Fractions as equal shares

The word fraction comes from the Latin word for broken: a whole is broken into equal parts. Shabnam and Mukta remember how this works.

• If one roti is shared equally between 2 children, each child gets half a roti, written 1/2 (we sometimes read it as 'one upon two').
• If one roti is shared equally among 4 children, each child gets 1/4 roti.

In the second group more children share the same one roti, so each gets a smaller share: 1/2 roti is more than 1/4 roti.

Then Beni asks Arvin which is greater, 1/5 or 1/9. Arvin guesses 1/9, because 9 is bigger than 5. Beni says that is a common mistake: think of shares! One roti shared among 5 children gives each 1/5 roti; shared among 9 children, each gets 1/9 roti. If you share with more people, you get less. So 1/9 < 1/5. In the same way, 1/100 is bigger than 1/200.

When one unit is divided into several equal parts, each part is called a fractional unit: 1/2, 1/3, 1/4, 1/5, …, 1/100 are all fractional units. A fraction tells us the size of an equal share. Three guavas of about the same size that together weigh 1 kg weigh about 1/3 kg each. 1 kg of rice packed equally into 4 packets makes packets of 1/4 kg each.

Four friends order 3 glasses of sugarcane juice and share it equally. Each glass shared by 4 gives each friend 1/4 glass, and there are 3 glasses, so each friend drinks 3/4 glass (three quarters of a glass).

Fraction words can be put in order of size too. From the smallest to the biggest: quarter, half, three quarters, one and a quarter, one and a half, two and a half.