Chapter 5: Sharing and Measuring

When you share a chocolate bar with your sister, how big is each piece? Welcome to the world of fractions , numbers that mean "part of a whole".

What we'll learn

• The meaning of half, quarter and third.
• How to write fractions like $\frac{1}{2}$, $\frac{1}{4}$, $\frac{3}{4}$.
• Equal sharing of objects and groups.
• Comparing two simple fractions.

The big idea

A fraction tells us how many equal parts of a whole we have. If you cut a roti into 2 equal pieces and take 1, you have $\frac{1}{2}$ of the roti.

The bottom number (denominator) says how many equal parts the whole is cut into. The top number (numerator) says how many of those parts we take. So $\frac{3}{4}$ means cut the whole into 4 equal parts and take 3.

Equal sharing is the heart of fractions. If 12 sweets are shared equally between 4 friends, each gets 12 ÷ 4 = 3 sweets. If only 1 pizza is shared between 4 friends, each gets $\frac{1}{4}$ of the pizza.

Comparing fractions can be tricky. $\frac{1}{2}$ is bigger than $\frac{1}{4}$ even though 4 is bigger than 2. That's because the more pieces you cut, the smaller each piece becomes.

Two fractions can equal each other. $\frac{1}{2}$ = $\frac{2}{4}$ = $\frac{4}{8}$. Same amount of chocolate, just cut into different sizes!

Explore with examples

1. Rina cuts a roti into 4 equal pieces and eats 1. What fraction is left?

Left = 4 − 1 = 3 pieces out of 4 = $\frac{3}{4}$.

2. Share 20 mangoes equally among 5 children. How many each?

20 ÷ 5 = 4 mangoes each.

3. Which is more: $\frac{1}{2}$ of a chocolate or $\frac{1}{3}$ of the same chocolate?

$\frac{1}{2}$ means 2 equal pieces; $\frac{1}{3}$ means 3 equal pieces. Bigger pieces in halves. So $\frac{1}{2}$ is more.

4. Colour $\frac{2}{6}$ of this strip.

Divide the strip into 6 equal parts and colour any 2. Notice $\frac{2}{6}$ is the same as $\frac{1}{3}$.

Hands-on activities

Paper Folding Fractions

Take a square paper. Fold it once , you have 2 equal parts ($\frac{1}{2}$ each). Fold again , 4 parts ($\frac{1}{4}$ each). Fold once more , 8 parts ($\frac{1}{8}$ each). Open and colour one part of each fold a different colour.

Fair Share

Take 15 grapes (or buttons). Share them equally between 3 people, then between 5 people. What if you try sharing between 4? What does that "extra" tell you?

Chapati Cut

Roll a small roti from atta or clay. Cut it into 3 equal pieces. Take 2 of them. You're holding $\frac{2}{3}$. Now cut each piece into 2 , you have $\frac{4}{6}$. Same amount!

Try it yourself

1. What is $\frac{1}{2}$ of 10?
2. What is $\frac{1}{4}$ of 16?
3. Which is bigger: $\frac{2}{3}$ or $\frac{1}{3}$?
4. Share 18 toffees among 6 children. How many each?
5. Draw a circle and shade $\frac{3}{4}$ of it.
6. Is $\frac{2}{4}$ the same as $\frac{1}{2}$? Why?
7. 6 ladoos to be shared by 4 children equally. How many full ladoos and what fraction each?

Recap

• A fraction is part of a whole when split into equal parts.
• $\frac{1}{2}$ is half, $\frac{1}{4}$ is a quarter, $\frac{1}{3}$ is a third.
• The bigger the denominator, the smaller each piece.
• Different fractions can mean the same amount (equivalent fractions).