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Mathematics — Numbers: Fractions

1. What is a fraction?

A fraction shows a part of a whole. It has two numbers separated by a line:

1 2

1 over 2

Numerator (top number): how many parts we have.
Denominator (bottom number): how many equal parts make the whole.

2. Types of fractions

Unit fraction: numerator = 1, e.g. 1/3.
Proper fraction: numerator < denominator, e.g. 2/5.
Improper fraction: numerator ≥ denominator, e.g. 7/4.
Mixed number: whole number + proper fraction, e.g. 1 3/4.

3. Fractions using shapes (visuals)

Example: show 1/4 and 2/4 of a circle (like sharing a chapati).

1/4 (one part shaded)

2/4 (two parts shaded)

4. Equivalent fractions

Fractions that name the same amount are equivalent. Example: 1/2 = 2/4 = 4/8.

1/2

2/4

4/8

5. Simplifying fractions

Divide numerator and denominator by the same number (common factor).

Example: Simplify 6/8

6 ÷ 2 = 3, 8 ÷ 2 = 4 → 6/8 = 3/4

6. Comparing fractions

To see which is larger:

Make the denominators the same and compare numerators (like 2/3 and 3/4 → 8/12 and 9/12 → 3/4 is larger).
Or use cross multiplication: a/b ? c/d. Compare a×d and b×c.

7. Adding and subtracting fractions

Case 1 — Same denominator:

2/5 + 1/5 = (2+1)/5 = 3/5

Case 2 — Different denominators:

Make denominators the same: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

8. Multiplying and dividing fractions

Multiplication: multiply numerators and denominators.

2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2

Division: invert (reciprocal) the divisor and multiply.

3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8

9. Fractions on a number line

Example: place 1/4, 1/2, 3/4 on a number line from 0 to 1.

10. Everyday examples (Kenyan context)

Sharing a chapati among 4 friends: each gets 1/4.
Cutting a mango into 2: each half is 1/2.
If a packet of sweets has 10 and you eat 3, you ate 3/10 of the packet.

11. Practice questions

Write the numerator and denominator for the fraction 7/9.
Which is larger: 3/8 or 1/4? Show a short method.
Simplify 12/16.
Add: 3/7 + 2/7.
Find equivalent fractions for 2/3 (give two answers).
Multiply: 2/5 × 3/4.
Divide: 3/8 ÷ 3/4.

12. Answers

Numerator = 7, Denominator = 9.
Compare 3/8 and 1/4. Convert 1/4 = 2/8 so 3/8 > 2/8 → 3/8 is larger.
12/16 → divide by 4 = 3/4.
3/7 + 2/7 = (3+2)/7 = 5/7.
Equivalent fractions: 4/6, 6/9 (also 8/12, etc.).
2/5 × 3/4 = 6/20 = 3/10.
3/8 ÷ 3/4 = 3/8 × 4/3 = 12/24 = 1/2.

Tip: Always try to simplify your answer. When adding or subtracting with different denominators, find a common denominator first (often the lowest common multiple).

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