Mathematics — Numbers: Fractions

Age: 9 (Kenyan primary). These notes explain what fractions are, show easy pictures, and give short practice you can try at home (for example with chapati, mango or sweets).

1. What is a fraction?

A fraction shows a part of a whole. It has two numbers written like this: numerator / denominator.

• Denominator (bottom number) tells how many equal parts the whole is split into.
• Numerator (top number) tells how many of those parts we have.

2. Types of fractions

• Unit fraction: numerator is 1 (e.g. 1/2, 1/4).
• Proper fraction: numerator < denominator (e.g. 2/5).
• Improper fraction: numerator ≥ denominator (e.g. 5/4, 6/3).
• Mixed number: a whole number plus a proper fraction (e.g. 1 1/4).

3. Visual: improper to mixed

Example: 5/3. If you have 5 pieces and each whole needs 3 pieces, how many whole and parts?

So 5/3 = 1 2/3.

4. Equivalent fractions

Two fractions are equivalent if they show the same amount. Multiply or divide top and bottom by the same number.

We divided top and bottom of 2/4 by 2 to get 1/2. So 2/4 and 1/2 are the same amount.

5. Simplifying (put in simplest form)

1. Find a number that divides both top and bottom (a common factor).
2. Divide top and bottom by that number.

Example: simplify 6/8. Both 6 and 8 divide by 2 → 3/4. So 6/8 = 3/4.

6. Comparing fractions

If denominators are same, compare numerators: bigger numerator = bigger fraction.

If denominators are different, you can:

• change to equivalent fractions with same denominator, or
• use pictures (cut shapes to same sized parts) or convert to decimals (later).

7. Adding and subtracting fractions (same denominator)

Rule: keep the denominator, add or subtract the numerators.

If result is improper, change to mixed number: 3/2 = 1 1/2.

8. Short Kenya-style examples

• You share 1 chapati among 4 friends → each gets 1/4.
• You and a friend share 3 mangoes equally → each gets 3/2 = 1 1/2 mango.
• You have 6 sweets; you give each of 3 classmates 2 sweets → 6/3 = 2 whole sweets each.

9. Quick rules to remember

• Denominator = how many equal parts in the whole.
• Numerator = how many parts you have.
• To add/subtract, make denominators same first (if different) — for now, practise with same denominators.
• Simplify fractions by dividing top and bottom by a common number.

10. Practice (try these)

1. Write the numerator and denominator of 3/5.
2. What is 1/3 of a chapati if there are 3 friends?
3. Simplify 4/8.
4. Which is bigger: 2/7 or 3/7?
5. Find 1/4 + 2/4.
6. Change 7/4 into a mixed number.

Answers (click to view)

1. Numerator = 3, Denominator = 5.
2. Each friend gets 1/3 of the chapati.
3. 4/8 = 1/2 (divide top and bottom by 4).
4. 3/7 is bigger because 3 > 2 and denominators are same.
5. 1/4 + 2/4 = 3/4.
6. 7/4 = 1 3/4 (one whole and 3/4 left).

Teacher tip: Use real objects — cut paper circles or share snacks — children learn fractions fastest when they see and touch the parts.

End of notes