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CHAPTER 2 — ARITHMETIC EXPRESSIONS · SET 3
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test — Set 3 (Advanced)
General Instructions:
1. All questions are compulsory (Bonus is optional).
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
7. This is an advanced paper — think carefully before each step.
1. All questions are compulsory (Bonus is optional).
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Show all working clearly. Marks are awarded for steps.
7. This is an advanced paper — think carefully before each step.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Evaluate: 5 + 2 × {3 + (4 − 1)}
(a) 17 (b) 19 (c) 11 (d) 15
(a) 17 (b) 19 (c) 11 (d) 15
Q2.1
Arrange in descending order the values of: 3×15, 50−4, 90÷2, 4×10+8
(a) 4×10+8 > 50−4 > 3×15 = 90÷2 (b) 90÷2 > 50−4 > 3×15 > 4×10+8
(c) 3×15 > 50−4 > 4×10+8 > 90÷2 (d) 50−4 > 3×15 > 90÷2 > 4×10+8
(a) 4×10+8 > 50−4 > 3×15 = 90÷2 (b) 90÷2 > 50−4 > 3×15 > 4×10+8
(c) 3×15 > 50−4 > 4×10+8 > 90÷2 (d) 50−4 > 3×15 > 90÷2 > 4×10+8
Q3.1
Simplify: 75 − (30 − 15 + 5)
(a) 65 (b) 55 (c) 35 (d) 45
(a) 65 (b) 55 (c) 35 (d) 45
Q4.1
Evaluate: (18 + 6) ÷ (4 + 2) − 1
(a) 3 (b) 4 (c) 5 (d) 6
(a) 3 (b) 4 (c) 5 (d) 6
Q5.1
How many terms does the expression 2×3 + 4×5 − 6÷3 + 7 have?
(a) 7 (b) 5 (c) 4 (d) 3
(a) 7 (b) 5 (c) 4 (d) 3
Q6.1
If 8 × (m + 4) = 72, then m = ?
(a) 5 (b) 9 (c) 4 (d) 13
(a) 5 (b) 9 (c) 4 (d) 13
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Evaluate step by step: 4 × 3 + 6 × 2 ÷ 4 + 5
Show each operation in order.
Show each operation in order.
Q8.2
Remove brackets and simplify: 500 − (200 − 75 + 25)
State the rule used.
State the rule used.
Q9.2
Using the distributive property, calculate:
(a) 16 × 99 (b) 12 × 103
Show complete working for each.
(a) 16 × 99 (b) 12 × 103
Show complete working for each.
Q10.2
First find 13 × 105 using the distributive property.
Then use a similar approach to find 13 × 95. Show full working for both.
Then use a similar approach to find 13 × 95. Show full working for both.
Q11.2
Write a word problem whose answer is the expression 5 × 3 × 4 − 18.
Then solve the expression and state the answer in the context of your word problem.
Then solve the expression and state the answer in the context of your word problem.
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Remove brackets and simplify: 200 − (80 − 20 + 15 − 5)
Write the name of the rule at each step.
Write the name of the rule at each step.
Q13.3
A rectangle has width 6 cm and its length has two parts: 5 cm and 3 cm.
(a) Find the area by first adding the lengths: 6 × (5 + 3)
(b) Find the area using the distributive method: 6×5 + 6×3
(c) State the property demonstrated and confirm both methods give the same result.
(a) Find the area by first adding the lengths: 6 × (5 + 3)
(b) Find the area using the distributive method: 6×5 + 6×3
(c) State the property demonstrated and confirm both methods give the same result.
Q14.3
Simplify and compare the following two expressions:
(a) 100 − (40 + 20 − 10)
(b) 100 − (40 − 20 + 10)
Are the answers equal? Explain clearly why or why not.
(a) 100 − (40 + 20 − 10)
(b) 100 − (40 − 20 + 10)
Are the answers equal? Explain clearly why or why not.
Q15.3
Find the value of each expression, then arrange them in ascending order:
3×4×5 │ 100−(30+15) │ 4×(10+3) │ 200÷(4×5) │ 60−(5×8−10)
3×4×5 │ 100−(30+15) │ 4×(10+3) │ 200÷(4×5) │ 60−(5×8−10)
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
A school trip has 3 buses of 40 students each and 2 mini-vans of 12 students each.
(a) Write and evaluate an expression for the total number of students.
(b) Each student is given 3 meals during the trip. Write and evaluate an expression for the total number of meals.
(c) Each meal costs ₹65. Use the distributive property to write and evaluate an expression for the total food cost. Show full working.
(a) Write and evaluate an expression for the total number of students.
(b) Each student is given 3 meals during the trip. Write and evaluate an expression for the total number of meals.
(c) Each meal costs ₹65. Use the distributive property to write and evaluate an expression for the total food cost. Show full working.
Q17.5
Using the distributive property:
(a) Calculate 25 × 48 mentally. Show working clearly.
(b) Calculate 35 × 97 mentally. Show working clearly.
(c) A farmer plants 25 × 48 saplings in a field, and later removes 35 × 97 weeds. Is the number of weeds more or fewer than the saplings? Justify your answer.
(a) Calculate 25 × 48 mentally. Show working clearly.
(b) Calculate 35 × 97 mentally. Show working clearly.
(c) A farmer plants 25 × 48 saplings in a field, and later removes 35 × 97 weeds. Is the number of weeds more or fewer than the saplings? Justify your answer.
Bonus Question (Optional) [2 Marks]
Q18.2
★ Using the distributive property, find 25 × 48 in two completely different ways.
Show both methods and verify that they give the same answer.
Show both methods and verify that they give the same answer.
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Answer Key & Detailed Solutions
Q1. [1 Mark] — Answer: (a) 17
Work from innermost bracket outward:
Inner round bracket: (4 − 1) = 3
Curly bracket: {3 + 3} = 6
Multiplication: 2 × 6 = 12
Addition: 5 + 12 = 17
Inner round bracket: (4 − 1) = 3
Curly bracket: {3 + 3} = 6
Multiplication: 2 × 6 = 12
Addition: 5 + 12 = 17
Q2. [1 Mark] — Answer: (a)
Values: 3×15 = 45, 50−4 = 46, 90÷2 = 45, 4×10+8 = 40+8 = 48
Descending order: 48 > 46 > 45 = 45
So: 4×10+8 > 50−4 > 3×15 = 90÷2 ✓
Descending order: 48 > 46 > 45 = 45
So: 4×10+8 > 50−4 > 3×15 = 90÷2 ✓
Q3. [1 Mark] — Answer: (b) 55
Minus before bracket: all signs inside flip.
75 − (30 − 15 + 5) = 75 − 30 + 15 − 5 = 55
75 − (30 − 15 + 5) = 75 − 30 + 15 − 5 = 55
Q4. [1 Mark] — Answer: (a) 3
Brackets first: (18 + 6) = 24 and (4 + 2) = 6
24 ÷ 6 = 4
4 − 1 = 3
24 ÷ 6 = 4
4 − 1 = 3
Q5. [1 Mark] — Answer: (c) 4
Terms are separated by + or − signs (not within multiplication/division groups):
Term 1: 2×3 | Term 2: +4×5 | Term 3: −6÷3 | Term 4: +7
Total: 4 terms
Term 1: 2×3 | Term 2: +4×5 | Term 3: −6÷3 | Term 4: +7
Total: 4 terms
Q6. [1 Mark] — Answer: (a) m = 5
8 × (m + 4) = 72
Divide both sides by 8: m + 4 = 9
m = 9 − 4 = 5
Verify: 8 × (5 + 4) = 8 × 9 = 72 ✓
Divide both sides by 8: m + 4 = 9
m = 9 − 4 = 5
Verify: 8 × (5 + 4) = 8 × 9 = 72 ✓
Q7. [2 Marks]
Expression: 4 × 3 + 6 × 2 ÷ 4 + 5
Step 1 — Multiplication/Division left to right:
4 × 3 = 12
6 × 2 = 12, then 12 ÷ 4 = 3
Expression becomes: 12 + 3 + 5
Step 2 — Addition left to right: 12 + 3 + 5 = 20
Step 1 — Multiplication/Division left to right:
4 × 3 = 12
6 × 2 = 12, then 12 ÷ 4 = 3
Expression becomes: 12 + 3 + 5
Step 2 — Addition left to right: 12 + 3 + 5 = 20
Q8. [2 Marks]
Rule: When a minus (−) sign precedes a bracket, all signs inside the bracket flip.
500 − (200 − 75 + 25)
= 500 − 200 + 75 − 25
= 300 + 75 − 25
= 350
500 − (200 − 75 + 25)
= 500 − 200 + 75 − 25
= 300 + 75 − 25
= 350
Q9. [2 Marks]
(a) 16 × 99 = 16 × (100 − 1) = 1600 − 16 = 1584
(b) 12 × 103 = 12 × (100 + 3) = 1200 + 36 = 1236
(b) 12 × 103 = 12 × (100 + 3) = 1200 + 36 = 1236
Q10. [2 Marks]
13 × 105 = 13 × (100 + 5) = 1300 + 65 = 1365
13 × 95 = 13 × (100 − 5) = 1300 − 65 = 1235
13 × 95 = 13 × (100 − 5) = 1300 − 65 = 1235
Q11. [2 Marks]
Sample word problem: A storage box has 5 layers. Each layer has 3 rows and 4 columns of eggs. 18 eggs are found cracked and removed. How many eggs remain?
Expression: 5 × 3 × 4 − 18 = 60 − 18 = 42 eggs
Expression: 5 × 3 × 4 − 18 = 60 − 18 = 42 eggs
Q12. [3 Marks]
200 − (80 − 20 + 15 − 5)
Rule: Minus before bracket flips every sign inside.
= 200 − 80 + 20 − 15 + 5
= 120 + 20 − 15 + 5
= 140 − 15 + 5
= 125 + 5 = 130
Rule: Minus before bracket flips every sign inside.
= 200 − 80 + 20 − 15 + 5
= 120 + 20 − 15 + 5
= 140 − 15 + 5
= 125 + 5 = 130
Q13. [3 Marks]
(a) Total length first: 5 + 3 = 8 cm; Area = 6 × 8 = 48 cm²
(b) Distributive method: 6×5 + 6×3 = 30 + 18 = 48 cm²
(c) Distributive Property of Multiplication over Addition:
a × (b + c) = a×b + a×c
Both methods give 48 cm² ✓ — the results are identical.
(b) Distributive method: 6×5 + 6×3 = 30 + 18 = 48 cm²
(c) Distributive Property of Multiplication over Addition:
a × (b + c) = a×b + a×c
Both methods give 48 cm² ✓ — the results are identical.
Q14. [3 Marks]
(a) 100 − (40 + 20 − 10) = 100 − 40 − 20 + 10 = 50
(b) 100 − (40 − 20 + 10) = 100 − 40 + 20 − 10 = 70
NOT equal (50 ≠ 70).
Explanation: When the minus sign removes the bracket, every term inside changes sign. Changing the positions of + and − within the bracket changes which terms add and which subtract after removal — giving a different result.
(b) 100 − (40 − 20 + 10) = 100 − 40 + 20 − 10 = 70
NOT equal (50 ≠ 70).
Explanation: When the minus sign removes the bracket, every term inside changes sign. Changing the positions of + and − within the bracket changes which terms add and which subtract after removal — giving a different result.
Q15. [3 Marks]
Values:
3×4×5 = 60
100−(30+15) = 100−45 = 55
4×(10+3) = 4×13 = 52
200÷(4×5) = 200÷20 = 10
60−(5×8−10) = 60−(40−10) = 60−30 = 30
Ascending order: 10 < 30 < 52 < 55 < 60
3×4×5 = 60
100−(30+15) = 100−45 = 55
4×(10+3) = 4×13 = 52
200÷(4×5) = 200÷20 = 10
60−(5×8−10) = 60−(40−10) = 60−30 = 30
Ascending order: 10 < 30 < 52 < 55 < 60
Q16. [5 Marks]
(a) Total students: 3×40 + 2×12 = 120 + 24 = 144 students
(b) Total meals: 144 × 3 = 432 meals
(c) Total food cost using distributive property:
432 × 65 = 432 × (60 + 5)
= 432×60 + 432×5
= 25,920 + 2,160
= ₹28,080
(b) Total meals: 144 × 3 = 432 meals
(c) Total food cost using distributive property:
432 × 65 = 432 × (60 + 5)
= 432×60 + 432×5
= 25,920 + 2,160
= ₹28,080
Q17. [5 Marks]
(a) 25 × 48 = 25 × (50 − 2) = 1250 − 50 = 1200
(b) 35 × 97 = 35 × (100 − 3) = 3500 − 105 = 3395
(c) Saplings = 1200; Weeds = 3395
Since 3395 > 1200, the weeds (3395) are more than the saplings (1200).
In fact there are 3395 − 1200 = 2195 more weeds than saplings, so the comparison is not physically meaningful — you cannot remove more weeds than there are saplings.
(b) 35 × 97 = 35 × (100 − 3) = 3500 − 105 = 3395
(c) Saplings = 1200; Weeds = 3395
Since 3395 > 1200, the weeds (3395) are more than the saplings (1200).
In fact there are 3395 − 1200 = 2195 more weeds than saplings, so the comparison is not physically meaningful — you cannot remove more weeds than there are saplings.
Q18. [Bonus — 2 Marks]
Method 1: 25 × 48 = 25 × (50 − 2) = 1250 − 50 = 1200
Method 2: 25 × 48 = 25 × 4 × 12 = 100 × 12 = 1200
(Using the fact that 25×4 = 100, a handy shortcut)
Both methods give 1200 ✓
Method 2: 25 × 48 = 25 × 4 × 12 = 100 × 12 = 1200
(Using the fact that 25×4 = 100, a handy shortcut)
Both methods give 1200 ✓