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Fractions are where many students first feel that maths has stopped making sense. A bigger number on the bottom gives a smaller piece, and two fractions that look different can be equal. This post follows how NCERT's new Class 6 book teaches equivalent fractions and comparison, works through examples with numbers, and ends with a routine you can use this week.
What does the Class 6 Fractions chapter cover?
Chapter 7 of Ganita Prakash, NCERT's Class 6 mathematics book (first edition August 2024, Reprint 2026-27), starts from sharing. It moves through fractional units and equal shares, fractions as parts of a whole, measuring with fractional units, marking fractions on the number line, mixed fractions, equivalent fractions, comparing fractions, adding and subtracting fractions, and a section on history.
A fractional unit is a fraction with 1 on top, such as 1/2, 1/3 or 1/8. Every other fraction is built from these units: 3/8 is three units of 1/8.
What are equivalent fractions?
The book uses rotis. Look at three situations:
1 roti shared equally by 2 children
2 rotis shared equally by 4 children
3 rotis shared equally by 6 children
Each child gets the same amount every time, so 1/2 = 2/4 = 3/6. Fractions that give equal shares are called equivalent fractions. On a fraction wall made of paper strips, they line up at exactly the same length.
To make an equivalent fraction, multiply the numerator and denominator by the same number. 3/4 = 6/8 = 9/12 = 12/16. You are cutting each piece into smaller equal pieces, so you have more pieces, but the amount does not change.
How do you write a fraction in its simplest form?
A fraction is in lowest terms (simplest form) when its numerator and denominator have no common factor other than 1.
Worked example 1 (from the book). Simplify 16/20. Both numbers are divisible by 4, so 16 ÷ 4 = 4 and 20 ÷ 4 = 5, giving 4/5. Now 4 and 5 have no common factor except 1, so 4/5 is the simplest form.
The chapter says you can always do this in one step by dividing by the highest common factor, or in smaller steps. 24/36 can go 24/36 = 12/18 = 6/9 = 2/3, dividing by 2, 2 and then 3. Dividing by 12 at once gives the same 2/3.
How do you compare two fractions?
The chapter gives three cases, each with a reason you can say aloud.
Same denominator. 3/7 and 4/7 both use the unit 1/7. Four units are more than three, so 4/7 > 3/7.
Same numerator. 4/7 and 4/8 both share 4 rotis, but among 7 children or 8 children. More children means a smaller share each, so 4/7 > 4/8.
Different numerators and denominators. Rewrite both fractions with the same fractional unit.
Worked example 2 (from the book). Which is larger, 3/4 or 7/10? The book lists equivalent fractions of each until the denominators match. Using 20 as the common denominator:
3/4 = 15/20
7/10 = 14/20
15/20 > 14/20, so 3/4 > 7/10.
The book first goes up to 40, the product of the denominators (30/40 and 28/40), then notices that 20 also works.
Worked example 3. Compare 5/8 and 2/3. A common denominator is 8 × 3 = 24.
5/8 = 15/24
2/3 = 16/24
So 2/3 is larger, by 1/24.
Why do fractions feel harder than whole numbers?
Researchers call one cause the whole number bias: using rules that work for whole numbers where they do not apply. Ni and Zhou (2005) note in their review that many researchers agree children's difficulty with fractions is linked to their whole-number knowledge. A typical slip is thinking 1/8 is bigger than 1/6 because 8 is bigger than 6.
Getting this right matters. Using large data sets from the United States and the United Kingdom, Siegler and colleagues (2012) found that primary school students' knowledge of fractions and of division predicted their algebra knowledge and overall maths achievement in high school, 5 or 6 years later. This held even after accounting for other maths knowledge, general intellectual ability, working memory and family income and education.
Which mistakes cost the most marks?
Bigger denominator, bigger fraction. 1/8 is smaller than 1/6; picture the pieces.
Multiplying only the top or only the bottom. 3/4 is not equal to 6/4.
Stopping before lowest terms. 6/9 still shares the factor 3.
Comparing without a common unit. 3/4 and 7/10 cannot be compared by looking at 3 and 7.
Adding tops and bottoms. 1/2 + 1/3 is not 2/5; 2/5 is less than 1/2, which already shows it is wrong.
How should you practise this week?
Day 1: Fold paper strips into halves, quarters and eighths, and line up equal lengths.
Day 2: Write five fractions equal to 2/3 and five equal to 3/5.
Day 3: Simplify 18/24, 35/49, 45/60 and 28/42, first in steps and then in one step.
Day 4: Compare eight pairs, such as 5/6 and 7/9, and say the reason for each.
Day 5: Put 1/2, 3/8, 5/6, 2/3 and 3/4 in order from smallest to largest on a number line.
If the size of a fraction still feels hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. Fractions lead straight into decimals; see our post on decimals in Class 7. Simplest form uses the factors from prime time in Class 6.
At dinner tonight, split something into equal parts and name two equivalent fractions for one person's share.
