NCERT Solutions Ganita Prakash (Part 1) Chapter 8 –181Multiplying Fractional Units — Figure it Out
Book page 180 Updated on2026-09-05
Q1.
Find the following products. Use a unit square as a whole for representing the fractions: (a) 1⁄3 × 1⁄5 (b) 1⁄4 × 1⁄3 (c) 1⁄5 × 1⁄2 (d) 1⁄6 × 1⁄5
Answer
Cut the unit square into rows (first denominator) and columns (second denominator), then shade one cell.
Question
Rows × columns
Product
(a) 1/3 × 1/5
3 × 5 = 15 parts
1/15
(b) 1/4 × 1/3
4 × 3 = 12 parts
1/12
(c) 1/5 × 1/2
5 × 2 = 10 parts
1/10
(d) 1/6 × 1/5
6 × 5 = 30 parts
1/30
The picture for (a): one-third of one-fifth is one cell out of 15, that is 1⁄15.
Why it happens: the horizontal cuts and the vertical cuts are independent, so the number of small cells is always rows × columns.
Q2.
Now, find 1⁄12 × 1⁄18.
Answer
Drawing 216 little cells would be painful — use the pattern instead.
Number of rows = 18 (denominator of the multiplicand)
Number of columns = 12 (denominator of the multiplier)
Whole is cut into 18 × 12 = 216 equal parts
1/18 × 1/12 = 1/(18 × 12) = 1/216
In general, for two fractional units:
1⁄b × 1⁄d = 1/(b × d)
Tip: when a picture becomes clumsy, look at what the picture was doing and turn that into a rule. That is how every formula in this chapter is born.
Q3.
Find the following products. Use a unit square as a whole for representing the fractions and carrying out the operations. (a) 2⁄3 × 4⁄5 (b) 1⁄4 × 2⁄3 (c) 3⁄5 × 1⁄2 (d) 4⁄6 × 3⁄5
Answer
Now more than one cell gets shaded — as many as (numerator × numerator).
Question
Total parts
Parts shaded
Product
(a) 2/3 × 4/5
3 × 5 = 15
2 × 4 = 8
8/15
(b) 1/4 × 2/3
4 × 3 = 12
1 × 2 = 2
2/12 = 1/6
(c) 3/5 × 1/2
5 × 2 = 10
3 × 1 = 3
3/10
(d) 4/6 × 3/5
6 × 5 = 30
4 × 3 = 12
12/30 = 2/5
Why it happens: the shaded piece is a rectangle 2 cells wide and 4 cells tall inside a 3 × 5 grid — its area is 2 × 4 cells out of 3 × 5. That is Brahmagupta's rule appearing on its own.