NCERT Solutions for Class 7 maths Chapter 2: Arithmetic Expressions

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) 13 + 4 = 17
11 + 6 = 17
Therefore, 13 + 4 = 11 + 6

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
Clearly, 40 < 47 < 48 < 55 < 60
Therefore, 120 ÷ 3 < 67 – 20 < 67 – 19 < 5 × 11 < 35 + 25
Thus, (e) < (b) < (a) < (d) < (c).

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 = 28 + (-7) + 8
Terms: 28, -7, and 8
28 – 7 + 8
= 28 + (-7) + 8
= 21 + 8 = 29

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) 89 + 21 – 10
Riya and Siya are cousins. They went to the beach, from where Riya collected 89 stones and Siya collected 21 stones. When they reached home, their other younger sister asked them for some stones. They give her 10 stones from their collection. How many stones were left with both Riya and Siya?
89 + 21 – 10 = 89 + 21 + (-10) = 89 + 11 = 100

For each of the following situations, write the expression describing the situation, identify its terms, and find the value of the expression.
(а) 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) Number of gold coins Princess Elsa got = 100
Number of gold coins Princess Anna got = 100
Princess Elsa used the coins to start the business and doubled her coins.
So, the number of coins Princess Elsa has = 2 × 100
Princess Anna bought jewellery and has only half of the coins left.
So, the number of coins Princess Anna has =
Therefore, the total number of gold coins Princess Elsa and Princess Anna have together = 2 × 100 +
Thus, the expression describing the above situation is 2 × 100 +
Terms: 2 × 100,
Now, 2 × 100 + = 200 + 50 = 250

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

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)
= 14 + 12 + 10
= 14 + 22
= 36

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) (6 + 10) – 2 and 6 + (10 – 2)
(6 + 10) – 2 = 16 – 2 = 14
and 6 + (10 – 2) = 6 + 8 = 14
Clearly, (6 + 10) – 2 = 6 + (10 – 2)
Hence, the expressions in part (a) have the same value.

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)

Expressions having the same terms have the same value. Therefore, 319 – 537 and -537 + 319 have the same value.

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) = 34 – 21 = 13
(b) (56 – 14) – 8 = 42 – 8 = 34
(c) -22 – (12 + 10) + 22 = -22 – 22 + 22 = -22

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

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:
Here are a few expressions formed by using numbers 2, 3, and 5 and the operators ‘+’ and ‘-‘ and brackets having different values.
(2 + 3) – 5 = 5 – 5 = 0,
5 + (3 – 2) = 5 + 1 = 6,
-5 + (2 – 3) = -5 + (-1) = -6,
(-2 + 3) – 5 = 1 – 5 = – 4, etc.

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, she will always get the correct answer if she subtracts 10 from a number and then adds 1 to the result instead of directly subtracting 9 from the number, because subtracting 10 and adding 1, i.e., -10 + 1 = -9, is equivalent to subtracting 9 from the number.
As 36 – 9 = 27 or (36 – 10) + 1 = 26 + 1 = 27
(b) Do it yourself.

Consider the two expressions:
(a) 73 – 14 + 1
(b) 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:
Given expressions:
73 – 14 + 1 = 60 and 73 – 14 – 1 = 58
Now,
(a) 73 – (14 + 1) = 73- 15 = 58
(b) 73 – (14 – 1) = 73 – 13 = 60
(c) 73 + (-14 + 1) = 73 – 13 = 60
(d) 73 + (-14 – 1) = 73 + (-15) = 58
Hence, expressions (b) and (c) are equal to the expression 73 – 14 + 1, and expressions (a) and (d) are equal to the expression 73 – 14 – 1.

Fill in the blanks with numbers and boxes by signs, so that the expressions on both sides are equal.
(а) 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:
(а) 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 × (10 + 4) = 30 + 12
(f) (13 + 6) × 4 = 13 × 4 + 24
(g) 3 × (5 + 2) = 3 × 5 + 3 × 2
(h) (2 + 3) × 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 – 3) = 60 – 5 × 3
(n) (15 – 6) × 7 = 105 – 6 × 7
(o) 5 × (9 – 4) = 5 × 9 – 5 × 4
(p) (17 – 9) × 7 = 17 × 7 – 9 × 7

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 – 9) 23 × 17 + 23 × 9
(d) (34 – 28) × 42 34 × 42 – 28 × 42
Solution:
(a) (8 – 3) × 29 > (3 – 8) × 29
Because, (3 – 8) × 29 = -(8 – 3) × 29
⇒ (8 – 3) × 29 > (3 – 8) × 29

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 × (5 + 2) = 14
(b) 2 × (3 + 4) = 14
(c) 2 × (4 + 3) = 14
(d) 2 × (6 + 1) = 14

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:
For I: 5 × 4 + 4 × 8 = 20 + 32 = 52
or 4 × (4 + 8) + 4 = 4 × 12 + 4 = 52

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) Supplies of mangoes by Rahim in the market each day = 9 kg
Supplies of mangoes by Shyam in the market each day = 11 kg
Total supplies of mangoes in the market on each day = (9 + 11) kg
Therefore, total supplies of mangoes in the market in all 7 days = 7 × (9 + 11) kg
= 7 × 20
= 140 kg

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:
Number of days in a week except Tuesday and Saturday = 7 – 2
Since Melvin reads a two-page story every day except Tuesday and Saturday.
Therefore, number of stories read in a week = 1 × (7 – 2)
So, number of stories read in 8 weeks = 8 × 1 × (7 – 2)
= 8 × (7 – 2) or (7 – 2) × 8 [Expression (b)]
or 7 × 8 – 2 × 8 [Expression (g)]
Only expressions (b) and (g) describe this scenario.

Find different ways of evaluating the following expressions:
(а) 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 + 3 + 5 + 7 + 9) + (-2 – 4 – 6 – 8 – 10)
= 25 + (-30)
= -5
or
1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10
= (1 – 2) + (3 – 4) + (5 – 6) + (7 – 8) +(9 – 10)
= (-1) + (-1) + (-1) + (-1) + (-1)
= -5

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) 49 – 7 + 8 = 49 – 7 + 8
(∵ All the terms on both sides are the same)

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) 83 – 37 – 12 = 83 – 37 – 12 + (1 – 1)
= (83 + 1) – 37 – 1 – 12
= 84 – 38 – 12 (option (i))
= 34
Or
83 – 37 – 12 = -37 + 83 – 12
= 46 – 12
= 34 (option (iv))
Hence, (i) and (iv) are equal to the given expression 83 – 37 – 12.

Choose a number and create ten different expressions having that value.
Solution:
Do it yourself.