Fraction of an Amount: Divide Then Multiply

M12Fraction of an Amount

Find a fraction of a quantity by dividing and multiplying.

Fractions show parts of shapes… and of amounts!

What is 34 of 20?

Answer

Split 20 into 4 equal groups (20 ÷ 4 = 5). Take 3 groups (5 × 3 = 15).

💡 We can find a fraction of an amount by: dividing by the denominator, then multiplying by the numerator.

Learn the Method

1Read the question carefully.

Identify the fraction and the amount.

34 of 20

2Divide by the denominator.

Divide the amount by the bottom number.

20 ÷ 4 = 5

3Multiply by the numerator.

Multiply your answer by the top number.

5 × 3 = 15

4Write the answer.

This is the fraction of the amount.

Worked Example

Find 25 of 35.

Step 1 · Divide by the denominator

35 ÷ 5 = 7

→

Step 2 · Multiply by the numerator

7 × 2 = 14

→

✓ Answer

So, 25 of 35 is 14.

Watch Out! Common Mistakes

Forgetting the final multiply.

34 of 20 = 20 ÷ 4 = 5 ✕

Wrong! 5 is only 14 of 20. Multiply by the top number: 5 × 3 = 15.

Dividing by the numerator.

34 of 20 = 20 ÷ 3 × 4 = 26.67 ✕

Wrong! You must divide by the denominator (4), not the numerator (3).

Using the whole amount as the answer.

34 of 20 = 20 ✕

Wrong! A fraction of an amount must be less than the whole amount (when the fraction is less than 1).

⭐ Top Tip: divide first! 34 of 20 = 20 ÷ 4 × 3 = 5 × 3 = 15. Multiplying first (20 × 3 = 60, then ÷ 4) gives the same answer, but dividing first keeps the numbers small and easy.

⬇ Cheat Sheet

FRACTION OF AN AMOUNT

Divide the amount by the denominator.
Multiply by the numerator.
Write your answer.

Example: Find 34 of 20. 20 ÷ 4 = 5, 5 × 3 = 15.
Remember: divide first, then multiply!

📖 Continue Your Journey

✓ M1 What Are Fractions?✓ M2 Equivalent Fractions ✓ M3 Simplifying Fractions ✓ M4 Comparing Fractions ✓ M5 Ordering Fractions ✓ M6 Adding Fractions (Same Denominator)✓ M7 Adding Fractions (Different Denominator)✓ M8 Subtracting Fractions (Same Denominator)✓ M9 Multiplying Fractions ✓ M10 Dividing Fractions ✓ M11 Mixed Numbers M12 Fraction of an Amount M13 Percentage

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Next Lesson: M13 PercentagePercent means ‘out of 100’.

📄 Free printable: Download the Fraction of an Amount cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Divide the amount by the denominator: 20 ÷ 4 = 5.
Multiply the result by the numerator: 5 × 3 = 15. So 3/4 of 20 = 15.
Dividing first keeps the numbers small and easy.
Sense-check: a fraction of an amount (below 1) must be smaller than the whole amount.

Frequently asked questions

How do you find a fraction of an amount?

Divide the amount by the denominator, then multiply by the numerator. For 2/5 of 35: 35 ÷ 5 = 7, then 7 × 2 = 14.

Do you divide or multiply first?

Both orders give the same answer, but dividing first keeps the numbers smaller and easier — 20 ÷ 4 × 3 uses 5 × 3, while 20 × 3 ÷ 4 means working with 60.

What are common mistakes with fraction of an amount?

Stopping after the division (giving 1/4 of the amount instead of 3/4), dividing by the numerator instead of the denominator, and giving an answer bigger than the whole amount.

Where does this appear in real life?

Everywhere — sale discounts (1/3 off), sharing money, recipes and time. It is also one of the most frequent 11+ and SATs question types.