PSLE Math: Mastering Fractions and Ratios

Fractions and ratios make up roughly 30% of PSLE Math marks. That's not a typo—nearly a third of your child's math score depends on these two topics. Yet most students treat them as separate concepts, missing the connection that makes both easier to master.

Here's the thing: once you understand how fractions and ratios relate to each other, problem sums that seemed impossible suddenly make sense. This guide breaks down both topics with the techniques that actually work for PSLE.

Why Fractions and Ratios Trip Students Up

The biggest mistake? Treating fractions and ratios as completely different topics.

A fraction like 3/5 tells you "3 parts out of 5 total parts." A ratio like 3:2 tells you "3 parts to 2 parts." They're describing the same relationship from different angles. Students who grasp this connection solve problems faster because they can switch between forms depending on what the question asks.

The second issue is rushing through conversions. Many P6 students can do fraction operations mechanically but stumble when a word problem requires converting between fractions, ratios, and percentages mid-solution.

For a broader view of PSLE preparation strategies, understanding these foundational concepts is essential before tackling more complex problem sums.

Mastering Fractions: Core Techniques

Converting Between Forms

Every P6 student should be able to convert fluently between:

Quick conversion trick: To convert a fraction to percentage, make the denominator 100. Can't do that easily? Multiply top and bottom by whatever gets you close, then adjust.

3/4 → multiply by 25/25 → 75/100 → 75%

Operations with Fractions

PSLE tests four operations, but division causes the most errors. Here's the reliable method:

Dividing fractions: Keep the first fraction, flip the second, then multiply.

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Adding/subtracting with different denominators: Find the lowest common denominator (LCD) first. Don't just multiply the denominators—that creates unnecessarily large numbers.

1/4 + 2/6 → LCD is 12, not 24

= 3/12 + 4/12 = 7/12

Word Problem Strategy

For fraction word problems, identify these three things before calculating:

1. What's the whole? (The total amount)
2. What's the part? (What fraction represents)
3. What's being asked? (Find the part or find the whole?)

Example: Sarah spent 2/5 of her money on books and 1/4 on stationery. She had $42 left. How much did she have at first?

• Fraction spent: 2/5 + 1/4 = 8/20 + 5/20 = 13/20
• Fraction left: 1 - 13/20 = 7/20
• 7/20 of total = $42
• Total = $42 × 20/7 = $120

Mastering Ratios: Core Techniques

Understanding a:b and a:b:c

Ratios compare quantities. The order matters—a:b is different from b:a.

Two-part ratio (a:b): Compares two quantities

• Boys to girls = 3:2 means for every 3 boys, there are 2 girls

Three-part ratio (a:b:c): Compares three quantities

• Red:Blue:Green = 2:3:5 means for every 2 red, there are 3 blue and 5 green

Simplifying ratios: Divide all parts by their highest common factor (HCF).

• 12:18:24 → divide by 6 → 2:3:4

Dividing Quantities by Ratio

This question type appears in almost every PSLE paper.

Method: Find the total number of units, then find the value of one unit.

Example: $180 is divided between Ali and Ben in the ratio 4:5. How much does each person get?

• Total units: 4 + 5 = 9 units
• 1 unit = $180 ÷ 9 = $20
• Ali: 4 × $20 = $80
• Ben: 5 × $20 = $100

Before-After Ratio Problems

These are trickier because the ratio changes. The key is finding what stays constant.

Example: The ratio of John's stamps to Mary's stamps was 5:3. After John gave 20 stamps to Mary, the ratio became 3:5. How many stamps did John have at first?

Step 1: Make the "after" total equal to "before" total (no stamps were lost)

• Before: 5:3 → total 8 units
• After: 3:5 → total 8 units ✓

Step 2: Set up the comparison

• John before: 5 units, John after: 3 units
• Difference: 2 units = 20 stamps