Working with Fractions

Chapter focus

Fractions describe equal parts and rational quantities. Multiplication can find a fraction of a number, while division can split a quantity into equal groups or count how many fractional units fit.

NCERT CIET identifies fraction multiplication and division activities for this chapter. These original worked examples support the complete Ganita Prakash Part I lesson.

1. Multiply a fraction by a whole number

Multiplying 3/4 by 7 means seven groups of three-fourths: 7 × 3/4 = (7 × 3)/4 = 21/4 = 5 1/4. Equivalently, 3/4 of 7 is 5 1/4.

Reduce the final fraction where possible. If the numerator is larger than the denominator, write an improper fraction or convert it to a mixed number.

2. Divide a fraction by a natural number

Dividing a fraction into equal groups makes each share smaller. To divide by a non-zero whole number, multiply the denominator by that number:

(a/b) ÷ n = a/(b × n), for n ≠ 0.

Example: 1/3 ÷ 4 = 1/(3 × 4) = 1/12. One-third split into four equal parts gives one-twelfth in each part.

3. Multiply two fractions

Multiply the numerators together and the denominators together. Simplify before or after multiplication:

Example: 3/4 × 5/6 = 15/24 = 5/8.

A picture or area model can help: 3/4 of a rectangle shaded one way and 5/6 shaded another way overlap in 15 of 24 equal small regions.

4. Divide by a fraction

Division asks how many groups of the divisor fit into the dividend. Dividing by a fraction is equivalent to multiplying by its reciprocal:

(a/b) ÷ (c/d) = (a/b) × (d/c), when c/d ≠ 0.

Worked examples

2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4. There are four one-sixths in two-thirds.

1 3/4 ÷ 1/4 = 7/4 ÷ 1/4 = 7/4 × 4 = 7. Convert the mixed number to an improper fraction before dividing.

5. Estimate and check

Use benchmarks such as 0, 1/2 and 1 to judge whether an answer is sensible. For example, 3/4 × 5 is less than 5 but greater than half of 5, so 3 3/4 is a reasonable result; 15/4 = 3 3/4.

Multiplication and division are inverse operations. If 2/3 ÷ 1/6 = 4, check by multiplying: 4 × 1/6 = 4/6 = 2/3.

Common errors to avoid

• When multiplying fractions, multiply numerator by numerator and denominator by denominator; do not add denominators.
• When dividing by a fraction, invert the divisor only.
• Convert a mixed number to an improper fraction before applying fraction operations.
• Keep track of whether the problem asks for a number of groups or the size of each share.

Practice: draw or calculate

Chapter summary

Multiplication finds groups or parts of quantities. Division by a whole number shares a fraction into smaller equal parts; division by a fraction counts fractional-sized groups and uses the reciprocal. Estimate first and verify with the inverse operation.

Open Ganita Prakash Part I on NCERT · NCERT CIET Grade 7 resources