Equivalent ratios after PSLE is a useful post-PSLE Mathematics bridge because it makes one familiar idea precise before Secondary 1 combines more symbols, faster working and less room for guesswork.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. If a mistake keeps returning, the Punggol Mathematics diagnostic guide helps identify whether the difficulty is fluency, interpretation, strategy or execution.
At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT. The goal is not to rush ahead, but to make the important connection stable enough that later algebra feels familiar.
WhatsApp eduKatePunggol about a post-PSLE Mathematics transition plan
The short answer: equivalent ratios keep the same multiplicative relationship
2:3, 4:6 and 10:15 are equivalent ratios.
Each new ratio is made by multiplying or dividing both parts by the same non-zero factor.
Why both sides must change together
If 2:3 becomes 4:3, only the first quantity doubled. The relationship changed.
If both quantities double, 2:3 becomes 4:6 and the relationship stays the same.
Worked example: find a missing ratio value
2:5 = 6:x.
The first part has been multiplied by 3, so the second part must also be multiplied by 3.
x = 15.
Use division to simplify ratios
18:30 can be simplified by dividing both parts by their HCF, 6.
18:30 = 3:5.
The ratio is simpler, but the comparison remains unchanged.
Equivalent ratios connect to fractions
The ratio 2:3 can be represented by the fraction 2/3 when comparing the first quantity directly with the second.
Since 2/3 = 4/6 = 10/15, fraction equivalence and ratio equivalence share the same scaling structure.
Equivalent ratios connect to direct proportion
If two quantities stay in the ratio 2:3, scaling one by a factor requires scaling the other by the same factor.
That is the heart of direct proportion.
Read Direct Proportion After PSLE.
Worked example: recipe scaling
A recipe uses flour:sugar = 3:2. If flour becomes 450 g instead of 300 g, the scale factor is 450 ÷ 300 = 1.5.
Sugar must also scale by 1.5. If the original sugar was 200 g, the new amount is 300 g.
Units still matter
If a ratio compares 2 m with 50 cm, convert to a common unit before simplifying.
2 m : 50 cm = 200 cm : 50 cm = 4:1.
A ratio-scaling routine
- Write the ratio in the correct order.
- Identify the scale factor on one side.
- Apply the same factor to the other side.
- Convert units first if necessary.
- Simplify when useful.
- Check the two ratios express the same quotient.
Independent practice with answers
- Complete 3:4 = 9:x.
- Simplify 24:36.
- Are 5:8 and 15:24 equivalent?
- A 2:7 ratio is scaled so the first part is 10. Find the second part.
- Convert and simplify 1 m : 25 cm.
Answers: 12; 2:3; yes; 35; 4:1.
Frequently asked questions
Can I add the same number to both parts?
No. Equivalent ratios preserve multiplicative scaling, not additive change.
Why use the HCF to simplify?
It removes the largest common numerical factor in one step.
What should students read next?
Continue to Ratio, Rate and Percentage After PSLE and Scale Drawings After PSLE.
Continue through the post-PSLE Mathematics route
- After PSLE — Should My Child Start Secondary 1 Maths Early?
- Secondary 1 Math Readiness Checklist After PSLE
- Ratio, Rate and Percentage After PSLE
- Scale Drawings After PSLE
The post-PSLE period is best used to make meanings cleaner, not to race through chapters. A child who can explain the relationship is much better prepared for new notation later.
