NCERT Solutions Ganita Prakash (Part 1) Chapter 4 –94Section 4.4 Simplification of Algebraic Expressions — Figure it Out

Book page 93 Updated on2026-09-05

Q1.

Add the numbers in each picture below. Write their corresponding expressions and simplify them. Try adding the numbers in each picture in a couple different ways and see that you get the same thing.

Answer

Picture (i) — two rows: 5y, –6, x and x, 2, 5y.

Way 1 (row-wise): (5y – 6 + x) + (x + 2 + 5y)
Way 2 (like terms): (5y + 5y) + (x + x) + (–6 + 2)
= 10y + 2x + (–4)
= 2x + 10y – 4

Picture (ii) — 2p and 3q appear 4 times each; the number tiles are –2, 3, 3, –2.

Way 1 (like terms): 4 × 2p + 4 × 3q + (–2 + 3 + 3 – 2)
= 8p + 12q + 2
Way 2 (column-wise): (2p + 3q) + (3q + 2p) + (–2 + 3 + 2p + 3q) + (3 – 2 + 3q + 2p)
= 8p + 12q + 2

Picture (iii) — the four corners are –5g and every other circle is 5k (12 of them).

Way 1 (like terms): 4 × (–5g) + 12 × 5k
= –20g + 60k
Way 2 (columns): first column (–5g + 5k + 5k – 5g) = –10g + 10k
middle two columns = 8 × 5k = 40k
last column = –10g + 10k
Total = 60k – 20g

Why it happens: Terms can be added in any order and grouped in any way, so however you sweep across the picture — by rows, by columns, or by collecting like symbols — the simplified answer must come out the same.

Q2.

Simplify each of the following expressions: (a) p + p + p + p, p + p + p + q, (b) p + q + p – q, (c) p – q + p – q, (d) p + q – p + q, (e) p + q – (p + q), (f) p – q – p – q, (g) 2d – d – d – d, (h) 2d – d – d – c, (i) 2d – d – (d – c), (j) 2d – (d – d) – c, (k) 2d – d – c – c

Answer

Expression	Working	Simplest form
(a) p + p + p + p	4 lots of p	4p
(a) p + p + p + q	3 lots of p, one q	3p + q
(b) p + q + p – q	(p + p) + (q – q)	2p
(c) p – q + p – q	(p + p) + (–q – q)	2p – 2q
(d) p + q – p + q	(p – p) + (q + q)	2q
(e) p + q – (p + q)	p + q – p – q	0
(f) p – q – p – q	(p – p) + (–q – q)	–2q
(g) 2d – d – d – d	(2 – 1 – 1 – 1)d	–d
(h) 2d – d – d – c	(2 – 1 – 1)d – c = 0 – c	–c
(i) 2d – d – (d – c)	2d – d – d + c	c
(j) 2d – (d – d) – c	2d – 0 – c	2d – c
(k) 2d – d – c – c	(2 – 1)d – 2c	d – 2c

Why it happens: Compare (h) and (i). In (h) we subtract d and then subtract c. In (i) the bracket makes us subtract d but add c, because a minus sign outside flips every sign inside. One bracket changes the whole answer.

Check it yourself: Put d = 5, c = 2. (h) gives 10 – 5 – 5 – 2 = –2 = –c ✔. (i) gives 10 – 5 – (5 – 2) = 5 – 3 = 2 = c ✔.

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