To express A as a fraction of B, write A as the numerator and B as the denominator: \(\frac{A}{B}\). Then simplify by dividing both by their HCF. Units must match — if they don't, convert first.
\[\text{A as a fraction of B} = \frac{A}{B} \quad \text{(simplify if possible)}\]
Example 1 — Express 18 as a fraction of 24
Step 1
Write as fraction: \(\frac{18}{24}\)
Step 2
Find the largest common factor (HCF) of 18 and 24 by listing factors: 18 → 1,2,3,6,9,18. 24 → 1,2,3,4,6,8,12,24. The largest one they share is 6.
Check your answer makes sense: The fraction must be less than 1 (if A is truly a part of B). If you get a fraction greater than 1, recheck which is the part and which is the whole.
✓ Quick Check 1 — Part over Whole
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Same Units First — Converting Before You Compare
You can only express one quantity as a fraction of another if they are in the same units. Convert first, then form the fraction.
Check units are the same → convert if needed → write part/whole → simplify
Example 3 — Express 30 cm as a fraction of 2 m
Step 1
Units differ. Convert 2 m to cm: \(2 \times 100 = 200\) cm
Step 2
Form fraction: \(\frac{30}{200}\)
Step 3
Simplify — largest common factor of 30 and 200 = 10: \(\frac{30 \div 10}{200 \div 10} = \mathbf{\frac{3}{20}}\)
Example 4 — Express 250 g as a fraction of 2 kg
Step 1
Convert 2 kg to g: \(2 \times 1000 = 2000\) g
Step 2
Fraction: \(\frac{250}{2000}\)
Step 3
Simplify — largest common factor = 250: \(\frac{250 \div 250}{2000 \div 250} = \mathbf{\frac{1}{8}}\)
Always convert to the smaller unit. If comparing cm and m, convert m to cm. If comparing g and kg, convert kg to g. This avoids decimals in your fraction.
✓ Quick Check 2 — Unit Conversion and Fractions
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Real-Life — Test Scores, Probability and Budgets
This skill appears constantly in exam questions. The key is identifying which number is the part and which is the whole, then simplifying carefully.
Example 5 — In a class of 36, 12 passed a test. What fraction passed?
Step 1
Part = 12 (passed), whole = 36 (total)
Step 2
Same units — both counts of students
Step 3
Fraction: \(\frac{12}{36}\)
Step 4
Simplify — largest common factor = 12: \(\mathbf{\frac{1}{3}}\) passed
Example 6 — A bag has 3 red, 5 blue and 2 green counters. What fraction are red?
Step 1
Total = \(3 + 5 + 2 = 10\) counters
Step 2
Red = 3. Fraction: \(\frac{3}{10}\)
Step 3
Largest common factor of 3 and 10 = 1 — already in simplest form. Answer: \(\mathbf{\frac{3}{10}}\)
✓ Quick Check 3 — Real-Life Problems
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Practice: Express as a Fraction
Write each answer as a fraction in its simplest form. Click Check All when done.
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Question
Answer
Result
1
Express 16 as a fraction of 40
2
Express 45 cm as a fraction of 3 m
3
6 out of 16 sweets are mint. Fraction?
4
Express 12 as a fraction of 30
5
Express 250 g as a fraction of 1 kg
6
9 out of 15 counters are red. Fraction?
7
Express 18 as a fraction of 45
8
Express 20 minutes as a fraction of 2 hours
9
14 out of 21 students passed. Fraction?
10
Express 8 as a fraction of 36
⚠ Things to Watch Out For
Putting numbers in the wrong order: A as a fraction of B = A/B (A on top, B on bottom). "15 as a fraction of 25" = 15/25 = 3/5. Reversing gives 25/15, a completely different answer.
Not converting to the same units: "30 cm as a fraction of 2 m" — convert first: 2 m = 200 cm. Then 30/200 = 3/20. Comparing cm to m directly gives wrong answers.
Forgetting to simplify: 15/25 should be simplified to 3/5. Always give the fraction in its simplest form.
Using the wrong "whole": Identify which quantity is the whole (denominator). "What fraction of the class got A grades?" — the whole class size goes on the bottom.
Fractions greater than 1: If A > B, the fraction will be greater than 1 — this is fine. "20 as a fraction of 15" = 20/15 = 4/3 = 1⅓.