NCERT Solutions Ganita Prakash (Part 1) Chapter 8 –182Multiplying Numerators and Denominators; Simplifying to Lowest Form — In-text Questions

Book page 181 Updated on2026-09-05

Q1.

Now, find ⁵⁄₁₂ × ⁷⁄₁₈.

Answer

Follow the same two steps, but with the general numbers.

Whole cut into 18 rows and 12 columns = 12 × 18 parts
7/18 ÷ 12 = 7/(12 × 18)
Multiply by 5: (5 × 7)/(12 × 18)
= 35/216

⁵⁄₁₂ × ⁷⁄₁₈ = ³⁵⁄₂₁₆

In general — Brahmagupta's formula (Brāhmasphuṭasiddhānta, 628 CE):

^a⁄_b × ^c⁄_d = (a × c)/(b × d)

Did you know? The same formula works when one number is a whole number — just write it with denominator 1. For example 3 × ³⁄₄ = ³⁄₁ × ³⁄₄ = ⁹⁄₄.

Q2.

Multiply the following fractions and express the product in its lowest form: ¹²⁄₇ × ⁵⁄₂₄

Answer

Cancel the common factor before multiplying.

12/7 × 5/24 = (12 × 5)/(7 × 24)
12 and 24 share the factor 12
12 ÷ 12 = 1, 24 ÷ 12 = 2
= (1 × 5)/(7 × 2)
= 5/14

Why it is allowed: a fraction does not change when its numerator and denominator are divided by the same number. Cancelling first keeps the numbers small — multiplying first would give ⁶⁰⁄₁₆₈, which still simplifies to ⁵⁄₁₄.

Q3.

Let us use the same technique to do one more multiplication. ¹⁴⁄₁₅ × ²⁵⁄₄₂

Answer

Cancel across the numerators and denominators, then multiply.

14/15 × 25/42 = (14 × 25)/(15 × 42)
14 and 42 share 14 → 1 and 3
25 and 15 share 5 → 5 and 3
= (1 × 5)/(3 × 3)
= 5/9

Did you know? Reducing a fraction to its lowest terms is called apavartana in India. The Jaina scholar Umasvati (c. 150 CE) used it as a simile even in a philosophical work.

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