Arithmetic Expressions Class 7 Solutions Ganita Prakash Maths Chapter 2✦ Step-by-step
HBSE 7th Class Maths Solutions Chapter 2 Arithmetic Expressions (NCERT Ganita Prakash) — every question worked out step by step. Tap Solve step by step to reveal the working one line at a time.
Class 7 Maths Chapter 2 Arithmetic Expressions Solutions
Key ideas used in this chapter
Termsa + and a − split an expression into terms
Bracketsa + (b − c) = a + b − c; a − (b + c) = a − b − c
Distributivea × (b + c) = a×b + a×c
Balanceto keep both sides equal, undo each change
2.1 Simple Expressions — Figure It Out (Page 25)
Q1Fill the blanks
(a) 13 + 4 = __ + 6 (b) 22 + __ = 6×5 (c) 8×__ = 64÷2 (d) 34 − __ = 25
(a)
LHS = 13 + 4 = 17; so blank + 6 = 17 ⇒ blank = 17 − 6 = 11
(b)
RHS = 6×5 = 30; so 22 + blank = 30 ⇒ blank = 30 − 22 = 8
(c)
RHS = 64÷2 = 32; so 8×blank = 32 ⇒ blank = 32 ÷ 8 = 4
(d)
34 − blank = 25 ⇒ blank = 34 − 25 = 9
Q2Ascending order
(a) 67−19 (b) 67−20 (c) 35+25 (d) 5×11 (e) 120÷3
Step 1
evaluate each: 48, 47, 60, 55, 40
Answer
40 < 47 < 48 < 55 < 60 ⇒ (e), (b), (a), (d), (c)
Q.Compare without computing
(a) 245+289 __ 246+285 (b) 273−145 __ 272−144 (c) 364+587 __ 363+589
(a)
add 1 to the smaller first term: 246+289 vs 246+286 ⇒ 289>286 ⇒ >
(b)
273−145 = 272−144 (both are 128 apart the same way) ⇒ =
(c)
364+588 vs 364+589 ⇒ 588<589 ⇒ <
2.2 Reading & Evaluating — Figure It Out (Pages 34–35)
Q1Evaluate by terms
(a) 28−7+8 (b) 39−2×6+11 (c) 40−10+10+10 (d) 48−10×2+16÷2 (e) 6×3−4×8×5
(a)
(28−7) + 8 = 21 + 8 = 29
(b)
2×6 = 12 first; 39 − 12 + 11 = 27 + 11 = 38
(c)
(40−10) + 10 + 10 = 30 + 20 = 50
(d)
10×2=20 and 16÷2=8; 48 − 20 + 8 = 36
(e)
6×3=18, 4×8×5=160; 18 − 160 = −142
Q2Story & value
Write a situation and find the value: (a) 89+21−10 (b) 5×12−6 (c) 4×9+2×6
(a)
jar: 89 + 21 − 10 = 110 − 10 = 100
(b)
5 rows of 12, 6 leave: 5×12 − 6 = 60 − 6 = 54
(c)
4 baskets of 9 + 2 of 6: 36 + 12 = 48
Q3Situations
(a) Elsa doubles 100 coins, Anna keeps half of 100 — total. (b) Metro adult ₹40, child ₹20: cost for (i) 4 adults, 3 children (ii) two groups of 3 adults.
(a)
(100×2) + (100÷2) = 200 + 50 = 250 coins
(b)(i)
(4×40) + (3×20) = 160 + 60 = ₹220
(b)(ii)
(3×40) + (3×40) = 120 + 120 = ₹240
2.3 Removing Brackets — Figure It Out (Pages 37–38)
Q2Remove brackets
(a) 14+(12+10) (b) 14−(12+10) (c) 14+(12−10) (d) 14−(12−10) (e) −14+(12−10) (f) 14−(−12−10)
Rule
a + bracket keeps the signs; a − bracket flips every sign inside.
(a),(b)
14+12+10; 14−12−10
(c),(d)
14+12−10; 14−12+10
(e),(f)
−14+12−10; 14+12+10 (both signs in (f) flip)
Q3Equal when?
(a) (6+10)−2 vs 6+(10−2) (b) 16−(8−3) vs (16−8)−3 (c) 27−(18+4) vs 27+(−18−4)
(a)
16−2 = 14 and 6+8 = 14 ⇒ equal
(b)
16−5 = 11 but 8−3 = 5 ⇒ not equal
(c)
27−22 = 5 and 27+(−22) = 5 ⇒ equal
Q5Add brackets
(a) 34−9+12 = 13 (b) 56−14−8 = 34 (c) −22−12+10+22 = −22
(a)
34 − (9 + 12) = 34 − 21 = 13
(b)
(56 − 14) − 8 = 42 − 8 = 34
(c)
−22 − (12 + 10) + 22 = −22 − 22 + 22 = −22
Q6, Q8, Q9Reasoning with terms
(Q6) 423+__ = 419+__ ; 207−68 = 210−__. (Q8) Why does “−10 then +1” equal −9? (Q9) Which equal 73−14+1 and which equal 73−14−1?
Q6
423+419 = 419+423 (swap). For 210 (3 more than 207) subtract 3 more: 210−71
Q8
−9 = −10 + 1, so 36 − 9 = 36 − 10 + 1 = 27 ✓
73−14+1 = 60
equals (b) 73−(14−1) and (c) 73+(−14+1)
73−14−1 = 58
equals (a) 73−(14+1) and (d) 73+(−14−1)
2.4 Distributive Property — Figure It Out (Pages 41–42)
Q1Distributive fills
Complete, e.g. (c) 3×(5+8) = 3×5 + 3×__ ; (i) 5×(9−2) = 5×9 − 5×__ ; (o) 5×(__−__) = 5×9 − 5×4.
Rule
a×(b+c) = a×b + a×c; a×(b−c) = a×b − a×c
(c)
3×5 + 3×8
(i)
5×9 − 5×2
(o)
5×(9 − 4) = 5×9 − 5×4
Q2Compare by reasoning
(a) (8−3)×29 __ (3−8)×29 (b) 15+9×18 __ (15+9)×18 (c) 23×(17−19) __ 23×17+23×9 (d) (34−28)×42 __ 34×42−28×42
(a)
5×29 vs −5×29 ⇒ positive > negative ⇒ >
(b)
15+162 = 177 vs 24×18 = 432 ⇒ <
(c)
23×(−2) = −46 vs a big positive ⇒ <
(d)
distributive: 6×42 = 252 = 34×42 − 28×42 ⇒ =
Q3, Q4Make 14 & add a grid
(Q3) Ways to make a×(b+c) = 14. (Q4) Add a number grid two different ways.
Q3
2×(2+5), 2×(3+4), 7×(1+1), 7×(0+2) — each equals 14
Q4 by rows
e.g. rows 16 + 20 + 16 = 52
Q4 by value
count each number: (4×five 4's) + (8×four 8's) = 20 + 32 = 52 — same total
Figure It Out (Pages 42–44)
Q1Word problems
(a) Rahim 9 kg + Shyam 11 kg mangoes daily for 7 days. (b) Binu earns ₹20000, spends ₹5000+₹5000+₹2000/month — yearly saving. (c) Snail climbs 3 cm/day, slips 2 cm/night, post 10 cm — which day reaches top?
(a)
7×9 + 7×11 = 7×(9+11) = 7×20 = 140 kg
(b)
monthly saving 20000 − 12000 = 8000; year = 8000×12 = ₹96,000
(c)
net 1 cm/day ⇒ 7 cm in 7 days; on day 8 it climbs 3 ⇒ 10 cm. Day 8.
Q2, Q3Choose expr & evaluate
(Q2) Melvin reads daily except Tue & Sat — stories in 8 weeks & which expression. (Q3) (a) 1−2+3−…−10 (b) 1−1+1−…−1.
Q2
per week 7−2 = 5; in 8 weeks (7−2)×8 = 40 ⇒ (b) and (g) 7×8−2×8
Q3 (a)
pair up: (1−2)+(3−4)+… = 5×(−1) = −5
Q3 (b)
five (1−1) pairs = 0
Q4Compare
(b) 83×42−18 __ 83×40−18 (d) 23×48−35 __ 23×(48−35) (e) (16−11)×12 __ −11×12+16×12 (h) 36×(28−16) __ 35×(27−15)
(b)
3486−18 vs 3320−18 ⇒ >
(d)
1104−35 = 1069 vs 23×13 = 299 ⇒ >
(e)
5×12 = 60 = −132+192 ⇒ =
(h)
36×12 = 432 vs 35×12 = 420 ⇒ >
Q5Equal without computing
(a) Which equal 83−37−12? (b) Which equal 93 + 37×44 + 76?
(a) = 34
(i) 84−38−12 = 34 and (iv) −37+83−12 = 34
(b) = 1797
(iv) 37×44 + 93 + 76 = 1628 + 169 = 1797