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Fractions

    Introduction

    Fractional Units and Equal Shares

    Fractional Units as Parts of a Whole

    Measuring Using Fractional Units

    Marking Fraction Lengths on the Number Line

    Improper and Mixed Fractions

    Equivalent Fractions

    Comparing Fractions

    Addition and Subtraction of Fractions

    A Pinch of History

    Summary

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Fractions > Fractional Units and Equal Shares

Fractional Units and Equal Shares

Beni: Which fraction is greater — 15 or 19?

Arvin: is bigger than .

So I would guess that 19 is greater than 15. Am I right?

Beni: ! That is a common mistake. Think of these fractions as shares.

Arvin: If one roti is shared among 5 children, each one gets a share of roti.

If one roti is shared among 9 children, each one gets a share of 19 roti?

Beni: Exactly! Now think again - which share is higher?

Arvin: If I share with more people, I will get less. So, 19 15.

Beni: You got it!

When one unit is divided into several equal parts, each part is called a fractional unit. These are all units:

12, 13, 14,15,16,17,18.....110.....150....1100.

We also sometimes refer to fractional units as ‘unit fractions.’

Fill in the blanks with fractions.

1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh kg.

2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is kg.

3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank glass of sugarcane juice.

4. The big fish weighs 12 kg. The small one weighs 14 kg. Together they weigh kg.

5. Arrange these fraction words in order of size from the smallest to the biggest in the empty box below:

One and a half, three quarters, one and a quarter, half, quarter,two and a half.

half
three quarters
one and a quarter
quarter
One and a half
two and a half

Fractions have been used and named in India since ancient times.

In the Rig Veda, the fraction 34 is referred to as tri-pada.

This has the same meaning as the words for 34 in many Indian languages today, e.g., ʻteen paavʼ in colloquial Hindi and ‘mukkaal’ in Tamil.

Indeed, words for fractions used today in many Indian languages go back to ancient times.

Find out and discuss the words for fractions that are used in the different languages spoken in your home, city, or state.

Ask your grandparents, parents, teachers, and classmates what words they use for different fractions, such as for one and a half, three quarters, one and a quarter, half, quarter, and two and a half, and write them here: