Working with Fractions - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Fractions appear whenever a whole is divided into equal parts: food, distance, time, money, recipes, and probability. This chapter moves beyond naming fractions into operating with them and interpreting what the answer means.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Fraction meaning

A fraction a/b means a parts out of b equal parts. The denominator tells the size of each part; the numerator tells how many such parts.

Equivalent fractions

Fractions can look different but represent the same value: 1/2 = 2/4 = 5/10. Equivalent fractions help in comparison and addition.

Operations

Addition and subtraction need like denominators. Multiplication can be seen as 'part of a part'. Division by a fraction asks how many of that fraction fit.

3. Rules and formulas to remember

• Equivalent fraction: a/b = (a x k)/(b x k). k cannot be zero.
• Add like fractions: a/b + c/b = (a + c)/b. Same denominator required.
• Multiply fractions: a/b x c/d = ac/bd. Simplify before or after multiplying.
• Fraction of quantity: a/b of N = (a x N)/b. Useful in word problems.

4. Worked examples

Example 1: Add 3/8 + 1/8.

Same denominator: (3 + 1)/8 = 4/8 = 1/2.

Example 2: Add 2/3 + 1/4.

LCM of 3 and 4 is 12. 2/3 = 8/12, 1/4 = 3/12. Sum = 11/12.

Example 3: Find 3/5 of 80.

80 divided by 5 = 16, then 16 x 3 = 48.

Example 4: Multiply 7/9 x 3/14.

Cancel 7 with 14 and 3 with 9: result = 1/6.

5. Activity corner

Use paper strips of the same length. Fold one into halves, one into thirds, one into sixths. Students can physically compare 1/2, 1/3, and 1/6 and see why common denominators help.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Adding denominators directly Fix: 1/3 + 1/3 = 2/3, not 2/6.
• Mistake: Comparing only numerators Fix: 3/8 is less than 3/5 because fifths are larger parts.
• Mistake: Forgetting to simplify Fix: Reduce answers when possible unless the question asks otherwise.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Simplify 12/18.
2. Find 5/6 - 1/3.
3. Find 2/7 of 63.
4. Multiply 4/5 x 15/16.
5. Which is greater: 5/8 or 3/4?
6. Why do unlike fractions need common denominators for addition?

9. Answer key

1. Simplify 12/18. Answer: 2/3.

2. Find 5/6 - 1/3. Answer: 1/2.

3. Find 2/7 of 63. Answer: 18.

4. Multiply 4/5 x 15/16. Answer: 3/4.

5. Which is greater: 5/8 or 3/4? Answer: 3/4, because 3/4 = 6/8.

6. Why do unlike fractions need common denominators for addition? Answer: Because the parts must be of the same size before combining.

10. Quick revision

• Main themes: fractions, equivalent fractions, operations, word problems.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.