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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
2.1 Simple Expressions
Figure It Out (Page 25)
Question 1.
Fill in the blanks to make the expressions equal on both sides of the ‘=’ sign:
(a) 13 + 4 = __________ + 6
(b) 22 + __________ = 6 × 5
(c) 8 × __________ = 64 ÷ 2
(d) 34 – __________ = 25
Solution:
(a) LHS = 13 + 4 = 17
RHS = ? + 6 = 17
∴ ? = 17 – 6 = 11
(b) RHS = 6 × 5 = 30
LHS = ? + 22 = 30
∴ ? = 30 – 22 = 8
(c) RHS = 64 ÷ 2 = 32
LHS = 8 × ? = 32
∴ ? 32 ÷ 8 = 4
(d) 34 – ? = 25
∴ ? = 34 – 25 = 9
Question 2.
Arrange the following expressions in ascending (increasing) order of their values:
(a) 67 – 19
(b) 67 – 20
(c) 35 + 25
(d) 5 × 11
(e) 120 ÷ 3
Solution:
(a) 67 – 19 = 48
(b) 67 – 20 = 47
(c) 35 + 25 = 60
(d) 5 × 11 = 55
(e) 120 ÷ 3 = 40
In ascending order: 40, 47, 48, 55, 60
i.e., (e), (b), (a), (d), (c)
Use ‘>’ or ‘<’ or ‘=’ in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case. (Page 26)
(a) 245 + 289 
246 + 285
(b) 273 – 145 272 – 144
(c) 364 + 587 363 + 589
(d) 124 + 245 129 + 245
(e) 213 – 77 214 – 76
Solution:
(a) We add 1 to both sides
245 + 1 + 289 ______ 246 + 285 + 1
246 + 289 ______ 246 + 286
Now, 289 > 286
So, LHS > RHS
(b) We add 1 to both sides
273 + 1 – 145 ______ 272 + 1 – 144
273 – 144 ______ 273 – 144
Same expression on both sides
So, LHS = RHS
(c) We add 1 to both sides
364 + 587 + 1 ______ 363 + 1 + 589
364 + 588 ______ 364 + 589
588 < 589
So LHS < RHS
(d) and (e) Do yourself.
2.2 Reading and Evaluating Complex Expressions
Figure It Out (Pages 34 – 35)
Question 1.
Find the values of the following expressions by writing the terms in each case.
(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
Solution:
(a) (28 – 7) + 8
= 21 + 8
= 29
(b) 39 – 2 × 6 + 11
= (39 – 12) + 11
= 27 + 11
= 38
(c) (40 – 10) + (10 + 10)
= 30 + 20
= 50
(d) 48 – (10 × 2) + (16 ÷ 2)
= (48 – 20) + 8
= 28 + 8
= 36
(e) (6 × 3) – (4 × 8) × 5
= 18 – 32 × 5
= 18 – 160
= -142
Question 2.
Write a story/situation for each of the following expressions and find their values:
(а) 89 + 21 – 10
(b) 5 × 12 – 6
(c) 4 × 9 + 2 × 6
Solution:
(a) Ajar had 89 biscuits, and 21 more were put into it. Now 10 were taken out. How many are left in the jar?
= (89 + 21) – 10
= 110 – 10
= 100
(b) School students were standing in 5 rows of 12 students each. 6 students had to leave for a sports day. How many are left standing?
= 5 × 12 – 6
= 60 – 6
= 54
(c) 4 baskets have 9 apples each, and 2 baskets have 6 apples each. How many apples do these baskets have in all?
= (4 × 9) + (2 × 6)
= 36 + 12
= 48
Question 3.
For each of the following situations, write the expression describing the situation, identify its terms, and find the value of the expression.
(a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa used the coins to start a business and doubled her coins. Princess Anna bought jewellery and has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have.
(b) A metro train ticket between two stations is ₹ 40 for an adult and ₹ 20 for a child. What is the total cost of the tickets?
(i) for four adults and three children?
(ii) for two groups having three adults each?
(c) Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.
Solution:
(a) Value = 100 × 2 + 50
= 200 + 50
= 250
(b) (i) Value = (4 × 40) + (3 × 20)
= 160 + 60
= 220
(ii) Value = (3 × 40) + (3 × 40)
= 120 + 120
= 240
(c) Total height = 2 border width + 6 grill width + 7 gaps
= (2 × 3 + 6 × 2 + 7 × 5) cm
= 6 + 12 + 35
= 53 cm
2.3 Removing Brackets and Tinkering with the Terms
Figure It Out (Pages 37 – 38)
Question 1.
Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal.
(a) 24 + (6 – 4) = 24 + 6 
________
(b) 38 + (________ ________) = 38 + 9 – 4
(c) 24 – (6 + 4) = 24 6 – 4
(d) 24 – 6 – 4 = 24 – 6 ________
(e) 27 – (8 + 3) = 27 8 3
(f) 27 – (________ ________) = 27 – 8 + 3
Solution:
(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 – 6 4
(e) 27 – (8 + 3) = 27 8 3
(f) 27 – (8 3) = 27 – 8 + 3
Question 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)
Solution:
(a) 14 + 12 + 10
(b) 14 – 12 – 10
(c) 14 + 12 – 10
(d) 14 – 12 + 10
(e) -14 + 12 – 10
(f) 14 + 12 + 10
Question 3.
Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal?
(a) (6 + 10) – 2 and 6 + (10 – 2)
(b) 16 – (8 – 3) and (16 – 8) – 3
(c) 27 – (18 + 4) and 27 + (-18 – 4)
Solution:
(a) LHS = 6 + 10 – 2
= 16 – 2
= 14
RHS = 6 + (10 – 2)
= 6 + 8
= 14
LHS = RHS
(b) LHS = 16 – (8 – 3)
= 16 – 5
= 11
RHS = (16 – 8) – 3
= 8 – 3
= 5
Here, LHS > RHS
LHS ≠ RHS
(c) LHS = 27 – (18 + 4)
= 27 – 22
= 5
RHS = 27 + (-18 – 4)
= 27 + (-22)
= 27 – 22
= 5
LHS = RHS
Question 4.
In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms.
(a) 319 + 537, 319 – 537, -537 + 319, 537 – 319
(b) 87 + 46 – 109, 87 + 46 – 109, 87 + 46 – 109, 87 – 46 + 109, 87 – (46 + 109), (87 – 46) + 109
Solution:
(a) 319 – 537 and -537 + 319 have same value.
(b) 87 – 46 + 109 and (87 – 46) + 109 have same value.
Question 5.
Add brackets at appropriate places in the expressions such that they lead to the values indicated.
(a) 34 – 9 + 12 = 13
(b) 56 – 14 – 8 = 34
(c) -22 – 12 + 10 + 22 = -22
Solution:
(a) 34 – (9 + 12) = 13
(b) (56 – 14) – 8 = 34
(c) -22 – (12 + 10) + 22 = -22
Question 6.
Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal.
(a) 423 + __________ = 419 + __________
(b) 207 – 68 = 210 – __________
Solution:
(a) 423 + 419 = 419 + 423
(b) 207 – 68 = 210 – 71
Question 7.
Using the numbers 2, 3, and 5, and the operators ‘+’ and ‘-‘, and brackets, as necessary, generate expressions to give as many different values as possible.
For example, 2 – 3 + 5 = 4 and 3 – (5 – 2) = 0.
Solution:
(i) 2 + (3 + 5) = 10
(ii) 2 – (3 + 5) = -6
(iii) 3 – (2 + 5) = -4
(iv) 5 – (2 + 3) = 0
(v) 5 + 3 – 2 = 6
(vi) 2 + 3 – 5 = 0
(vii) 2 – 3 + 5 = 4
Question 8.
Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it.
For example, 36 – 9 = 26 + 1.
(a) Do you think she always gets the correct answer? Why?
(b) Can you think of other similar strategies? Give some examples.
Solution:
(a) Yes; -9 = -10 + 1
For example: 25 – 9 = 25 – 10 + 1 = 16
(b) To add 99 to a number, factor and add a hundred, then subtract 1.
For example, to add 99 to 176
176 + 100 – 1 = 276 – 1 = 275
Question 9.
Consider the two expressions: (i) 73 – 14 + 1, (ii) 73 – 14 – 1. For each of these expressions, identify the expressions from the following collection that are equal to it.
(a) 73 – (14 + 1)
(b) 73 – (14 – 1)
(c) 73 + (-14 + 1)
(d) 73 + (-14 – 1)
Solution:
(i) 73 – 14 + 1 = 59 + 1 = 60
(ii) 73 – 14 – 1 = 59 – 1 = 58
(a) 73 – 15 = 58
(b) 73 – 13 = 60
(c) 73 – 13 = 60
(d) 73 – 15 = 58
Hence, (i), (b,) and (c) are the same as (i)
(ii) (a) and (d) are same as (ii)
2.4 More on Removing Brackets and Tinkering Terms
Figure It Out (Pages 41 – 42)
Question 1.
Fill in the blanks with numbers and boxes by signs, so that the expressions on both sides are equal.
(a) 3 × (6 + 7) = 3 × 6 + 3 × 7
(b) (8 + 3) × 4 = 8 × 4 + 3 × 4
(c) 3 × (5 + 8) = 3 × 5 
3 × ________
(d) (9 + 2) × 4 = 9 × 4 2 × ________
(e) 3 × (________ + 4) = 3 ________ + ________
(f) (________ + 6) × 4 = 13 × 4 + ________
(g) 3 × (________ + ________) = 3 × 5 + 3 × 2
(h) (________ + ________) × ________ = 2 × 4 + 3 × 4
(i) 5 × (9 – 2) = 5 × 9 – 5 × ________
(j) (5 – 2) × 7 = 5 × 7 – 2 × ________
(k) 5 × (8 – 3) = 5 × 8 5 × ________
(l) (8 – 3) × 7 = 8 × 7 3 × 7
(m) 5 × (12 – ________) = ________ 5 × ________
(n) (15 – ________) × 7 = ________ 6 × 7
(o) 5 × (________ – ________) = 5 × 9 – 5 × 4
(p) (________ – ________) × ________ = 17 × 7 – 9 × 7
Solution:
(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
(e) 3 × (1 + 4) = 3 × 1 + 3 × 4
(f) (13 + 6) × 4 = 13 × 4 + 6 × 4
(g) 3 × (5 + 2) = 3 × 5 + 3 × 2
(h) (2 + 3) x 4 = 2 × 4 + 3 × 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
(m) 5 × (12 – 4) = 5 × 12 5 × 4
(n) (15 – 6) × 7 = 15 × 7 6 × 7
(o) 5 × (9 – 4) = 5 × 9 – 5 × 4
(p) (17 – 9) × 7 = 17 × 7 – 9 × 7
Question 2.
In the boxes below, fill in ‘<’, ‘>’ or ‘=’ after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out, and not by evaluating the expressions.
(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
Solution:
(a) LHS = 5 × 29 = 145
RHS = -5 × 29 = – 145
LHS > RHS
(b) LHS = 15 + 162 = 177
RHS = 24 × 18 = 432
LHS < RHS
(c) LHS = 23 × 8 = 184
RHS = 391 + 207 = 598
LHS < RHS
(d) LHS = 6 × 42 = 252
RHS = 1428 – 1176 = 252
LHS = RHS
Question 3.
Here is one way to make 14: 2 × (1 + 6) = 14. Are there other ways of getting 14? Fill them out below:
(a) ______ × (______ + ______) = 14
(b) ______ × (______ + ______) = 14
(c) ______ × (______ + ______) = 14
(d) ______ × (______ + ______) = 14
Solution:
(a) 2 × (2 + 5) = 14
(b) 2 × (3 + 4) = 14
(c) 7 × (1 + 1) = 14
(d) 7 × (2 + 0) = 14
Question 4.
Find out the sum of the numbers given in each picture below in at least two different ways. Describe how you solved it through expressions.
Solution:
(i) Way-1 (Sum Rows)
Row 1 + Row 2 + Row 3
= (4 + 8 + 4) + (8 + 4 + 8) + (4 + 8 + 4)
= 16 + 20 + 16
= 52
Way-2 (Group by Number)
Number of 4s × 5 + Number of 8s × 4
= 4 × 5 + 8 × 4
= 20 + 32
= 52
(ii) Way-1 (Sum Rows)
Row 1: 5 + 6 + 6 + 5 = 22
Row 2: 6 + 5 + 5 + 6 = 22
Row 3: 6 + 5 + 5 + 6 = 22
Row 4: 5 + 6 + 6 + 5 = 22
Each row sums to 22
There are 4 rows.
Total = 4 × 22 = 88
Expression = 4 × (5 + 6 + 6 + 5)
Way-2 (Group by Number)
Number of 5s × 8 + Number of 6s × 8
= 5 × 8 + 6 × 8
= 40 + 48
= 88
Figure It Out (Pages 42 – 44)
Question 1.
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 the 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 number 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 the 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 top. In how many days will the snail get the treat?
Solution:
(a) No. of mangoes = (7 × 9 + 7 × 11) kg
= 7 × (9 + 11) kg
= 7 × 20 kg
= 140 kg
(b) Earning per month = ₹ 20,000
Expenses = ₹ 5,000 + ₹ 5000 + ₹ 2,000 = ₹ 12,000
Savings = ₹ 20,000 – ₹ 12,000 = ₹ 8,000
Annual savings = ₹ 12 × 8,000 = ₹ 96,000
(c) 1st day = (3 – 2) cm = 1 cm
In 7 days = 7 × 1 cm = 7 cm
On 8th day = (7 + 3) cm = 10 cm
Snail will reach the top on the 8th day.
Question 2.
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
Solution:
No. of stories read in one week = (7 – 2)
No. of stories read in 8 week = (7 – 2) × 8 = 7 × 8 – 2 × 8
∴ Option (b) and (g) are correct.
Question 3.
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
Solution:
(a) (1 – 2) + (3 – 4) + (5 – 6) + (7 – 8) + (9 – 10)
= (-1) + (-1) + (-1) + (-1) + (-1)
= -1 × 5
= -5
or
(1 + 3 + 5 + 7 + 9) – (2 + 4 + 6 + 8 + 10)
= 25 – 30
= -5
(b) (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1) + (1 – 1)
= 0 + 0 + 0 + 0 + 0
= 0
or
(1 + 1 + 1 + 1 + 1) – (1 + 1 + 1 + 1 + 1)
= 5 – 5
= 0
Question 4.
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)
Solution:
(a) LHS = (49 – 7) + 8
= 42 + 8
= 50
RHS = 49 – (7 – 8)
= 49 – (-1)
= 49 + 1
= 50
LHS = RHS
(b) LHS = (83 × 42) – 18
= 3486 – 18
= 3468
RHS = 83 × 40 – 18
= 3320 – 18
= 3302
LHS > RHS
(c) LHS = 145 – 17 × 8
= 145 – 136
= 9
RHS = 145 – 17 × 6
= 145 – 102
= 43
LHS < RHS
(d) LHS = 23 × 48 – 75
= 1104 – 75
= 1029
RHS = 23 × (48 – 35)
= 23 × 13
= 299
LHS > RHS
(e) LHS = (16 – 11) × 12
= 5 × 12
= 60
RHS = -11 × 12 + 16 × 12
= -132 + 192
= 60
LHS = RHS
(f) LHS = (76 – 53) × 88
= 23 × 88
= 2024
RHS = 88 × (53 – 76)
= 88 × (-23)
= -2024
LHS > RHS
(g) LHS = 25 × (42 + 16)
= 25 × 58
= 1450
RHS = 25 × (43 + 15)
= 25 × 58
= 1450
LHS = RHS
(h) LHS = 36 × (28 – 16)
= 36 × 12
= 432
RHS = 35 × (27 – 15)
= 35 × 12
= 420
LHS > RHS
Question 5.
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 that 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
Solution:
(a) Given expression: (83 – 37) – 12
= 46 – 12
= 34
(i) (84 – 38) – 12
= 46 – 12
= 34
(ii) 84 – (37 + 12)
= 84 – 49
= 35
(iii) (83 – 38) – 13
= 45 – 13
= 32
(iv) (-37 + 83) – 12
= 46 – 12
= 34
∴ (i) and (iv) give the same value.
(b) 93 + (37 × 44) + 76
= (93 + 1628) + 76
= 1721 + 76
= 1797
(i) 37 + 93 × 44 + 76
= 37 + 4092 + 76
= 4205
(ii) 93 + 37 × 76 + 44
= 93 + 2812 + 44
= 2949
(iii) (93 + 37) × (44 + 76)
= 130 × 120
= 15600
(iv) 37 × 44 + 93 + 76
= 1628 + 169
= 1797
Hence, (iv) gives the same value.
Question 6.
Choose a number and create ten different expressions having that value.
Solution:
Let the number be ‘0’.
4 – 4 = 0
3 × 6 – 18 = 0
7 + 4 – 11 = o
2 × (6 – 6) = 0
7 × (6 + 2) – 56 = 0
(8 – 3) × 0 = 0
(7 – 2) × 5 – 25 = 0
-4 + 8 × 2 – 12 = 0
(9 + 4) – (10 + 3) = 0
(7 × 3) + 4 – 25 = 0