P5 Fractions: The Complete Guide to Add, Subtract & Multiply

Fractions are the topic P5 students love to hate — but once you master the 3 key skills (LCD, regrouping, and cancellation), every question becomes a recipe. Let’s break it down step by step.

What You Need Before Starting

Before diving in, make sure you’re comfortable with:

Equivalent fractions — $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$
Simplifying — dividing top and bottom by the same number
Mixed numbers vs improper fractions — $2\frac{3}{4} = \frac{11}{4}$

If these feel shaky, our Fraction Calculator below lets you practise converting and simplifying.

Part 1: Adding & Subtracting Fractions (Unlike Denominators)

When the denominators are different, you can’t add or subtract directly. You need a common denominator first.

Step-by-Step Method

Find the LCD (Lowest Common Denominator)
Convert each fraction to an equivalent fraction with the LCD
Add or subtract the numerators
Simplify if possible

Example 1: Adding Fractions

Calculate $\frac{2}{3} + \frac{1}{5}$

Step 1: Find the LCD of 3 and 5. The LCD is 15.

Step 2: Convert each fraction:

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \qquad \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$

Step 3: Add the numerators:

$\frac{10}{15} + \frac{3}{15} = \frac{13}{15}$

Answer: $\frac{13}{15}$

Example 2: Subtracting Fractions

Calculate $\frac{5}{6} - \frac{3}{4}$

Step 1: Find the LCD of 6 and 4. The LCD is 12.

Step 2: Convert each fraction:

$\frac{5}{6} = \frac{10}{12} \qquad \frac{3}{4} = \frac{9}{12}$

Step 3: Subtract the numerators:

$\frac{10}{12} - \frac{9}{12} = \frac{1}{12}$

Answer: $\frac{1}{12}$

💡 Finding the LCD Quickly

List the multiples of the larger denominator and stop as soon as the smaller denominator divides into it evenly. For 6 and 4: multiples of 6 are 6, 12 — and 4 goes into 12. Done!

Part 2: Adding & Subtracting Mixed Numbers

Adding Mixed Numbers

Method: Add the whole numbers first, then add the fractions using a common denominator. If the fraction part becomes improper, carry over.

Example 3: Adding Mixed Numbers (With Carry Over)

Calculate $2\frac{3}{4} + 1\frac{1}{2}$

Step 1: Add the whole numbers: $2 + 1 = 3$

Step 2: Find LCD of 4 and 2. The LCD is 4.

Step 3: Add the fractions: $\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}$

Step 4: Carry over: $3 + 1\frac{1}{4} = 4\frac{1}{4}$

Answer: $4\frac{1}{4}$

Subtracting Mixed Numbers (The Regrouping Trick)

This is where most students trip up. When the fraction you’re subtracting is bigger than the fraction you’re subtracting from, you need to regroup (borrow 1 from the whole number).

Example 4: Subtracting with Regrouping

Calculate $3\frac{1}{4} - 1\frac{5}{8}$

Step 1: Find the LCD of 4 and 8. The LCD is 8.

Step 2: Convert: $3\frac{1}{4} = 3\frac{2}{8}$

Step 3: Problem! $\frac{2}{8} < \frac{5}{8}$ — we can’t subtract. Regroup!

$3\frac{2}{8} = 2 + \frac{8}{8} + \frac{2}{8} = 2\frac{10}{8}$

Step 4: Now subtract:

$2\frac{10}{8} - 1\frac{5}{8} = 1\frac{5}{8}$

Answer: $1\frac{5}{8}$

Example 5: Subtracting from a Whole Number

What is $5 - 1\frac{3}{7}$ ?

Step 1: Regroup 5 — borrow 1 whole and write it as $\frac{7}{7}$ :

$5 = 4\frac{7}{7}$

Step 2: Subtract:

$4\frac{7}{7} - 1\frac{3}{7} = 3\frac{4}{7}$

Answer: $3\frac{4}{7}$

⚠️ Common Mistake: Forgetting to Regroup

Students often write $3\frac{2}{8} - 1\frac{5}{8} = 2\frac{3}{8}$ by subtracting $5 - 2 = 3$ in the numerator (flipping the subtraction). Always check: is the top fraction smaller? If yes, you must regroup first.

Part 3: Multiplying a Fraction by a Whole Number

The Word “Of” = Multiply

In math, “of” means multiply. When a question says ” $\frac{2}{5}$ of 15”, it means $\frac{2}{5} \times 15$ .

Method: Divide the whole number by the denominator, then multiply by the numerator.

Example 6: Fraction OF a Whole Number

Find $\frac{3}{4}$ of 12.

Step 1: Divide 12 into 4 equal parts: $12 \div 4 = 3$

Step 2: Take 3 of those parts: $3 \times 3 = 9$

Answer: 9

Example 7: Fraction × Whole Number

Calculate $\frac{5}{6} \times 9$

Step 1: Multiply the numerator by the whole number: $5 \times 9 = 45$

Step 2: Keep the denominator: $\frac{45}{6}$

Step 3: Simplify: $\frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}$

Answer: $7\frac{1}{2}$

💡 Shortcut: Cancel Before You Multiply

In Example 7, notice that 9 and 6 share a common factor of 3. Cancel first: $\frac{5}{\cancel{6}^2} \times \cancel{9}^3 = \frac{15}{2}$ . Much easier!

Part 4: Multiplying Two Fractions

The Algorithm

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Multiply the numerators together, multiply the denominators together, then simplify.

Example 8: Multiplying Two Fractions

Calculate $\frac{3}{4} \times \frac{8}{7}$

Step 1: Multiply numerators: $3 \times 8 = 24$

Step 2: Multiply denominators: $4 \times 7 = 28$

Step 3: Simplify: $\frac{24}{28} = \frac{6}{7}$

Answer: $\frac{6}{7}$

Cancellation: The Smart Shortcut

Cancellation means simplifying before you multiply, so you work with smaller numbers. Look for common factors between any numerator and any denominator.

Example 9: Cancellation in Action

Calculate $\frac{5}{6} \times \frac{9}{10}$ using cancellation.

Step 1: Look for common factors across the fractions:

5 (numerator) and 10 (denominator) share factor 5
9 (numerator) and 6 (denominator) share factor 3

Step 2: Cancel:

$\frac{\cancel{5}^1}{\cancel{6}^2} \times \frac{\cancel{9}^3}{\cancel{10}^2} = \frac{1}{2} \times \frac{3}{2}$

Step 3: Multiply: $\frac{1 \times 3}{2 \times 2} = \frac{3}{4}$

Answer: $\frac{3}{4}$

Example 10: Another Cancellation

Find $\frac{7}{10} \times \frac{5}{14}$ using cancellation.

Step 1: Look for common factors:

7 and 14 share factor 7
5 and 10 share factor 5

Step 2: Cancel and multiply:

$\frac{\cancel{7}^1}{\cancel{10}^2} \times \frac{\cancel{5}^1}{\cancel{14}^2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Answer: $\frac{1}{4}$

💡 Why Cancellation Matters

Without cancellation: $\frac{7 \times 5}{10 \times 14} = \frac{35}{140}$ — now you need to simplify a big fraction. With cancellation: you go straight to $\frac{1}{4}$ . Always cancel first!

Part 5: Multiplying Mixed Numbers

To multiply a mixed number by a whole number:

Convert the mixed number to an improper fraction
Multiply
Convert back to a mixed number

Example 11: Mixed Number × Whole Number

Calculate $5 \times 2\frac{3}{4}$

Step 1: Convert $2\frac{3}{4}$ to improper: $(2 \times 4 + 3) \div 4 = \frac{11}{4}$

Step 2: Multiply: $5 \times \frac{11}{4} = \frac{55}{4}$

Step 3: Convert back: $55 \div 4 = 13$ remainder $3$ , so $13\frac{3}{4}$

Answer: $13\frac{3}{4}$

Part 6: Word Problems

Fraction word problems appear in almost every PSLE paper. Here are the key types.

Type 1: Fraction of a Total

Example 12: Fraction of a Total

There are 35 apples in a basket. $\frac{4}{5}$ of them are red. How many red apples are there?

Step 1: $\frac{4}{5}$ of 35 means $\frac{4}{5} \times 35$

Step 2: Divide 35 into 5 parts: $35 \div 5 = 7$

Step 3: Take 4 parts: $4 \times 7 = 28$

Answer: 28 red apples

Type 2: Two-Step (Fraction of a Remainder)

Example 13: Fraction of a Remainder

James had 120 marbles. He gave $\frac{3}{8}$ of them to his brother. He then gave $\frac{2}{3}$ of the remaining marbles to his sister. How many marbles did James have left?

Step 1: Given to brother: $\frac{3}{8} \times 120 = 45$ marbles

Step 2: Remaining: $120 - 45 = 75$ marbles

Step 3: Given to sister: $\frac{2}{3} \times 75 = 50$ marbles

Step 4: Left with James: $75 - 50 = 25$ marbles

Answer: 25 marbles

Type 3: Multi-Step Challenge

Example 14: Challenge Problem

A baker made 72 cupcakes. $\frac{1}{3}$ of them were chocolate. $\frac{5}{8}$ of the remainder were vanilla. The rest were strawberry. How many strawberry cupcakes were there?

Step 1: Chocolate: $\frac{1}{3} \times 72 = 24$ cupcakes

Step 2: Remainder: $72 - 24 = 48$ cupcakes

Step 3: Vanilla: $\frac{5}{8} \times 48 = 30$ cupcakes

Step 4: Strawberry: $48 - 30 = 18$ cupcakes

Answer: 18 strawberry cupcakes

⚠️ Don't Take the Fraction of the Wrong Total

In Example 14, the vanilla fraction ( $\frac{5}{8}$ ) is of the remainder (48), NOT of the original total (72). Always read carefully: “of the remaining” tells you to use the leftover amount.

Quick Reference Table

Operation	Method	Key Step
Add/Subtract (unlike)	Find LCD, convert, then add/subtract numerators	LCD = smallest number both denominators divide into
Add mixed numbers	Add wholes, add fractions, carry over if needed	If fraction > 1, move the extra whole over
Subtract mixed numbers	Convert to LCD, regroup if needed, then subtract	If top fraction < bottom fraction, borrow 1 whole
Fraction × whole	Multiply numerator by whole, keep denominator	Cancel common factors first
Fraction × fraction	Multiply tops, multiply bottoms	Cancel across before multiplying
Mixed × whole	Convert to improper, multiply, convert back	Remember: $a\frac{b}{c} = \frac{ac + b}{c}$

Try It Yourself

Use our interactive Fraction Calculator to check your working. Enter any two fractions and see the full step-by-step solution.

Fraction Calculator

What do you want to do?

First Fraction

Second Fraction

Common Mistakes to Avoid

Mistake	Example	Fix
Adding denominators	$\frac{2}{3} + \frac{1}{5} = \frac{3}{8}$	Find LCD first, then add numerators only
Forgetting to regroup	$3\frac{2}{8} - 1\frac{5}{8} = 2\frac{3}{8}$	If top fraction is smaller, borrow 1 whole
Not simplifying	$\frac{24}{28}$ left unsimplified	Always check for common factors in your answer
Wrong “of” total	Taking fraction of original instead of remainder	Read carefully — “of the remaining” means use the leftover
Skipping cancellation	Multiplying big numbers then simplifying	Cancel across fractions before multiplying

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P5 Fractions: Add, Subtract & Multiply (Complete Guide)