NCERT Book Class 6 Maths Fractions PDF Download

Chapter 7: Fractions

Recall that when some whole number of things are shared equally among some number of people, fractions tell us how much each share is.

Shabnam: Do you remember, if one roti is divided equally between two children, how much roti will each child get?

Mukta: Each child will get half a roti.

Shabnam: The fraction 'one half' is written as \( \frac{1}{2} \). We also sometimes read this as 'one upon two.'

Mukta: If one roti is equally shared among 4 children, how much roti will one child get?

Shabnam: Each child's share is \( \frac{1}{4} \) roti.

Mukta: And which is more \( \frac{1}{2} \) roti or \( \frac{1}{4} \) roti?

Shabnam: When 2 children share 1 roti equally, each child gets \( \frac{1}{2} \) roti. When 4 children share 1 roti equally, each child gets \( \frac{1}{4} \) roti. Since, in the second group more children share the same one roti, each child gets a smaller share. So, \( \frac{1}{2} \) roti is more than \( \frac{1}{4} \) roti.

7.1 Fractional Units and Equal Shares

Beni: Which fraction is greater - \( \frac{1}{5} \) or \( \frac{1}{9} \)?

Arvin: 9 is bigger than 5. So I would guess that \( \frac{1}{9} \) is greater than \( \frac{1}{5} \). Am I right?

Beni: No! 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 \( \frac{1}{5} \) roti. If one roti is shared among 9 children, each one gets a share of \( \frac{1}{9} \) roti?

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

Arvin: If I share with more people, I will get less. So, \( \frac{1}{9} < \frac{1}{5} \).

Beni: You got it!

Teacher's Note

When comparing unit fractions (fractions with numerator 1), the one with the smaller denominator is always larger. Think of it this way: if you divide something into fewer pieces, each piece is bigger. So \( \frac{1}{2} > \frac{1}{3} > \frac{1}{4} \), even though 2 < 3 < 4. This is the opposite of what happens with whole numbers.

When one unit is divided into several equal parts, each part is called a fractional unit. These are all fractional units: \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \ldots, \frac{1}{10}, \ldots, \frac{1}{50}, \ldots, \frac{1}{100} \), etc.

We also sometimes refer to fractional units as unit fractions.

Figure it Out

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 \( \frac{1}{2} \) kg. The small one weighs \( \frac{1}{4} \) kg. Together they weigh ____ kg.

Knowledge from the past!

Fractions have been used and named in India since ancient times. In the Rig Veda, the fraction \( \frac{3}{4} \) is referred to as tri-pada. This has the same meaning as the words for \( \frac{3}{4} \) in many Indian languages today, e.g., 'teen paav' 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:

__________ __________ __________ __________ __________ __________

Teacher's Note

Learning fraction words in your own language helps you understand fractions better. Every language has its own way of naming fractions, and many of these come from ancient times. When you know these words, you connect maths to your daily life and culture.

1. 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. Write your answer here.

Key Points

• A fraction represents a part of a whole that has been divided into equal pieces. When you write \( \frac{1}{n} \), it means one whole has been split equally into \( n \) parts.
• A unit fraction always has 1 as the numerator. When comparing unit fractions, the smaller the denominator, the larger the fraction - so \( \frac{1}{3} \) is bigger than \( \frac{1}{5} \) because 3 parts make bigger pieces than 5 parts.
• Fractions help us describe equal sharing. If you share one item among more people, each person gets a smaller share.

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