7 = 20:x:
4x=140 → x=35.
This algebraic verification is useful, but scaling should remain the first intuitive method at Primary level.
Equivalent ratio change is multiplicative, not additive
2:5 = 6:?
A learner notices2→6 is +4 and writes5+4=9.
But2:5 is not equivalent to6:9.
2/5=0.4 while6/9=2/3.
The correct scale is×3, so5×3=15.
Ratio equivalence preserves multiplication, not equal additive differences.
The difference between ratio terms does not stay fixed
2:5 has difference3.
Scaled by4 →8:20 has difference12.
The ratio is equivalent even though the difference changed.
What stays fixed is the multiplicative relationship between corresponding terms.
A scale factor can be a fraction
12:18 = 8:?
12→8 is×2/3.
18×2/3=12.
Alternatively simplify12:18 to2:3. To reach first term8, multiply by4 →8:12.
Simplifying often avoids fractional scale factors.
Three-part equivalent ratios require the same factor for all three terms
2:3:5 = 8:12:?
2→8 is×4 and3→12 confirms×4.
5×4=20.
All three terms must preserve the same scale.
The missing term can be in the middle
4:?:10 = 12:21:30.
4→12 is×3.
10→30 also×3.
Therefore middle term×3=21.
Middle term=7.
Check:4:7:10 scaled by3 gives12:21:30.
Ratio order must not change during equivalence
A:B=3:7.
An equivalent ratio is6:14.
14:6 is not equivalent to3:7 in the same A:B order; it corresponds to B:A.
If the labels reverse, the ratio terms must reverse too.
Convert measurement units before finding a ratio
2 m : 50 cm is not simplified from2:50 directly.
2 m=200 cm.
200:50=4:1.
If a missing-term question mixes measurement units, align the units before testing equivalence.
Equivalent ratio terms are not the same as actual quantities unless the scale is fixed
3:5 and12:20 are equivalent relationships.
But a real collection might contain30 red and50 blue objects, or300 and500. The ratio alone does not determine actual size.
This protects the learner from confusing a completed equivalent-ratio exercise with a full word problem.
Missing first term
?:28 = 3:7.
7→28 is×4.
3×4=12.
Write12:28 and simplify by4 to3:7 as a check.
Missing second term
9:15 = 21:?
Simplify9:15 →3:5.
3→21 is×7.
5×7=35.
When both terms are large, reduce to simplest form
84:126 = 10:?
84:126 simplifies by42 to2:3.
2→10 is×5.
3×5=15.
Trying to find84→10 directly creates an awkward scale factor. Simplification reveals the invariant ratio first.
The current Primary 6 ratio notation excludes fraction and decimal ratio terms
Primary 6 ratio work uses whole-number terms in the stated syllabus. A relationship such as1.5:2.5 can be converted to3:5 as an enrichment representation, but this page does not present decimal-ratio notation as an additional required syllabus topic.
The boundary matters because extension examples should not be mistaken for core exam requirements.
A ratio table makes repeated scaling visible
| A | B | Scale |
|---|---|---|
| 2 | 5 | ×1 |
| 4 | 10 | ×2 |
| 6 | 15 | ×3 |
| 20 | 50 | ×10 |
Every row lies on the same proportional relationship.
Main worked workshop: twenty original equivalent-ratio tasks
1.
2:3 = 8:?
Answer:12.
2.
5:7 = 20:?
Answer:28.
3.
?:24 = 3:8.
Answer:9.
4.
14:21 = 6:?
Answer:9.
5.
24:36 = ?:15.
Answer:10.
6.
18:30 = 12:?
Answer:20.
7.
45:60 = ?:16.
Answer:12.
8.
56:72 = 7:?
Answer:9.
9.
2:4:7 = 6:12:?
Answer:21.
10.
3:5:8 = 12:?:32.
Answer:20.
11.
?:15:21 = 4:5:7.
Answer:12.
12.
A learner writes2:5=6:9 because both terms increased by4.
Repair: use×3 →6:15.
13.
A learner writes4:7=28:16.
Repair: positions were reversed;4→28 is×7, so7→49.
14.
A learner completes6:10=18:25.
Repair:6→18 is×3, so10→30.
15.
32:48 = 14:?
Answer: simplify2:3;14 corresponds to×7; missing21.
16.
75:125 = ?:20.
Answer: simplify3:5;5→20×4; first12.
17.
9:12 = 30:?
Answer:40.
18.
21:49 = ?:14.
Answer:6.
19.
4:6:9 = 20:30:?
Answer:45.
20.
10:25 = 18:?
Answer:45.
Diagnose the first weak link
Additive scaling: learner adds the same amount instead of multiplying by the same factor.
Correspondence error: learner compares terms within one ratio instead of matching positions across ratios.
One-term scaling: learner changes one side and leaves the other unchanged.
Order reversal: learner swaps A:B into B:A.
Unit mismatch: learner forms a ratio before converting measurement units.
Three checks for every missing-term answer
- Scale check: did the same factor act on corresponding terms?
- Simplest-form check: do both complete ratios simplify to the same form?
- Cross-product check: for a two-term ratio, do the cross-products agree?
Example:3:8=15:40.
Scale factor×5; both simplify to3:8;3×40=8×15=120.
Word context: recipe scaling
Flour:sugar=5:2. A larger batch uses750 g flour. How much sugar?
5 units→750, so one unit150 g.
2 units→300 g.
Equivalent ratio750:300 simplifies to5:2.
This is equivalent-ratio reasoning in a practical context.
Word context: class groups
Boys:girls=4:5. If there are28 boys at the same ratio, girls=35.
4→28×7, so5→35.
The missing-term method reconstructs the group count directly.
Equivalent ratios support direct allocation but are not the whole allocation problem
In Guide62, a total is divided across ratio units. Here, the focus is different: one equivalent ratio is partially known and the scale factor must be preserved.
Knowing the distinction helps prevent two related topics from collapsing into one memorised procedure.
Independent transfer check
- 3:4=15:?
- ?:18=5:6
- 28:42=8:?
- 45:75=?:25
- 2:7:9=10:35:?
- ?:24:36=3:4:6
- Explain why2:5 and6:9 are not equivalent.
- Explain why scaling3:7 to15:? requires×5 on both terms.
- Convert1 m:25 cm to a whole-number ratio before simplifying.
- Verify8:12=14:21 by two different methods.
Independent-check answers
1.20.
2.15.
3.12.
4.15.
5.45.
6.18.
7.2→6 is×3 but5→9 is×1.8; the scale factors differ.
8.15=3×5, so corresponding7 must also×5=35.
9.100 cm:25 cm=4:1.
10. Both simplify to2:3; cross-products8×21=12×14=168.
Wintour V1.0 return test
Move the unknown through every position, scale up and down, use two- and three-part ratios, and hide the scale factor behind large numbers. A learner who still preserves correspondence has learned equivalence rather than a box-filling pattern.
Then change the context to recipe, pupils, money or measurement. The same factor should remain the invariant.
The learner’s final card
Which terms correspond? What multiplication or division turns one known term into the other? Did I use that same factor on every corresponding term? Can I simplify both completed ratios to the same form?
Continue through Batch 16
Use Guide 61 and Guide 62. Continue with Guide 64: Decimal Division and Rounding Accuracy.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All examples and solutions are original eduKate teaching material. This page is subordinate to the established ratio owner and isolates the missing-term equivalence skill.