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

Accepted Answer

(a) 13 + 4 = 17
11 + 6 = 17
Therefore, 13 + 4 = 11 + 6
(b) Since 6 × 5 = 30
22 + 8 = 30
Therefore, 22 + 8 = 6 × 5
(c) Since 64 ÷ 2 = 32
8 × 4 = 32
Therefore, 8 × 4 = 64 ÷ 2
(d) Since 34 – 25 = 9
Therefore, 34 – 9 = 25

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

Accepted Answer

(a) 67 – 19 = 48
(b) 67 – 20 = 47
(c) 35 + 25 = 60
(d) 5 × 11 = 55
(e) 120 ÷ 3 = 40
Clearly, 40 ’ or ‘

Question 3

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 ti

Accepted Answer

(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 = $\frac{100}{2}$
Therefore, the total number of gold coins Princess Elsa and Princess Anna have together = 2 × 100 + $\frac{100}{2}$
Thus, the expression describing the above situation is 2 × 100 + $\frac{100}{2}$
Terms: 2 × 100, $\frac{100}{2}$
Now, 2 × 100 + $\frac{100}{2}$ = 200 + 50 = 250
(b) (i) Metro train ticket for an adult = ₹ 40
So, the metro train ticket for four adults = 4 × 40
Metro train ticket for a child = ₹ 20
So, the metro train ticket for three children = 3 × 20
Therefore, the expression describing the total cost of tickets for four adults and three children is 4 × 40 + 3 × 20
Terms: 4 × 40, 3 × 20
Now, 4 × 40 + 3 × 20 = 160 + 60 = 220
(ii) Metro train ticket for an adult = ₹ 40
So, the metro train ticket for a group of three adults = 3 × 40
Therefore, the expression describing the total cost of tickets for the two groups having three adults each is 2 × (3 × 40).
Terms: 2 × (3 × 40)
Now, 2 × (3 × 40) = 2 × 120 = 240
(c) By observing the given picture, the total height of the window = number of gaps × 5 cm + number of grills × 2 cm + number of borders × 3 cm = 7 × 5 + 6 × 2 + 2 × 3
Terms: 7 × 5, 6 × 2, 2 × 3
Now, 7 × 5 + 6 × 2 + 2 × 3 = 35 + 12 + 6 = 47 + 6 = 53
Tinker the Terms I
NCERT In-Text Questions (Pages 36-37)
Some expressions are given in the following three columns. In each column, one or more terms are changed from the first expression. Go through the example (in the first column) and fill in the blanks, doing as little computation as possible.
Solution:
Figure it Out (Pages 37-38)

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

Accepted Answer

(a)
Expressions having the same terms have the same value. Therefore, 319 – 537 and -537 + 319 have the same value.
(b)
Expressions having the same terms have equal values.
Therefore, 87 + 46 – 109, 87 + 46 – 109, 87 + 46 – 109 have the same value.
Also, 87 – 46 + 109 and (87 – 46) + 109 have the 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

Accepted Answer

(a) 34 – (9 + 12) = 34 – 21 = 13
(b) (56 – 14) – 8 = 42 – 8 = 34
(c) -22 – (12 + 10) + 22 = -22 – 22 + 22 = -22

Source: This question is from Arithmetic Expressions, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Arithmetic Expressions: Add, Brackets, Places, Expressions, Lead, Values. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Arithmetic ExpressionsQ1: Fill in the blanks to make the expressions equal on both sides of the ‘=’ sign: (a) 13 + 4 =...
Q2: Arrange the following expressions in ascending (increasing) order of their values. (a) 67 – 19 (b)...
Q3: For each of the following situations, write the expression describing the situation, identify its...
Q4: In each of the sets of expressions below, identify those that have the same value. Do not evaluate...
Q6: Using only reasoning of how terms change their values, fill the blanks to make the expressions on...
Practice more questions from Arithmetic Expressions &mdash; Mathematics, Class 7 CBSE

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 – ________

Accepted Answer

(a) 423 + 419 = 419 + 423
(b) 207 – 68 = 210 – 71

Source: This question is from Arithmetic Expressions, Mathematics &mdash; Class 7, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Arithmetic Expressions: Reasoning, Terms, Change, Values, Fill, Blanks. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 7 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Arithmetic ExpressionsQ1: Fill in the blanks to make the expressions equal on both sides of the ‘=’ sign: (a) 13 + 4 =...
Q2: Arrange the following expressions in ascending (increasing) order of their values. (a) 67 – 19 (b)...
Q3: For each of the following situations, write the expression describing the situation, identify its...
Q4: In each of the sets of expressions below, identify those that have the same value. Do not evaluate...
Q7: Using the numbers 2, 3, and 5, and the operators ‘+’ and ‘-‘, and brackets, as necessary, generate...
Practice more questions from Arithmetic Expressions &mdash; Mathematics, Class 7 CBSE

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

Accepted Answer

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.

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.

Accepted Answer

(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.

Question 9

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)

Accepted Answer

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.
Removing Brackets-II
NCERT In-Text Questions (Pages 39-40)
If another friend, Sangmu, joins them and orders the same items, what will be the expression for the total amount to be paid?
Solution:
If another friend, Sangmu, joins them (Lhamo and Norbu) and orders the same items, then the expression for the total amount will be 3 × (43 + 24).
5 × 4 + 3 ≠ 5 × (4 + 3). Can you explain why?
Is 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5?
Solution:
Expression 5 × 4 + 3 means 3 more than 5 × 4, which is equal to 23, but 5 × (4 + 3) means 5 times (4 + 3), which is equal to 35.
Hence, 5 × 4 + 3 ≠ 5 × (4 + 3)
5 × (4 + 3), 5 × (3 + 4), and (3 + 4) × 5 have the same meaning, which is 5 times the sum of 3 and 4, and give the same value.
Hence, 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5
Tinker the Terms II
NCERT In-Text Questions (Page 41)
Use this method to find the following products:
(а) 95 × 8
(b) 104 × 15
(c) 49 × 50
Is this quicker than the multiplication procedure you use generally?
Solution:
(a) 95 × 8 = (100 – 5) × 8
= 100 × 8 – 5 × 8
= 800 – 40
= 760
(b) 104 × 15 = (100 + 4) × 15
= 100 × 15 + 4 × 15
= 1500 + 60
= 1560
(c) 49 × 50 = (50 – 1) × 50
= 50 × 50 – 50 × 1
= 2500 – 50
= 2450
Yes, this procedure is quicker than the general multiplication procedure.
Which other products might be quicker to find, like the ones above?
Solution:
Do it yourself.
Figure it Out (Pages 41-42)