CMDLearn

Learn

NCERT Class 6 Maths Chapter 7, Fractions, explained simply

CMDLearn ·

Chapter 7 of Ganita Prakash, the new NCERT Maths book for Class 6, teaches fractions the way children first meet them at home: by sharing. Two friends, Mukta and Shabnam, share rotis and pieces of chikki, and every rule in the chapter grows out of one question: how much does each person get?

This guide walks through the chapter section by section, in plain words, with worked answers and a short practice set at the end. Keep the textbook open next to it. Our explanations are our own; the textbook is the authority.

The one big idea: the fractional unit

When one whole is divided into equal parts, each part is a fractional unit (the book also calls it a unit fraction): 1/2, 1/3, 1/4, 1/5 and so on. Almost everything else in the chapter is about counting fractional units. The book suggests reading 3/4 not only as "three quarters" but as "3 times 1/4": that one phrase tells the child both the size of the piece (1/4) and how many pieces there are (3).

1. Fractional units and equal shares (section 7.1)

One roti shared equally by 2 children gives each 1/2. Shared by 4 children, each gets 1/4, which is less. The more people share one thing, the smaller each share.

The book uses this to fix a very common mistake. Asked which is greater, 1/5 or 1/9, many children say 1/9 "because 9 is bigger than 5". Think of the shares instead: one roti for 5 children, or one roti for 9 children? Each of the 9 gets a smaller piece, so 1/9 < 1/5, and in the same way 1/100 is bigger than 1/200.

2. Fractional units as parts of a whole (section 7.2)

Here the whole is a piece of chikki. Broken into 2 equal pieces, each piece is 1/2 of the chikki. The word "equal" matters: a chikki broken into one big and one small piece has not been halved. The book also shows a chikki cut into 6 equal pieces in two different ways: the pieces have different shapes but the same size, so each is still 1/6.

3. Measuring with fractional units, and reading fractions (section 7.3)

Fold a paper strip in half, then in half again, and it has 4 equal parts of 1/4 each. Two of them make 2/4, three make 3/4, four make 4/4, the whole strip. Quantities are measured by collecting fractional units: 1/2 + 1/2 + 1/2 is 3 times 1/2.

In 5/6, the top number 5 is the numerator (how many units) and the bottom number 6 is the denominator (which unit: sixths).

4. Fractions on the number line (section 7.4)

The length from 0 to 1 is one unit. To mark 1/5, split that unit into 5 equal parts; each part is 1/5 long, and 3 of them from 0 reach 3/5. The book asks how many fractions lie between 0 and 1. There is no end to them: between any two fractions you can always find another, for example halfway between them.

5. Mixed fractions (section 7.5)

When the numerator is smaller than the denominator, the fraction is less than 1; when it is larger, the fraction is more than 1. Such a fraction can be split into whole units and a part: 3/2 = 1 + 1/2, and 8/3 = 2 + 2/3, written 2 2/3 and read "two and two thirds". That is a mixed number (or mixed fraction): a whole part and a fractional part less than 1.

Going back is just counting units. In the book, Jaya turns 3 3/4 into a fraction: each whole is 4 quarters, so 3 wholes are 12 quarters, plus 3 more is 15/4.

6. Equivalent fractions and lowest terms (section 7.6)

Using a fraction wall of paper strips, the book shows that 1/2, 2/4 and 4/8 are exactly the same length: 1/2 = 2/4 = 4/8. These are equivalent fractions, the same amount written with different fractional units. The sharing view says the same thing: 1 roti for 2 children, 2 rotis for 4 children and 3 rotis for 6 children all give each child the same share.

Multiplying (or dividing) the numerator and the denominator by the same number gives an equivalent fraction. A fraction is in lowest terms (simplest form) when its numerator and denominator have no common factor except 1. To get there, divide both by their highest common factor: 16/20 ÷ 4/4 gives 4/5.

7. Comparing fractions (section 7.7)

The book's two steps: (1) change the fractions into equivalent fractions with the same denominator, the same fractional unit; (2) then compare the numerators.

Its example: which is greater, 4/5 or 7/9? A common multiple of 5 and 9 is 45, so 4/5 = 36/45 and 7/9 = 35/45. Since 36 > 35, 4/5 > 7/9. Mukta and Shabnam use the same idea for chikki: 1 chikki for 2 children (1/2 = 4/8) or 5 chikkis for 8 children (5/8)? The second group gets more.

8. Adding and subtracting fractions (section 7.8)

Meena eats 1/2 of a chikki and her brother eats 1/4. Cut the half into two quarters and you can see they ate 3 quarters together: 1/2 + 1/4 = 3/4.

With the same fractional unit, just add the units: 2/5 + 1/5 = 3/5, and 4/7 + 6/7 = 10/7 = 1 3/7. With different units, first make them the same. The book calls this Brahmagupta's method, after the mathematician who first described it in general in 628 CE:

  1. Find equivalent fractions with a common fractional unit (use a common multiple of the denominators).
  2. Add (or subtract) the numerators and keep the denominator.
  3. Write the answer in lowest terms if needed.

So 1/4 + 1/3 = 3/12 + 4/12 = 7/12, and 2/3 + 1/5 = 10/15 + 3/15 = 13/15. The same method works for subtraction.

9. A pinch of history (section 7.9)

In ancient India a fraction was called bhinna in Sanskrit, meaning "broken", and also bhaga or ansha, meaning a part. The way the whole world writes fractions today began in India: the Bakhshali manuscript (around 300 CE) already wrote one half as a 1 above a 2. The line between the numbers was added later by the Moroccan mathematician Al-Hassar in the 12th century.

Practice: 8 questions with answers

Try these on paper first. Answers are below.

  1. Which is bigger, 1/7 or 1/10? Say why in one line.
  2. 3 rotis are shared equally among 4 children. How much roti does each child get?
  3. Write 11/4 as a mixed fraction.
  4. Write 5 2/3 as a fraction.
  5. Write 18/24 in lowest terms.
  6. Which is bigger, 3/4 or 5/7?
  7. Add 2/5 + 1/3.
  8. Subtract 5/6 − 1/4.

Answers: 1) 1/7: one thing shared by 7 people gives bigger pieces than shared by 10. 2) 3/4 of a roti each (3 rotis divided by 4 children). 3) 2 3/4, since 8 quarters make 2 wholes and 3 quarters are left. 4) 17/3 (5 wholes are 15 thirds, plus 2). 5) 3/4, dividing both by 6. 6) 3/4: with denominator 28, 3/4 = 21/28 and 5/7 = 20/28. 7) 11/15 (6/15 + 5/15). 8) 7/12 (10/12 − 3/12).

Tips for parents and teachers

For practice, our free printable worksheets have fractions for Classes 4 to 6 and adding, subtracting and comparing fractions, in English, Hindi and Marathi with answer keys.

Where CMDLearn fits

CMDLearn is building an AI tutor for Classes 1 to 10 in Hindi, Marathi and English. Our first lesson teaches this very chapter: a teacher on screen uses the book's own roti and chikki examples, turns each section into a small game, and asks the child to explain their thinking instead of handing over answers. It is not available yet; join the waitlist to hear when early access to the AI tutor opens.

Source

Section numbers, the characters, the examples and the history are from the NCERT chapter. All explanations, answers and practice questions on this page are our own; every number was checked by calculation.

Practise this class: Class 6 worksheets, chapter by chapter · free practice, marked instantly