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NCERT Class 7 Maths Chapter 2 Arithmetic Expressions Solutions Question Answer
Ganita Prakash Class 7 Chapter 2 Solutions Arithmetic Expressions
NCERT Class 7 Maths Ganita Prakash Chapter 2 Arithmetic Expressions Solutions Question Answer
Arithmetic Expressions: Questions and Solutions
Page 2: Figure it Out
1. Fill in the blanks to make the expressions equal on both sides of the = sign:
- (a) 13 + 4 = _ + 6
Solution: 13 + 4 = 17. To make the right side 17, the blank must be 11 (11 + 6 = 17). - (b) 22 + _ = 6 × 5
Solution: 6 × 5 = 30. To make the left side 30, the blank must be 8 (22 + 8 = 30). - (c) 8 × _ = 64 ÷ 2
Solution: 64 ÷ 2 = 32. To make the left side 32, the blank must be 4 (8 × 4 = 32). - (d) 34 – _ = 25
Solution: The blank must be 9 (34 – 9 = 25).
2. Arrange the following expressions in ascending (increasing) order of their values:
- (a) 67 – 19 = 48
- (b) 67 – 20 = 47
- (c) 35 + 25 = 60
- (d) 5 × 11 = 55
- (e) 120 ÷ 3 = 40
Solution: (e), (b), (a), (d), (c)
Page 3: Figure it Out
1. Use ‘>’, ‘<‘ or ‘=’ in each of the following expressions to compare them without complicated calculations:
- (a) 245 + 289 __ 246 + 285
Solution: > (The second term drops by 4, but the first term only increases by 1, making the left side larger). - (b) 273 – 145 __ 272 – 144
Solution: = (Both numbers are reduced by 1, keeping the difference identical). - (c) 364 + 587 __ 363 + 589
Solution: < (The first term drops by 1, but the second term increases by 2, making the right side larger). - (d) 124 + 245 __ 129 + 245
Solution: < (129 is greater than 124, and the second term is the same). - (e) 213 – 77 __ 214 – 76
Solution: < (The left side starts with a smaller number and subtracts a larger amount, making it smaller than the right side).
Page 5 & 6: Try This
Complete the table expressing them as sum of terms:
- Expression: 13 – 2 + 6
Sum of terms: 13 + (-2) + 6
Terms: 13, -2, 6 - Expression: 5 + 6 × 3
Sum of terms: 5 + (6 × 3)
Terms: 5, 6 × 3 - Expression: 4 + 15 – 9
Sum of terms: 4 + 15 + (-9)
Terms: 4, 15, -9 - Expression: 23 – 2 × 4 + 16
Sum of terms: 23 + (-2 × 4) + 16
Terms: 23, -2 × 4, 16 - Expression: 28 + 19 – 8
Sum of terms: 28 + 19 + (-8)
Terms: 28, 19, -8
Page 11 & 12: Figure it Out
1. Find the values of the following expressions by writing the terms in each case:
- (a) 28 – 7 + 8 = 28 + (-7) + 8 = 29
- (b) 39 – 2 × 6 + 11 = 39 + (-12) + 11 = 38
- (c) 40 – 10 + 10 + 10 = 40 + (-10) + 10 + 10 = 50
- (d) 18 – 10 × 2 + 16 ÷ 2 = 18 + (-20) + 8 = 6
- (e) 6 × 3 – 4 × 8 × 5 = 18 + (-160) = -142
2. Write an expression/solve for the situations:
- (a) Princess Anna & Elsa: Elsa doubled her coins (2 × c), and Anna has half left (c ÷ 2). Total: (2 × c) + (c ÷ 2)
- (b) Metro Ticket:
- (i) 4 adults and 3 children: 4 × 40 + 3 × 20 = 160 + 60 = 220
- (ii) Two groups of 3 adults: 2 × (3 × 40) = 2 × 120 = 240
- (c) Window Height: Total height = (Number of Borders × 3 cm) + (Number of Grills × 2 cm) + (Number of Gaps × 5 cm). Assuming a standard window with top/bottom borders, 4 grills, and 5 gaps: 2 × 3 + 4 × 2 + 5 × 5 = 6 + 8 + 25 = 39 cm
Page 14 & 15: Figure it Out
1. Fill in the blanks with numbers, and boxes with operation signs:
- (a) 24 + (6 – 4) = 24 + 6 – 4
- (b) 38 + (9 – 4) = 38 + 9 – 4
- (c) 24 – (6 + 4) = 24 – 6 – 4
- (d) 24 – 6 – 4 = 24 – 10
- (e) 27 – (8 + 3) = 27 – 8 – 3
- (f) 27 – (8 – 3) = 27 – 8 + 3
2. Remove the brackets and write the expression having the same value:
- (a) 14 + 12 + 10
- (b) 14 – 12 – 10
- (c) 14 + 12 – 10
- (d) 14 – 12 + 10
- (e) -14 + 12 – 10
- (f) 14 + 12 + 10
3. Find the values of the following expressions and guess if they are equal:
- (a) (6 + 10) – 2 and 6 + (10 – 2) → Both equal 14.
- (b) 16 – (8 – 3) and (16 – 8) – 3 → First is 11, second is 5 (Not equal).
- (c) 27 – (18 + 4) and 27 + (-18 – 4) → Both equal 5.
4. Identify expressions that have the same value:
- (a) None have the same value.
- (b) 87 – 46 + 109 and (87 – 46) + 109 have the same value.
5. Add brackets at appropriate places:
- (a) 34 – (9 + 12) = 13
- (b) (56 – 14) – 8 = 34 (or simply no brackets are needed due to left-to-right rules)
- (c) -22 – (12 + 10) + 22 = -22
6. Fill the blanks to make expressions equal:
- (a) 423 + 1 = 419 + 5 (Answers may vary; the right side addition must be 4 greater than the left)
- (b) 207 – 68 = 210 – 71
9. Consider expressions a) 73 – 14 + 1 and b) 73 – 14 – 1. Identify equal expressions:
- Expression (a) is equal to: 73 – (14 – 1) and 73 + (-14 + 1)
- Expression (b) is equal to: 73 – (14 + 1) and 73 + (-14 – 1)
Page 18: Math Talk
1. Fill in the blanks with numbers:
- (a) 3 × (6 + 7) = 3 × 6 + 3 × 7
- (b) (8 + 3) × 4 = 8 × 4 + 3 × 4
- (c) 3 × (5 + 8) = 3 × 5 + 3 × 8
- (d) (9 + 2) × 4 = 9 × 4 + 2 × 4
- (i) 5 × (9 – 2) = 5 × 9 – 5 × 2
- (j) (5 – 2) × 7 = 5 × 7 – 2 × 7
- (k) 5 × (8 – 3) = 5 × 8 – 5 × 3
- (l) (8 – 3) × 7 = 8 × 7 – 3 × 7
Page 19, 20 & 21: Figure it Out
1. Read the situations, write expressions, and find values:
- (a) Mangoes: 7 × (9 + 11) = 7 × 20 = 140 kg
- (b) Savings: 12 × (20000 – 5000 – 5000 – 2000) = 12 × 8000 = &rupee;96,000
- (c) Snail: It nets 1 cm per day (3 – 2). On the 8th day, it climbs 3 cm from 7 cm to reach the top. Expression: (3 – 2) × 7 + 3 = 10. It will take 8 days.
2. Stories in 8 weeks:
Reads 1 story per day for 5 days a week for 8 weeks.
Correct expressions: (b) (7 – 2) × 8 and (g) 7 × 8 – 2 × 8. Total is 40 stories.
3. Find different ways of evaluating:
- (a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 = (1 – 2) + (3 – 4) … = -1 × 5 = -5
- (b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 = (1 – 1) + … = 0
4. Compare pairs using ‘<‘, ‘>’ or ‘=’:
- (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)
5. Identify equal expressions without computation:
- (a) 83 – 37 – 12 is equal to (iv) -37 + 83 – 12
- (b) 93 + 37 × 44 + 76 is equal to (iv) 37 × 44 + 93 + 76
Page 22: Puzzle Time
1. Expression Engineer (Using four 4s to get 1 to 5):
- 1 = 44 ÷ 44
- 2 = (4 ÷ 4) + (4 ÷ 4)
- 3 = (4 + 4 + 4) ÷ 4
- 4 = 4 + (4 – 4) × 4
- 5 = (4 × 4 + 4) ÷ 4
Page 2: Figure it Out
1. Fill in the blanks to make the expressions equal on both sides of the = sign:
- (a) $13 + 4 = \_ + 6$Solution: $13 + 4 = 17$. To make the right side 17, the blank must be 11 ($11 + 6 = 17$).
- (b) $22 + \_ = 6 \times 5$Solution: $6 \times 5 = 30$. To make the left side 30, the blank must be 8 ($22 + 8 = 30$).
- (c) $8 \times \_ = 64 \div 2$Solution: $64 \div 2 = 32$. To make the left side 32, the blank must be 4 ($8 \times 4 = 32$).
- (d) $34 – \_ = 25$Solution: The blank must be 9 ($34 – 9 = 25$).
2. Arrange the following expressions in ascending (increasing) order of their values:
- (a) $67 – 19 = 48$
- (b) $67 – 20 = 47$
- (c) $35 + 25 = 60$
- (d) $5 \times 11 = 55$
- (e) $120 \div 3 = 40$Solution: (e), (b), (a), (d), (c)
Page 3: Figure it Out
1. Use ‘>’, ‘<‘ or ‘=’ in each of the following expressions to compare them without complicated calculations:
- (a) $245 + 289$ __ $246 + 285$Solution: > (The second term drops by 4, but the first term only increases by 1, making the left side larger).
- (b) $273 – 145$ __ $272 – 144$Solution: = (Both numbers are reduced by 1, keeping the difference identical).
- (c) $364 + 587$ __ $363 + 589$Solution: < (The first term drops by 1, but the second term increases by 2, making the right side larger).
- (d) $124 + 245$ __ $129 + 245$Solution: < (129 is greater than 124, and the second term is the same).
- (e) $213 – 77$ __ $214 – 76$Solution: < (The left side starts with a smaller number and subtracts a larger amount, making it smaller than the right side).
Page 5 & 6: Try This (Table)
Complete the table expressing them as sum of terms:
- Expression: $13 – 2 + 6$Sum of terms: $13 + (-2) + 6$Terms: 13, -2, 6
- Expression: $5 + 6 \times 3$Sum of terms: $5 + (6 \times 3)$Terms: 5, $6 \times 3$
- Expression: $4 + 15 – 9$Sum of terms: $4 + 15 + (-9)$Terms: 4, 15, -9
- Expression: $23 – 2 \times 4 + 16$Sum of terms: $23 + (-2 \times 4) + 16$Terms: 23, $-2 \times 4$, 16
- Expression: $28 + 19 – 8$Sum of terms: $28 + 19 + (-8)$Terms: 28, 19, -8
Page 11 & 12: Figure it Out
1. Find the values of the following expressions by writing the terms in each case:
- (a) $28 – 7 + 8$ = $28 + (-7) + 8$ = 29
- (b) $39 – 2 \times 6 + 11$ = $39 + (-12) + 11$ = 38
- (c) $40 – 10 + 10 + 10$ = $40 + (-10) + 10 + 10$ = 50
- (d) $18 – 10 \times 2 + 16 \div 2$ = $18 + (-20) + 8$ = 6
- (e) $6 \times 3 – 4 \times 8 \times 5$ = $18 + (-160)$ = -142
2. Write an expression/solve for the situations:
- (a) Princess Anna & Elsa: Elsa doubled her coins ($2 \times c$), and Anna has half left ($c \div 2$). Total: $(2 \times c) + (c \div 2)$
- (b) Metro Ticket: * (i) 4 adults and 3 children: $4 \times 40 + 3 \times 20 = 160 + 60$ = 220
- (ii) Two groups of 3 adults: $2 \times (3 \times 40) = 2 \times 120$ = 240
- (c) Window Height: Total height = (Number of Borders $\times$ 3 cm) + (Number of Grills $\times$ 2 cm) + (Number of Gaps $\times$ 5 cm). Assuming a standard window with top/bottom borders, 4 grills, and 5 gaps: $2 \times 3 + 4 \times 2 + 5 \times 5 = 6 + 8 + 25$ = 39 cm
Page 14 & 15: Figure it Out
1. Fill in the blanks with numbers, and boxes with operation signs:
- (a) $24 + (6 – 4) = 24 + 6 – 4$
- (b) $38 + (9 – 4) = 38 + 9 – 4$
- (c) $24 – (6 + 4) = 24 – 6 – 4$
- (d) $24 – 6 – 4 = 24 – 10$
- (e) $27 – (8 + 3) = 27 – 8 – 3$
- (f) $27 – (8 – 3) = 27 – 8 + 3$
2. Remove the brackets and write the expression having the same value:
- (a) $14 + 12 + 10$
- (b) $14 – 12 – 10$
- (c) $14 + 12 – 10$
- (d) $14 – 12 + 10$
- (e) $-14 + 12 – 10$
- (f) $14 + 12 + 10$
3. Find the values of the following expressions and guess if they are equal:
- (a) $(6 + 10) – 2$ and $6 + (10 – 2)$ $\rightarrow$ Both equal 14.
- (b) $16 – (8 – 3)$ and $(16 – 8) – 3$ $\rightarrow$ First is 11, second is 5 (Not equal).
- (c) $27 – (18 + 4)$ and $27 + (-18 – 4)$ $\rightarrow$ Both equal 5.
4. Identify expressions that have the same value:
- (a) None have the same value.
- (b) $87 – 46 + 109$ and $(87 – 46) + 109$ have the same value.
5. Add brackets at appropriate places:
- (a) $34 – (9 + 12) = 13$
- (b) $(56 – 14) – 8 = 34$ (or simply no brackets are needed due to left-to-right rules)
- (c) $-22 – (12 + 10) + 22 = -22$
6. Fill the blanks to make expressions equal:
- (a) $423 + 1 = 419 + 5$ (Answers may vary; the right side addition must be 4 greater than the left)
- (b) $207 – 68 = 210 – 71$
9. Consider expressions a) $73 – 14 + 1$ and b) $73 – 14 – 1$. Identify equal expressions:
- Expression (a) is equal to: $73 – (14 – 1)$ and $73 + (-14 + 1)$
- Expression (b) is equal to: $73 – (14 + 1)$ and $73 + (-14 – 1)$
Page 18: Math Talk
1. Fill in the blanks with numbers:
- (a) $3 \times (6 + 7) = 3 \times 6 + 3 \times 7$
- (b) $(8 + 3) \times 4 = 8 \times 4 + 3 \times 4$
- (c) $3 \times (5 + 8) = 3 \times 5 + 3 \times 8$
- (d) $(9 + 2) \times 4 = 9 \times 4 + 2 \times 4$
- (i) $5 \times (9 – 2) = 5 \times 9 – 5 \times 2$
- (j) $(5 – 2) \times 7 = 5 \times 7 – 2 \times 7$
- (k) $5 \times (8 – 3) = 5 \times 8 – 5 \times 3$
- (l) $(8 – 3) \times 7 = 8 \times 7 – 3 \times 7$
Page 19, 20 & 21: Figure it Out
1. Read the situations, write expressions, and find values:
- (a) Mangoes: $7 \times (9 + 11) = 7 \times 20$ = 140 kg
- (b) Savings: $12 \times (20000 – 5000 – 5000 – 2000) = 12 \times 8000$ = ₹96,000
- (c) Snail: It nets 1 cm per day (3 – 2). On the 8th day, it climbs 3 cm from 7 cm to reach the top. Expression: $(3 – 2) \times 7 + 3 = 10$. It will take 8 days.
2. Stories in 8 weeks:
- Reads 1 story per day for 5 days a week for 8 weeks.
- Correct expressions: (b) $(7 – 2) \times 8$ and (g) $7 \times 8 – 2 \times 8$. Total is 40 stories.
3. Find different ways of evaluating:
- (a) $1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 = (1 – 2) + (3 – 4) …$ = $-1 \times 5$ = -5
- (b) $1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 = (1 – 1) + …$ = 0
4. Compare pairs using ‘<‘, ‘>’ or ‘=’:
- (a) $49 – 7 + 8$ = $49 – 7 + 8$
- (b) $83 \times 42 – 18$ > $83 \times 40 – 18$
- (c) $145 – 17 \times 8$ < $145 – 17 \times 6$
- (d) $23 \times 48 – 35$ > $23 \times (48 – 35)$
- (e) $(16 – 11) \times 12$ = $-11 \times 12 + 16 \times 12$
- (f) $(76 – 53) \times 88$ > $88 \times (53 – 76)$
- (g) $25 \times (42 + 16)$ = $25 \times (43 + 15)$
- (h) $36 \times (28 – 16)$ > $35 \times (27 – 15)$
5. Identify equal expressions without computation:
- (a) $83 – 37 – 12$ is equal to (iv) $-37 + 83 – 12$
- (b) $93 + 37 \times 44 + 76$ is equal to (iv) $37 \times 44 + 93 + 76$
Page 22: Puzzle Time
1. Expression Engineer (Using four 4s to get 1 to 5):