Fractions | Mathematics Grade 6 CBSE

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The six ideas of fractions

A fraction names a part of a whole — but it can be renamed, compared, added and placed on a number line. Tap each term to see what it means with a quick example.

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The three big ideas

A fraction shows equal parts of a whole. The whole must first be split into equal parts — unequal pieces are not fractions.
In a fraction like 3/4, the bottom number (denominator) tells how many equal parts the whole is divided into, and the top number (numerator) tells how many of those parts are taken.
Every fraction has a place on the number line: to mark 3/4, divide the gap from 0 to 1 into 4 equal steps and count 3 of them.
A proper fraction (like 3/4) is less than 1; an improper fraction (like 5/4) is 1 or more.

Worked example. A pizza is cut into 8 equal slices. Meera eats 3 slices. What fraction did she eat, and where does it sit on a number line from 0 to 1?

Parts taken = 3, total equal parts = 8, so she ate 3/8.

On the number line, split 0 to 1 into 8 equal steps; 3/8 is the third mark — closer to 0 than to 1.

Common mistake: calling unequal pieces a fraction. 3/8 only makes sense when all 8 slices are the same size.

Equivalent fractions name the same amount. Multiply (or divide) the numerator and the denominator by the same non-zero number and the value does not change: 1/2 = 2/4 = 3/6 = 4/8.
Dividing top and bottom by their common factor gives the simplest form — for example 6/9 = 2/3.
Comparing like fractions (same denominator): the one with the bigger numerator is larger, e.g. 5/7 > 3/7.
Comparing unlike fractions (different denominators): first rewrite them as equivalent fractions with the same denominator, then compare numerators.

Worked example. Who ate more chocolate — Anil who ate 2/3 of a bar, or Sara who ate 3/4 of an identical bar?

Make the denominators the same. A common denominator of 3 and 4 is 12.

2/3 = 8/12 and 3/4 = 9/12. Since 9/12 > 8/12, Sara ate more.

Common mistake: judging by the numerator alone. 2/3 is not smaller than 3/4 just because 2 < 3 — you must compare them on the same denominator.

To add or subtract like fractions (same denominator), add or subtract only the numerators and keep the denominator unchanged: 2/9 + 4/9 = 6/9.
Simplify the answer if you can: 4/10 = 2/5.
A mixed number is a whole number with a fraction, like 2¾. It equals an improper fraction: 2¾ = (2×4 + 3)/4 = 11/4.
To turn an improper fraction back into a mixed number, divide: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2¾.

Worked example. A glass holds 7/8 litre of milk. A child drinks 3/8 litre. How much is left?

Same denominator, so subtract the numerators: 7/8 − 3/8 = (7 − 3)/8 = 4/8.

Simplify: 4/8 = 1/2 litre left.

Common mistake: adding the denominators too — 2/9 + 4/9 is 6/9, not 6/18. The denominator names the size of each part and stays the same.

Where you'll meet it

Fractions at work

In the kitchen

A recipe asks for ½ cup of dahi and ¾ cup of flour. Measuring cups are marked in fractions, and doubling a recipe means doubling each fraction — fractions keep the cooking fair.

Sharing a bill

Four friends split a ₹240 snack equally — each owes 1/4 of the total, ₹60. Fractions turn "share it equally" into an exact amount.

Reading a scale

A measuring tape, a fuel gauge that shows half a tank, or a clock at quarter past — all use fractions to describe a part of a whole at a glance.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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