Mathematics — Numbers: Fractions

Age: 10 (Kenyan context) — Short notes and simple visuals to help you understand fractions.

1. What is a fraction?

A fraction shows a part of a whole. It looks like this:

1/4
numerator (top) = 1
denominator (bottom) = 4

- Numerator (nambari ya juu): how many equal parts we have.
- Denominator (nambari ya chini): how many equal parts make the whole.

Example in real life: If you share a cake among 4 children and one child gets 1 piece, that child has 1/4 of the cake.

2. Visuals — showing fractions

Each row shows a whole split into equal parts. Coloured parts are the fraction.

1/4
1 part shaded of 4 → 1/4
3/4
3 parts shaded of 4 → 3/4
1/2 = 2/4
Half (1/2) is same as two parts out of four (2/4)

3. Types of fractions

  • Proper fraction: numerator < denominator (e.g., 3/5).
  • Improper fraction: numerator ≥ denominator (e.g., 7/4). It is more than or equal to 1.
  • Mixed number: whole number and a proper fraction together (e.g., 1 3/4).
Convert improper to mixed: divide numerator by denominator. Example: 7 ÷ 4 = 1 remainder 3 → 7/4 = 1 3/4.

4. Equivalent fractions and simplifying

Equivalent fractions are different fractions that show the same part of a whole. Multiply or divide numerator and denominator by the same number.

1/2 = 2/4 = 3/6
6/8 simplified = 3/4
Divide top and bottom by 2 (common factor): 6÷2 / 8÷2 = 3/4

5. Comparing fractions

- If denominators are the same, the fraction with the larger numerator is bigger (3/5 < 4/5).
- If denominators are different, find common denominator or cross-multiply.

Example: Which is larger — 3/4 or 2/3?
Cross-multiply: 3×3 = 9 and 4×2 = 8 → 9 > 8 so 3/4 > 2/3.

6. Adding and subtracting fractions

- Same denominator: add or subtract numerators, keep the denominator. Example: 1/4 + 2/4 = 3/4.
- Different denominators: change to a common denominator first. Example: 1/3 + 1/6 → change 1/3 to 2/6 → 2/6 + 1/6 = 3/6 = 1/2.

7. Multiplying & dividing (short note)

- Multiply: multiply numerators and denominators: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.
- Divide: flip (reciprocal) the second fraction and multiply: (2/3) ÷ (3/4) = (2/3) × (4/3) = 8/9.

8. Practice (try these)

  1. Shade 2 out of 6 squares. What fraction is shaded? (Answer below)
  2. Simplify 8/12. (Answer below)
  3. Add: 1/4 + 2/8. (Answer below)
  4. Convert 11/4 to a mixed number. (Answer below)
  5. Which is greater: 5/8 or 3/5? (Answer below)
Answers
1) 2/6 (can simplify to 1/3).
2) 8/12 = divide by 4 → 2/3.
3) 1/4 + 2/8 → 1/4 + 1/4 = 2/4 = 1/2 (because 2/8 = 1/4).
4) 11 ÷ 4 = 2 remainder 3 → 11/4 = 2 3/4.
5) Compare 5/8 and 3/5 by cross-multiplying: 5×5 = 25, 8×3 = 24 → 5/8 > 3/5.

9. Tips for learning fractions

  • Draw pictures (bars or squares) — they help see the parts.
  • Always simplify your answers when possible.
  • Use everyday examples: sharing chapati, cutting mango slices or a cake.
  • Practice converting between improper fractions and mixed numbers often.
Note: Some Swahili words to help — numerator = "nambari ya juu", denominator = "nambari ya chini".

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