What is a fraction?

A fraction is a number that names "a part of something". When a whole roti is cut into 4 equal pieces and you eat one piece, you have eaten $\frac{1}{4}$ of the roti.

What is this?

Every fraction has two numbers separated by a line. The bottom number , the denominator , tells how many equal parts the whole was cut into. The top number , the numerator , tells how many of those parts we are talking about.

So $\frac{3}{4}$ means: cut the whole into 4 equal parts and take 3 of them. The line in the middle quietly says "out of". Three out of four.

The two parts must be equal in size. If a chapati is cut into uneven pieces, we can't call any one of them "one-fourth". One-fourth means truly equal sharing.

Fractions also describe parts of a group, not just one object. If a basket has 12 mangoes and 3 are ripe, the ripe ones make $\frac{3}{12}$ of the basket. The whole here is the whole basket of 12.

When the numerator and denominator are the same, like $\frac{4}{4}$, we have the whole , 4 out of 4 parts is everything. When the numerator is 0, like $\frac{0}{5}$, we have nothing at all.

Worked examples

Example 1. A pizza is cut into 8 equal slices. Sara eats 3 slices. What fraction did she eat?

• Total slices = 8 (denominator).
• Slices eaten = 3 (numerator).
• Sara ate $\frac{3}{8}$ of the pizza.

Example 2. In a class of 30 children, 10 are wearing blue uniforms. What fraction wear blue?

• Out of 30 children, 10 wear blue.
• Fraction = $\frac{10}{30}$.

Example 3. Draw a rectangle and shade $\frac{2}{5}$ of it.

• Divide the rectangle into 5 equal strips.
• Shade any 2 strips.
• The shaded part is $\frac{2}{5}$.

Try it

1. A cake is cut into 6 equal pieces. Mira eats 1 piece. What fraction is left?
2. A box has 20 chocolates. Ankit eats 4. What fraction did he eat?
3. Write the fraction for: 5 out of 9 equal parts.
4. Draw a circle and shade $\frac{3}{4}$ of it.
5. What does $\frac{7}{7}$ stand for?

Hands-on

Paper-fold thirds. Take a strip of paper. Fold it carefully into 3 equal parts. Open it out. Colour one part. You have just made $\frac{1}{3}$.

Fruit fractions. Take 8 grapes. Eat 3. What fraction did you eat? What fraction is left? Say it aloud.