Every fraction has two parts:

• Numerator – the top number, which tells us how many parts we have
• Denominator – the bottom number, which tells us into how many equal parts the whole has been divided

Example: In the fraction $\frac{3}{4}$

• Numerator = 3 (we have 3 parts)
• Denominator = 4 (the whole is divided into 4 equal parts)

We can understand fractions by dividing real objects into equal parts.

Halves ($\frac{1}{2}$)

When we divide something into two equal parts, each part is called a half or $\frac{1}{2}$.

Example: Mussa cut an orange into two equal pieces. He gave one piece to his sister Neema.

• Each piece is $\frac{1}{2}$ of the orange
• Neema got $\frac{1}{2}$ of the orange
• Mussa kept $\frac{1}{2}$ of the orange

Quarters ($\frac{1}{4}$)

When we divide something into four equal parts, each part is called a quarter or $\frac{1}{4}$.

Example: Musa divided a soap bar into four equal pieces. He gave one piece to his sister.

• The whole soap bar = $\frac{4}{4}$
• One piece given = $\frac{1}{4}$ of the soap bar

Thirds ($\frac{1}{3}$)

When we divide something into three equal parts, each part is called a third or $\frac{1}{3}$.

We read fractions by saying the numerator first, then the denominator:

• $\frac{1}{2}$ → "one half"
• $\frac{1}{3}$ → "one third"
• $\frac{1}{4}$ → "one quarter" or "one fourth"
• $\frac{2}{3}$ → "two thirds"
• $\frac{3}{4}$ → "three quarters"

Question: A mother gave mangoes to her three children. Rashid got 2 mangoes, Irene got 2 mangoes, and Likweme got 2 mangoes. What fraction of mangoes did Rashid get?

Solution:

Step 1: Find the total number of mangoes Total = 2 + 2 + 2 = 6 mangoes

Step 2: Write as a fraction Rashid got 2 mangoes out of 6 mangoes Fraction = $\frac{2}{6}$

Answer: Rashid got $\frac{2}{6}$ of the mangoes.

• $\frac{4}{4}$ = one whole (all parts)
• $\frac{1}{2}$ = a half
• $\frac{1}{4}$ = a quarter
• $\frac{1}{3}$ = a third

1. How many $\frac{1}{3}$ are there in a whole thing? Answer: 3
2. How many $\frac{1}{5}$ are there in a whole thing? Answer: 5
3. Musa cut an orange into two equal pieces. What fraction of the orange did each person get? Answer: $\frac{1}{2}$

In everyday life in Tanzania, we use fractions when sharing food and items. For example, if you buy one chapati from a duka and share it equally with your friend, each of you gets half ($\frac{1}{2}$) of the chapati. Similarly, when a mother divides a cake among her children, or when a farmer divides his harvest into equal parts, they are using fractions — just like we learned by dividing objects into equal pieces.