Arithmetic Expressions — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Arithmetic Expressions" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Arithmetic Expressions" — 8 important questions with detailed answers for CBSE boar…
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NCERT Solutions for Class 7 Mathematics — Arithmetic Expressions. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Arithmetic Expressions — All 8 Questions Solved
Q1. Simplify: 12 + 8 ÷ 4 - 2
Step 1: Apply BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)
Step 2: First, perform division:
8 ÷ 4 = 2
Expression becomes: 12 + 2 - 2
Step 3: Perform addition and subtraction from left to right:
12 + 2 = 14
14 - 2 = 12
Answer: 12
Q2. Simplify: 36 ÷ 6 × 3 + 2
Step 1: Apply BODMAS
Step 2: Perform division and multiplication from left to right:
36 ÷ 6 = 6
6 × 3 = 18
Expression becomes: 18 + 2
Step 3: Perform addition:
18 + 2 = 20
Answer: 20
Q3. Evaluate: 2 × (15 - 5) ÷ 2
Step 1: Apply BODMAS - evaluate brackets first
(15 - 5) = 10
Step 2: Expression becomes: 2 × 10 ÷ 2
Step 3: Perform multiplication and division from left to right:
2 × 10 = 20
20 ÷ 2 = 10
Answer: 10
Q4. Simplify: 100 - 10 × 5 + 8
Step 1: Apply BODMAS
Step 2: Perform multiplication first:
10 × 5 = 50
Expression becomes: 100 - 50 + 8
Step 3: Perform subtraction and addition from left to right:
100 - 50 = 50
50 + 8 = 58
Answer: 58
Q5. Find the value of: 8 + [5 × (6 - 2)]
Step 1: Apply BODMAS - evaluate innermost brackets first
(6 - 2) = 4
Step 2: Expression becomes: 8 + [5 × 4]
Step 3: Evaluate the square bracket:
5 × 4 = 20
Expression becomes: 8 + 20
Step 4: Perform addition:
8 + 20 = 28
Answer: 28
Q6. Simplify: 24 ÷ (12 - 4) × 2
Step 1: Apply BODMAS - evaluate brackets first
(12 - 4) = 8
Step 2: Expression becomes: 24 ÷ 8 × 2
Step 3: Perform division and multiplication from left to right:
24 ÷ 8 = 3
3 × 2 = 6
Answer: 6
Q7. Evaluate: 9 - 3 × 2 + 1
Step 1: Apply BODMAS
Step 2: Perform multiplication first:
3 × 2 = 6
Expression becomes: 9 - 6 + 1
Step 3: Perform subtraction and addition from left to right:
9 - 6 = 3
3 + 1 = 4
Answer: 4
Q8. Simplify: (20 + 10) ÷ (3 + 2)
Step 1: Apply BODMAS - evaluate brackets first
(20 + 10) = 30
(3 + 2) = 5
Step 2: Expression becomes: 30 ÷ 5
Step 3: Perform division:
30 ÷ 5 = 6
Answer: 6
Arithmetic Expressions — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. Simplify: 5 + 3 × 2
- A. 16
- B. 11
- C. 10
- D. 13
Answer: B. 11 — According to BODMAS/PEMDAS, multiplication is performed before addition. So, 3 × 2 = 6, and then 5 + 6 = 11.
MCQ 2. Calculate: (-7) + 4
- A. -11
- B. 11
- C. -3
- D. 3
Answer: C. -3 — When adding a negative number and a positive number, we subtract their absolute values and keep the sign of the number with the larger absolute value. |7| - |4| = 3, and since 7 is larger and negative, the answer is -3.
MCQ 3. Evaluate: 18 ÷ 6 + 5 - 2
- A. 6
- B. 8
- C. 10
- D. 3
Answer: A. 6 — Following BODMAS/PEMDAS, division is done first: 18 ÷ 6 = 3. Then, perform addition and subtraction from left to right: 3 + 5 - 2 = 8 - 2 = 6.
MCQ 4. Simplify: 4 × (7 - 3)
- A. 28
- B. 16
- C. 10
- D. 20
Answer: B. 16 — According to BODMAS/PEMDAS, operations inside the brackets are performed first. So, 7 - 3 = 4, and then 4 × 4 = 16.
MCQ 5. Evaluate: 25 - [20 ÷ (8 - 3)]
- A. 21
- B. 5
- C. 19
- D. 4
Answer: A. 21 — First, solve the innermost bracket: 8 - 3 = 5. Then, perform division: 20 ÷ 5 = 4. Finally, subtract: 25 - 4 = 21.
MCQ 6. What is the product of (-5) and 6?
- A. 30
- B. -30
- C. 1
- D. -11
Answer: B. -30 — When multiplying integers with different signs, the product is negative. So, 5 × 6 = 30, and the result is -30.
MCQ 7. Find the value of 15 × 8 + 15 × 2.
- A. 150
- B. 120
- C. 170
- D. 210
Answer: A. 150 — Using the distributive property, 15 × (8 + 2) = 15 × 10 = 150. Alternatively, calculate each product first: 15 × 8 = 120 and 15 × 2 = 30, then add them: 120 + 30 = 150.
MCQ 8. Subtract (-10) from 20.
- A. 10
- B. -10
- C. 30
- D. -30
Answer: C. 30 — Subtracting a negative number is equivalent to adding its positive counterpart. So, 20 - (-10) = 20 + 10 = 30.
MCQ 9. Simplify: 12 × 3 ÷ 6 + 7
- A. 13
- B. 10
- C. 7
- D. 9
Answer: A. 13 — According to BODMAS/PEMDAS, multiplication and division are performed from left to right. So, 12 × 3 = 36, then 36 ÷ 6 = 6, and finally 6 + 7 = 13.
MCQ 10. Calculate: 50 - {20 + [30 - (10 - 5)]}
- A. 5
- B. 15
- C. 0
- D. 10
Answer: A. 5 — Start with the innermost bracket: 10 - 5 = 5. Then, [30 - 5] = 25. Next, {20 + 25} = 45. Finally, 50 - 45 = 5.
MCQ 11. What is (-48) divided by 6?
- A. 8
- B. -8
- C. -6
- D. 6
Answer: B. -8 — When dividing integers with different signs, the quotient is negative. So, 48 ÷ 6 = 8, and the result is -8.
MCQ 12. Evaluate: -15 + (-7) - (-10)
- A. -32
- B. -12
- C. -22
- D. -15
Answer: B. -12 — First, -15 + (-7) = -15 - 7 = -22. Then, -22 - (-10) = -22 + 10 = -12.
MCQ 13. A shopkeeper sold 5 kg of apples at ₹60 per kg and 3 kg of oranges at ₹40 per kg. What is the total revenue?
- A. ₹420
- B. ₹300
- C. ₹120
- D. ₹540
Answer: A. ₹420 — Revenue from apples = 5 × ₹60 = ₹300. Revenue from oranges = 3 × ₹40 = ₹120. Total revenue = ₹300 + ₹120 = ₹420.
MCQ 14. In the expression 7 + 3 × (5 - 2), which operation should be performed first?
- A. Addition
- B. Subtraction
- C. Multiplication
- D. Division
Answer: B. Subtraction — According to BODMAS/PEMDAS, operations inside brackets are performed first. Within the bracket, there is only subtraction (5 - 2).
MCQ 15. Simplify: 10 - [(-5) × 3 + (12 ÷ (-4))]
- A. 28
- B. 2
- C. 22
- D. -8
Answer: A. 28 — First, calculate inside the bracket: (-5) × 3 = -15. Then, 12 ÷ (-4) = -3. So, the bracket becomes [-15 + (-3)] = [-15 - 3] = -18. Finally, 10 - (-18) = 10 + 18 = 28.
MCQ 16. Which of the following shows the associative property for addition of integers?
- A. a + b = b + a
- B. a + (b + c) = (a + b) + c
- C. a × (b + c) = a × b + a × c
- D. a + 0 = a
Answer: B. a + (b + c) = (a + b) + c — The associative property of addition states that the way numbers are grouped in an addition problem does not change the sum.
MCQ 17. What is the additive inverse of -25?
- A. 25
- B. -25
- C. 1/25
- D. -1/25
Answer: A. 25 — The additive inverse of a number is the number that, when added to it, results in zero. For -25, the additive inverse is 25 because -25 + 25 = 0.
MCQ 18. If 3 × (x + 5) = 36, what is the value of x?
- A. 7
- B. 12
- C. 6
- D. 8
Answer: A. 7 — Divide both sides by 3: x + 5 = 36 ÷ 3 = 12. Then, subtract 5 from both sides: x = 12 - 5 = 7.
MCQ 19. Three friends, Amit, Bimal, and Charu, collected stamps. Amit collected 150 stamps. Bimal collected twice the number of stamps Amit collected. Charu collected 50 less than Bimal. Write an expression for the total number of stamps collected by all three.
- A. 150 + (2 × 150) + (2 × 150 - 50)
- B. 150 + 2 × 150 + 50
- C. 150 + (150 - 50) + (2 × 150)
- D. 150 + 2 × 150 + (150 + 50)
Answer: A. 150 + (2 × 150) + (2 × 150 - 50) — Amit's stamps = 150. Bimal's stamps = 2 × 150. Charu's stamps = (2 × 150) - 50. Total stamps = Amit + Bimal + Charu = 150 + (2 × 150) + (2 × 150 - 50).
MCQ 20. What is the value of (-10) × 0 × 7?
- A. 70
- B. -70
- C. 0
- D. 1
Answer: C. 0 — Any number multiplied by zero results in zero.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.