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NCERT Solutions Ganita Prakash (Part 1) Chapter 2 – 44Chapter Review Exercise — Figure it Out

Book page 42 Updated on2026-09-05

Q1.
Read the situations given below. Write appropriate expressions for each of them and find their values. (a) The district market in Begur operates on all seven days of a week. Rahim supplies 9 kg of mangoes each day from his orchard and Shyam supplies 11 kg of mangoes each day from his orchard to this market. Find the amount of mangoes supplied by them in a week to the local district market. (b) Binu earns ₹20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses every month. What is the amount Binu will save by the end of a year? (c) During the daytime a snail climbs 3 cm up a post, and during the night while asleep, accidentally slips down by 2 cm. The post is 10 cm high, and a delicious treat is on its top. In how many days will the snail get the treat?
Answer

(a) Mangoes at the Begur market

Both together supply (9 + 11) kg each day, for 7 days:
Expression = 7 × (9 + 11)
= 7 × 20 = 140 kg

The other way round: 7 × 9 + 7 × 11 = 63 + 77 = 140 kg ✓

(b) Binu’s yearly saving

Expression = 12 × 20000 – 12 × (5000 + 5000 + 2000)
= 240000 – 12 × 12000
= 240000 – 144000
= ₹96,000

Shorter route: monthly saving = 20000 – 12000 = ₹8000
Yearly saving = 12 × 8000 = ₹96,000 ✓

(c) The snail on the 10 cm post

In one full day-and-night the snail gains 3 – 2 = 1 cm.
After 7 such cycles: 7 × (3 – 2) = 7 cm
On the 8th day it climbs 3 cm more: 7 + 3 = 10 cm — the top!

Expression = 7 × (3 – 2) + 3 = 7 + 3 = 10
Answer: 8 days
Why it happens: The snail does not take 10 days. Once it reaches the top during the day it eats the treat and never slips back, so we only count full cycles until it is within 3 cm of the top — that is 7 cm after 7 days — and the last climb finishes the job on day 8.
Check it yourself: Day-ends are 1, 2, 3, 4, 5, 6, 7 cm. On day 8 it is at 7 + 3 = 10 cm before night falls.
Q2.
Melvin reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the expressions below describes this scenario? (a) 5 × 2 × 8 (b) (7 – 2) × 8 (c) 8 × 7 (d) 7 × 2 × 8 (e) 7 × 5 – 2 (f) (7 + 2) × 8 (g) 7 × 8 – 2 × 8 (h) (7 – 5) × 8
Answer

Melvin reads on 7 – 2 = 5 days a week, one story each of those days.

Stories in 8 weeks = (7 – 2) × 8 = 5 × 8 = 40 stories

The expressions that describe the scenario are (b) and (g).

ExpressionValueCorrect?
(a) 5 × 2 × 880No — this counts pages, not stories
(b) (7 – 2) × 840Yes — 5 reading days × 8 weeks
(c) 8 × 756No — all 56 days of 8 weeks
(d) 7 × 2 × 8112No
(e) 7 × 5 – 233No
(f) (7 + 2) × 872No
(g) 7 × 8 – 2 × 840Yes — all 56 days minus the 16 skipped days
(h) (7 – 5) × 816No — this counts the days he skips
Why it happens: (b) and (g) are the two sides of the distributive property: (7 – 2) × 8 = 7 × 8 – 2 × 8. One counts the reading days first; the other counts all days and then removes the Tuesdays and Saturdays. Both give 40.
Q3.
Find different ways of evaluating the following expressions: (a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 (b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1
Answer

(a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10

Way 1 — pair them up:
(1 – 2) + (3 – 4) + (5 – 6) + (7 – 8) + (9 – 10)
= (–1) + (–1) + (–1) + (–1) + (–1) = –5

Way 2 — collect positives and negatives:
(1 + 3 + 5 + 7 + 9) + (–2 – 4 – 6 – 8 – 10)
= 25 + (–30) = –5

Way 3 — left to right:
1 – 2 = –1; –1 + 3 = 2; 2 – 4 = –2; –2 + 5 = 3; 3 – 6 = –3;
–3 + 7 = 4; 4 – 8 = –4; –4 + 9 = 5; 5 – 10 = –5

(b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1

Way 1 — pair them up:
(1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) = 0 + 0 + 0 + 0 + 0 = 0

Way 2 — collect signs:
(1 + 1 + 1 + 1 + 1) + (–1 –1 –1 –1 –1) = 5 + (–5) = 0

Way 3 — count the terms: five terms of +1 and five terms of –1 cancel exactly → 0
Why it happens: Once every subtraction is rewritten as adding a negative term, the terms may be grouped and ordered any way we like. Pairing is fastest here because each pair has a neat value.
Tip: Be careful — 1 – 1 + 1 – 1 + … is not 1 – (1 + 1 – 1 + …). The brackets you insert must not change the signs.
Q4.
Compare the following pairs of expressions using ‘<’, ‘>’ or ‘=’ or by reasoning. (a) 49 – 7 + 8 ☐ 49 – 7 + 8 (b) 83 × 42 – 18 ☐ 83 × 40 – 18 (c) 145 – 17 × 8 ☐ 145 – 17 × 6 (d) 23 × 48 – 35 ☐ 23 × (48 – 35) (e) (16 – 11) × 12 ☐ –11 × 12 + 16 × 12 (f) (76 – 53) × 88 ☐ 88 × (53 – 76) (g) 25 × (42 + 16) ☐ 25 × (43 + 15) (h) 36 × (28 – 16) ☐ 35 × (27 – 15)
Answer
(a) 49 – 7 + 8 = 49 – 7 + 8  — identical expressions.

(b) 83 × 42 – 18 > 83 × 40 – 18  — 83 × 42 is 83 × 2 = 166 more than 83 × 40, and both lose 18.

(c) 145 – 17 × 8 < 145 – 17 × 6  — the left side takes away more (136 against 102).

(d) 23 × 48 – 35 > 23 × (48 – 35)  — the right side is 23 × 48 – 23 × 35, which removes far more than 35.

(e) (16 – 11) × 12 = –11 × 12 + 16 × 12  — the distributive property, terms just swapped.

(f) (76 – 53) × 88 > 88 × (53 – 76)  — the first bracket is +23, the second is –23.

(g) 25 × (42 + 16) = 25 × (43 + 15)  — both brackets equal 58.

(h) 36 × (28 – 16) > 35 × (27 – 15)  — both brackets equal 12, and 36 > 35.
LHSSignRHS
(a)50=50
(b)3468>3302
(c)9<43
(d)1069>299
(e)60=60
(f)2024>–2024
(g)1450=1450
(h)432>420
Why it happens: In every part it is enough to look at how the two sides differ. In (g) the bracket totals are the same (42 + 16 = 43 + 15 = 58), so the products must be equal — one number gained exactly what the other lost.
Q5.
Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression which is equal to the given expression. (a) 83 – 37 – 12 : (i) 84 – 38 – 12 (ii) 84 – (37 + 12) (iii) 83 – 38 – 13 (iv) –37 + 83 – 12. (b) 93 + 37 × 44 + 76 : (i) 37 + 93 × 44 + 76 (ii) 93 + 37 × 76 + 44 (iii) (93 + 37) × (44 + 76) (iv) 37 × 44 + 93 + 76
Answer

(a) 83 – 37 – 12 has terms 83, –37, –12.

OptionTermsEqual?
(i) 84 – 38 – 1284, –38, –12 — both first numbers up by 1, so 84 – 38 = 83 – 37Yes
(ii) 84 – (37 + 12)84, –37, –12 — one more than the givenNo
(iii) 83 – 38 – 1383, –38, –13 — takes away 2 moreNo
(iv) –37 + 83 – 12–37, 83, –12 — same terms, reorderedYes

So (i) and (iv) are equal to 83 – 37 – 12 (all three have value 34; (ii) is 35 and (iii) is 32).

(b) 93 + 37 × 44 + 76 has terms 93, 37 × 44, 76.

OptionTermsEqual?
(i) 37 + 93 × 44 + 7637, 93 × 44, 76 — the product is differentNo
(ii) 93 + 37 × 76 + 4493, 37 × 76, 44 — the product is differentNo
(iii) (93 + 37) × (44 + 76)a single product 130 × 120No
(iv) 37 × 44 + 93 + 7637 × 44, 93, 76 — same terms, reorderedYes

So only (iv) is equal to 93 + 37 × 44 + 76 (both are 1797).

Why it happens: Two expressions are equal when they have the same terms, whatever the order. In (b) swapping 93 and 37 changes which numbers sit inside the product, so the term itself changes — that is why (i) fails.
Q6.
Choose a number and create ten different expressions having that value.
Answer

Let us choose 36.

#ExpressionValue
130 + 636
240 – 436
36 × 636
472 ÷ 236
54 × 936
650 – 1436
7108 ÷ 336
812 × 336
92 × (15 + 3)36
105 × 8 – 436
Why it happens: A value can be built in endless ways — as a sum, a difference, a product, a quotient, or a mixture with brackets. All ten of these are joined by ‘=’ because they share the same value, not the same look.
Try This: Do the same for your age, and make sure at least three of your ten expressions use brackets.
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