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CBSE Important Questions Class 7 Maths Chapter 2 Arithmetic Expressions

CBSE Important Questions Class 7 Maths Chapter 2 – Arithmetic Expressions

Class 7 Maths Chapter 2 Arithmetic Expressions is the second chapter of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. An arithmetic expression is a group of numbers joined by operations like +, –, × and ÷. Students learn to find the terms of an expression, to follow the correct order of operations, to use brackets, and to understand the commutative, associative and distributive properties.

These CBSE important questions for Class 7 Maths Chapter 2 include multiple choice questions, a table to complete, dot-pattern figures, assertion-reason questions and word problems on cost, distance and comparing expressions. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 2 Arithmetic Expressions

Arithmetic Expressions (New NCERT)

Medium

Q.

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 – ____

Arithmetic Expressions (New NCERT)

Medium

Q.

In the boxes below, fill ‘<’, ‘>’ 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) x 29 ____ (3 – 8) x 29
(b) 15 + 9 x 18 ____ (15 + 9) x 18
(c) 23 x (17 – 9) ____ 23 x 17 + 23 x 9
(d) (34 – 28) x 42 ____ 34 x 42 – 28 x 42

Arithmetic Expressions (New NCERT)

Medium

Q.

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 which 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

Arithmetic Expressions (New NCERT)

Medium

Q.

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)

Arithmetic Expressions (New NCERT)

Medium

Q.

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

Arithmetic Expressions (New NCERT)

Medium

Q.

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

Arithmetic Expressions (New NCERT)

Medium

Q.

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 a 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 amount 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 a 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 its top. In how many days will the snail get the treat?

Arithmetic Expressions (New NCERT)

Medium

Q.

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.

Arithmetic Expressions (New NCERT)

Medium

Q.

Here is one way to make 14: 2 x (1 + 6) = 14. Are there other ways of getting 14? Fill them out below:
(a) ____ × (____ + ____) = 14
(b) ____ × (____ + ____) = 14
(c) ____ × (____ + ____) = 14
(d) ____ × (____ + ____) = 14

Arithmetic Expressions (New NCERT)

Medium

Q.

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

Arithmetic Expressions (New NCERT)

Medium

Q.

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.

Arithmetic Expressions (New NCERT)

Medium

Q.

Which other products might be quicker to find like the ones above?

Arithmetic Expressions (New NCERT)

Medium

Q.

Use this method to find the following products:
(a) 95 × 8
(b) 104 × 15
(c) 49 × 50
Is this quicker than the multiplication procedure you use generally?

Arithmetic Expressions (New NCERT)

Medium

Q.

97 × 25 = 100 × 25 – 3 × 25. Find this value.

Arithmetic Expressions (New NCERT)

Medium

Q.

Is 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5?

Arithmetic Expressions (New NCERT)

Medium

Q.

5 × 4 + 3 ≠ 5 × (4 + 3). Can you explain why?

Arithmetic Expressions (New NCERT)

Medium

Q.

If another friend, Sangmu, joins them and orders the same items, what will be the expression for the total amount to be paid? [Expression for Lhamo and Norbu who each ordered a vegetable cutlet costing ₹43 and a rasgulla costing ₹24 is 2 × (43 + 24)]

Arithmetic Expressions (New NCERT)

Medium

Q.

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)

Arithmetic Expressions (New NCERT)

Medium

Q.

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.

Arithmetic Expressions (New NCERT)

Medium

Q.

Choose a number and create ten different expressions having that value.

CBSE Important Questions Class 7 Maths Chapter 2 Arithmetic Expressions

Q1. Complete the table:

Table to complete: expressions written as the sum of their terms

Answer: Terms are the parts of an expression separated by + signs. A subtraction is written as adding a negative number, and a multiplication like 6 × 3 is kept together as one term. The completed table is given below.

Expression	Expression as the sum of its terms	Terms
13 – 2 + 6	13 + (–2) + 6	13, –2, 6
5 + 6 × 3	5 + (6 × 3)	5, (6 × 3)
4 + 15 – 9	4 + 15 + (–9)	4, 15, –9
23 – 2 × 4 + 16	23 + [(–2) × 4] + 16	23, (–2 × 4), 16
28 + 19 – 8	28 + 19 + (–8)	28, 19, –8

Q2. Which of the following property is applicable to the given: 2 × 3 = 3 × 2
(a) closure property
(b) commutative property
(c) associative property
(d) distributive property

Answer: (b) commutative property
The commutative property says that changing the order of the numbers in addition or multiplication does not change the answer (a × b = b × a). Here 2 × 3 = 6 and 3 × 2 = 6, so the order changed but the product stayed the same.

Q3. Evaluate 13 + 2 × 3 using the correct order of operations.
(a) 45
(b) 19
(c) 25
(d) 15

Answer: (b) 19
By the order of operations (DMAS), multiplication is done before addition. First 2 × 3 = 6, then 13 + 6 = 19.

Q4. Which of the following best describes the associative property?
(a) Swapping two numbers’ positions
(b) Rearranging brackets without changing value
(c) Multiplying a number by a sum
(d) Subtracting to get a difference

Answer: (b) Rearranging brackets without changing value
The associative property says that when we add or multiply three or more numbers, the way we group them with brackets does not change the answer. For example, (2 + 3) + 4 = 9 and 2 + (3 + 4) = 9. Option (a) is the commutative property and option (c) is the distributive property.

Q5. Ruby wrote the expression 6 × 5 + 3 during a game. What does it represent?
(a) 3 Groups of 5 with 6 extra
(b) 6 Groups of 5 with 3 extra
(c) 5 Groups of 3 with 3 extra
(d) Groups of 5 with 3 extra

Answer: (b) 6 Groups of 5 with 3 extra
6 × 5 means 6 groups of 5, and + 3 means 3 extra are added. So the expression represents 6 groups of 5, plus 3 extra, which equals 33.

Q6. Identify the correct term expansion for 13 – 2 + 6.
(a) 13, 2, 6
(b) –13, –2, 6
(c) 13, 2, –6
(d) 13, –2, 6

Answer: (d) 13, –2, 6
Write the expression as a sum: 13 + (–2) + 6. The –2 is a term because of the subtraction sign. So the terms are 13, –2 and 6.

Q7. Compare the following expressions without evaluating them:
(a) 400 – (120 + 25)
(b) 400 – 120 – 25
(c) 400 – (120 – 25)
Explain the difference in value and structure of these expressions.

Answer: (a) The bracket adds 120 and 25 first, so this expression subtracts the sum 145 from 400: 400 – 145.
(b) Subtracting 120 and then 25 is the same as subtracting their total 145. So (b) has the same value as (a): 400 – 120 – 25 = 400 – 145.
(c) Here the bracket gives the difference 120 – 25 = 95, so this expression is 400 – 95.
Subtracting a bigger number gives a smaller result, so 400 – 145 < 400 – 95.
Thus, (a) = (b) < (c).

Q8. A delivery van covers 60 km in the morning, then 45 km after lunch, and finally makes 3 trips of 15 km each in the evening.
(a) Write a mathematical expression to show the total distance covered.
(b) Simplify the expression.
(c) Explain the importance of using brackets if needed.

Answer: (a) Total distance = 60 + 45 + 3 × 15
(b) Multiplication first: 3 × 15 = 45. Then 60 + 45 + 45 = 150 km.
(c) No brackets are needed here because multiplication is done before addition, so 3 × 15 is automatically calculated first. Brackets would be needed only if we wanted the addition done before the multiplication, for example (60 + 45) × 3, which is not what the question means.

Q9. (a) Write the number 48 in four different ways using two numbers and the operations +, –, ×, ÷. For each expression, show that the value is 48 and explain the logic used.
(b) Write one expression that uses all four operations (+, –, ×, ÷) together and still evaluates to 48.

Answer: (a) Four different ways:
40 + 8 = 48 (direct sum of a multiple of 10 and a one-digit number)
50 – 2 = 48 (start a little above 48 and subtract the difference)
6 × 8 = 48 (a pair from the multiplication table of 48)
96 ÷ 2 = 48 (division is the reverse of multiplication: 48 × 2 = 96)
(b) Expression using all four operations:
(8 × 6) – 4 + (12 ÷ 3)
Brackets first: 8 × 6 = 48 and 12 ÷ 3 = 4, giving 48 – 4 + 4.
Then left to right: 48 – 4 = 44 and 44 + 4 = 48.
So (8 × 6) – 4 + (12 ÷ 3) = 48.

Q10. Observe the following figures. Each figure shows rows and columns of orange dots arranged in equal groups. Write 2 different arithmetic expressions for each figure to represent the total number of orange dots.
Figure 1:

Figure 1: 2 rows of 3 orange dots

Figure 2:

Figure 2: 2 rows of 4 orange dots

Figure 3:

Figure 3: 3 rows of 4 orange dots

Figure 4:

Figure 4: 3 rows of 5 orange dots

Answer: Figure 1: 2 rows and 3 columns → 2 × 3 = 6 dots, or 3 + 3 = 6 dots. Expressions: 2 × 3 and 3 + 3
Figure 2: 2 rows and 4 columns → 2 × 4 = 8 dots, or 4 + 4 = 8 dots. Expressions: 2 × 4 and 4 + 4
Figure 3: 3 rows and 4 columns → 3 × 4 = 12 dots, or 4 + 4 + 4 = 12 dots. Expressions: 3 × 4 and 4 + 4 + 4
Figure 4: 3 rows and 5 columns → 3 × 5 = 15 dots, or 3 + 3 + 3 + 3 + 3 = 15 dots. Expressions: 3 × 5 and 3 + 3 + 3 + 3 + 3

Q11. Riya wrote the expression (6 + 500) + 99 to calculate the total cost of buying 6 items of ₹500 each and paying an additional ₹99 delivery charge.
(a) Did she write it correctly? Justify your answer.
(b) Correct the expression if needed.
(c) Evaluate the expression correctly.

Answer: (a) No, Riya did not write the expression correctly. In (6 + 500) + 99, the numbers 6 and 500 are added, which gives ₹506 for 6 items. The cost of 6 items of ₹500 each must be found by multiplying: 6 × 500.
(b) Correct expression: (6 × 500) + 99 → 6 items at ₹500 each, plus the ₹99 delivery charge.
(c) 6 × 500 = ₹3000, and ₹3000 + 99 = ₹3099. The total cost is ₹3099.

Q12. The commutative property for subtraction of two whole numbers p and q is possible only if
(a) p > q
(b) p < q
(c) p = q
(d) None of these

Answer: (c) p = q
Commutative property for subtraction would mean p – q = q – p. Adding q and p to both sides gives 2p = 2q, so p = q. For example, if p = q = 5, then 5 – 5 = 0 = 5 – 5. If p and q are different (say 5 and 3), 5 – 3 = 2 but 3 – 5 = –2, so it does not hold.

Q13. Assertion (A): 7256 − (8398 − 6532) = (7256 − 8398) − 6532
Reason (R): Associativity does not hold true for subtraction of whole numbers.
Choose the correct option out of the choices given below:
(a) Both statements A and R are true, and R is the correct explanation of A.
(b) Both statements A and R are true, but R is not the correct explanation of A.
(c) Statement A is true, but statement R is false.
(d) Statement A is false, but statement R is true.

Answer: (d) Statement A is false, but statement R is true.
LHS = 7256 − (8398 − 6532) = 7256 − 1866 = 5390.
RHS = (7256 − 8398) − 6532 = (−1142) − 6532 = −7674.
Since 5390 ≠ −7674, Statement A is false. This example shows that grouping changes the answer, so associativity does not hold for subtraction. Statement R is true.

Q14. 18764 + 7564 ____ 7564 + 18764
(a) <
(b) >
(c) =
(d) None of these

Answer: (c) =
Both expressions add the same two numbers, 18764 and 7564, only in a different order. By the commutative property of addition, changing the order does not change the sum. So 18764 + 7564 = 7564 + 18764.

Q15. Which of the following is false?
(a) 85 + (−85) = 0
(b) (85 + 12) + 9 = 85 + (12 + 9)
(c) 46 − 75 = (40 + 6) − 75
(d) (68 − 24) − 10 = 68 − (24 − 10)

Answer: (d) (68 − 24) − 10 = 68 − (24 − 10)
(a) A number plus its opposite is 0, true. (b) Associative property of addition: both sides are 106, true. (c) 46 written as 40 + 6, both sides are −29, true. (d) LHS = 44 − 10 = 34 but RHS = 68 − 14 = 54. Since 34 ≠ 54, this statement is false. Subtraction is not associative.

Related Study Material on Extramarks

Q.1

$\begin{array}{l} What is the value of the following expression? \\ \frac{0 .1}{0 .01} + \frac{0 .01}{0 .1} \end{array}$

1.10.10

2.10.01

3.1.10

4.1.01

Marks:1

Ans Option1
Explanation

$\frac{0 .1}{0 .01} + \frac{0 .01}{0 .1} = 10 + \frac{1}{10} = 10 + 0 .1 = 10 .1$

Q.2 What is the value of 10.05 × 1.05?

1. 10.5125

2. 10.5525

3. 10.5515

4. 10.5425

Marks:1

Ans Option2
Explanation

1005 × 105 = 105525

Since 10.05 has 2 digits and 1.05 has 2 digits after the decimal point, therefore, the product must have 4 digits after decimal point.

10.05 × 1.05 = 10.5525

Q.3 Bob has given half of the whole cake to his sister Maria. Maria further divided it into three parts, ate only one part and kept the rest two parts in the fridge for later. What part of the whole cake has she kept in the fridge?

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{3}{2}$

Marks:1

Ans Option2
Explanation

$\begin{array}{l} Share= \frac{1}{2} \\ The part which Maria ate = \frac{1}{2} \div 3 \\ Remaining part = \frac{1}{2} - \frac{1}{6} = \frac{3 - 1}{6} = \frac{2}{6} = \frac{1}{3} \end{array}$

Q.4

$4 + \frac{3}{5} - \frac{2}{7}$

Marks:1
Ans

L.C.M of 1, 5, 7 = 35

$\begin{array}{l} ∴ 4 + \frac{3}{5} - \frac{2}{7} = \frac{140 + 21 - 10}{35} \\ = \frac{151}{35} \end{array}$

Q.5 What is the expanded form of 205.149?

Marks:1

$2 \times 1000 + 0 \times 100 + 5 \times 10 + 1 \times \frac{1}{10} + 4 \times \frac{1}{100} + 9 \times \frac{1}{1000}$ $2 \times 100 + 0 \times 10 + 5 \times 1 + 1 \times 1 + 4 \times \frac{1}{10} + 9 \times \frac{1}{100}$ $1 \times 100 + 4 \times 10 + 9 \times 1 + 2 \times \frac{1}{10} + 0 \times \frac{1}{100} + 5 \times \frac{1}{1000}$ $2 \times 100 + 0 \times 10 + 5 \times 1 + 1 \times \frac{1}{10} + 4 \times \frac{1}{100} + 9 \times \frac{1}{1000}$

Ans Option4
Explanation

Hundreds
(100)

Tens
(10)

Ones
(1)

Tenths

$(\frac{1}{10})$

Hundredths

$(\frac{1}{100})$

Thousandths

$(\frac{1}{1000})$

2

0

5

1

4

9

$\begin{array}{l} The expanded form of 205 .149 is: \\ 2 \times 100 + 0 \times 10 + 5 \times 1 + 1 \times \frac{1}{10} + 4 \times \frac{1}{100} + 9 \times \frac{1}{1000} \end{array}$

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