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CHAPTER 2 — ARITHMETIC EXPRESSIONS | SET 2
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test (Standard Level)
General Instructions:
1. All questions are compulsory.
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.
1. All questions are compulsory.
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.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
Using the distributive property, rewrite 8 × (100 − 1) and find its value.
Q2.1
How many terms does the expression 4 + 3 × 2 − 1 have?
Q3.1
Simplify: 60 − (25 − 10)
Q4.1
Write the distributive property for: a × (b + c)
Q5.1
Evaluate using correct order of operations: 5 + 6 × 2
Q6.1
Which has a greater value: 12 × 5 or 12 + 5? Show calculation.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Use the distributive property to calculate 8 × 99. Show the complete step-by-step working.
Q8.2
Count the number of terms in each expression:
(a) 4a + 3b − 2 (b) x × y × z
(a) 4a + 3b − 2 (b) x × y × z
Q9.2
Ravi had ₹200. He bought 3 books at ₹25 each and a pen for ₹15. Write an arithmetic expression for the money left and simplify it.
Q10.2
Simplify using the correct order of operations:
(a) 24 ÷ 6 + 3 × 4 (b) 50 − (12 + 8) × 2
(a) 24 ÷ 6 + 3 × 4 (b) 50 − (12 + 8) × 2
Q11.2
Are the two expressions equal? Show full working:
15 × 98 and 14 × 99
15 × 98 and 14 × 99
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Use the distributive property to calculate (show all steps):
(a) 7 × 108 (b) 9 × 97 (c) 15 × 102
(a) 7 × 108 (b) 9 × 97 (c) 15 × 102
Q13.3
A shopkeeper sold 12 bags at ₹125 each in the morning and 8 bags at ₹125 each in the evening. Write an expression for the total amount and use the distributive property to find it easily.
Q14.3
Simplify step by step, showing each operation clearly:
80 − [20 + (15 − 5) × 2]
80 − [20 + (15 − 5) × 2]
Q15.3
Find the value using the distributive property (reverse — factor out the common number):
(a) 25 × 4 + 25 × 6 (b) 36 × 7 − 36 × 3
(a) 25 × 4 + 25 × 6 (b) 36 × 7 − 36 × 3
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
(a) A hall has 25 rows of chairs with 18 chairs in each row. Use the distributive property to find the total number of chairs. (Show: 25 × 18 as 25 × 20 − 25 × 2)
(b) A second hall has 32 rows with 15 chairs each. Use the distributive property to calculate 32 × 15. (Show: 32 × 15 as 32 × 10 + 32 × 5)
(c) Which hall has more chairs, and by how many?
(b) A second hall has 32 rows with 15 chairs each. Use the distributive property to calculate 32 × 15. (Show: 32 × 15 as 32 × 10 + 32 × 5)
(c) Which hall has more chairs, and by how many?
Q17.5
Evaluate the following expression step by step. At each step, state which operation you are performing and why:
3 + 5 × 2 − 8 ÷ 4 + (6 − 2) × 3
(Marks are given for each correct step.)
3 + 5 × 2 − 8 ÷ 4 + (6 − 2) × 3
(Marks are given for each correct step.)
Bonus Question (Optional) [2 Marks]
Q18.2
★ Verify that a × (b − c) = a × b − a × c using a = 7, b = 15, c = 8. Also write in words what property this is called.
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Answer Key & Detailed Solutions
Q1. [1 Mark]
8 × (100 − 1) = 8 × 100 − 8 × 1 (distributive property)
= 800 − 8
= 792
= 800 − 8
= 792
Q2. [1 Mark]
Expression: 4 + 3 × 2 − 1
Terms are separated by + or −: 4, 3 × 2, 1
Answer: 3 terms
Terms are separated by + or −: 4, 3 × 2, 1
Answer: 3 terms
Q3. [1 Mark]
60 − (25 − 10)
= 60 − 15 (solve bracket first)
= 45
= 60 − 15 (solve bracket first)
= 45
Q4. [1 Mark]
Distributive Property:
a × (b + c) = a × b + a × c
(The number outside the bracket is multiplied by each number inside.)
a × (b + c) = a × b + a × c
(The number outside the bracket is multiplied by each number inside.)
Q5. [1 Mark]
5 + 6 × 2
= 5 + 12 (multiplication before addition)
= 17
= 5 + 12 (multiplication before addition)
= 17
Q6. [1 Mark]
12 × 5 = 60
12 + 5 = 17
12 × 5 has the greater value (60 > 17)
12 + 5 = 17
12 × 5 has the greater value (60 > 17)
Q7. [2 Marks]
8 × 99
= 8 × (100 − 1) [write 99 as 100 − 1] [1 mark]
= 8 × 100 − 8 × 1 [apply distributive property]
= 800 − 8
= 792 [1 mark]
= 8 × (100 − 1) [write 99 as 100 − 1] [1 mark]
= 8 × 100 − 8 × 1 [apply distributive property]
= 800 − 8
= 792 [1 mark]
Q8. [2 Marks]
(a) 4a + 3b − 2 [1 mark]
Terms separated by + or −: 4a, 3b, 2
Number of terms = 3
(b) x × y × z [1 mark]
No + or − present — the whole thing is one product.
Number of terms = 1
Terms separated by + or −: 4a, 3b, 2
Number of terms = 3
(b) x × y × z [1 mark]
No + or − present — the whole thing is one product.
Number of terms = 1
Q9. [2 Marks]
Expression for money left: [1 mark]
Money spent = 3 × 25 + 15
Money left = 200 − (3 × 25 + 15)
Simplifying: [1 mark]
= 200 − (75 + 15)
= 200 − 90
= ₹110
Money spent = 3 × 25 + 15
Money left = 200 − (3 × 25 + 15)
Simplifying: [1 mark]
= 200 − (75 + 15)
= 200 − 90
= ₹110
Q10. [2 Marks]
(a) 24 ÷ 6 + 3 × 4 [1 mark]
Division and multiplication first (left to right):
= 4 + 12
= 16
(b) 50 − (12 + 8) × 2 [1 mark]
Brackets first: (12 + 8) = 20
= 50 − 20 × 2
Multiplication next: 20 × 2 = 40
= 50 − 40
= 10
Division and multiplication first (left to right):
= 4 + 12
= 16
(b) 50 − (12 + 8) × 2 [1 mark]
Brackets first: (12 + 8) = 20
= 50 − 20 × 2
Multiplication next: 20 × 2 = 40
= 50 − 40
= 10
Q11. [2 Marks]
15 × 98: [1 mark]
= 15 × (100 − 2) = 1500 − 30 = 1470
14 × 99: [1 mark]
= 14 × (100 − 1) = 1400 − 14 = 1386
1470 ≠ 1386, so the two expressions are NOT equal.
(15 × 98 is greater by 84.)
= 15 × (100 − 2) = 1500 − 30 = 1470
14 × 99: [1 mark]
= 14 × (100 − 1) = 1400 − 14 = 1386
1470 ≠ 1386, so the two expressions are NOT equal.
(15 × 98 is greater by 84.)
Q12. [3 Marks]
(a) 7 × 108 [1 mark]
= 7 × (100 + 8) = 7 × 100 + 7 × 8 = 700 + 56 = 756
(b) 9 × 97 [1 mark]
= 9 × (100 − 3) = 9 × 100 − 9 × 3 = 900 − 27 = 873
(c) 15 × 102 [1 mark]
= 15 × (100 + 2) = 15 × 100 + 15 × 2 = 1500 + 30 = 1530
= 7 × (100 + 8) = 7 × 100 + 7 × 8 = 700 + 56 = 756
(b) 9 × 97 [1 mark]
= 9 × (100 − 3) = 9 × 100 − 9 × 3 = 900 − 27 = 873
(c) 15 × 102 [1 mark]
= 15 × (100 + 2) = 15 × 100 + 15 × 2 = 1500 + 30 = 1530
Q13. [3 Marks]
Expression for total amount: [1 mark]
Total = 12 × 125 + 8 × 125
Using distributive property (reverse): [1 mark]
= (12 + 8) × 125 [factor out 125]
= 20 × 125
Final answer: [1 mark]
= 20 × 125 = ₹2,500
(This shows why distributive property saves calculation effort!)
Total = 12 × 125 + 8 × 125
Using distributive property (reverse): [1 mark]
= (12 + 8) × 125 [factor out 125]
= 20 × 125
Final answer: [1 mark]
= 20 × 125 = ₹2,500
(This shows why distributive property saves calculation effort!)
Q14. [3 Marks]
80 − [20 + (15 − 5) × 2]
Step 1: Innermost bracket: (15 − 5) = 10 [1 mark]
= 80 − [20 + 10 × 2]
Step 2: Multiplication inside []: 10 × 2 = 20 [1 mark]
= 80 − [20 + 20]
= 80 − [40]
Step 3: Final subtraction: 80 − 40 = 40 [1 mark]
Step 1: Innermost bracket: (15 − 5) = 10 [1 mark]
= 80 − [20 + 10 × 2]
Step 2: Multiplication inside []: 10 × 2 = 20 [1 mark]
= 80 − [20 + 20]
= 80 − [40]
Step 3: Final subtraction: 80 − 40 = 40 [1 mark]
Q15. [3 Marks]
(a) 25 × 4 + 25 × 6 [1½ marks]
Common factor = 25
= 25 × (4 + 6) [reverse distributive]
= 25 × 10
= 250
(b) 36 × 7 − 36 × 3 [1½ marks]
Common factor = 36
= 36 × (7 − 3) [reverse distributive]
= 36 × 4
= 144
Common factor = 25
= 25 × (4 + 6) [reverse distributive]
= 25 × 10
= 250
(b) 36 × 7 − 36 × 3 [1½ marks]
Common factor = 36
= 36 × (7 − 3) [reverse distributive]
= 36 × 4
= 144
Q16. [5 Marks]
(a) Hall 1: 25 × 18 [2 marks]
= 25 × 20 − 25 × 2 [write 18 = 20 − 2]
= 500 − 50
= 450 chairs
(b) Hall 2: 32 × 15 [2 marks]
= 32 × 10 + 32 × 5 [write 15 = 10 + 5]
= 320 + 160
= 480 chairs
(c) Comparison: [1 mark]
Hall 2 has more chairs: 480 − 450 = 30 more chairs
= 25 × 20 − 25 × 2 [write 18 = 20 − 2]
= 500 − 50
= 450 chairs
(b) Hall 2: 32 × 15 [2 marks]
= 32 × 10 + 32 × 5 [write 15 = 10 + 5]
= 320 + 160
= 480 chairs
(c) Comparison: [1 mark]
Hall 2 has more chairs: 480 − 450 = 30 more chairs
Q17. [5 Marks]
Expression: 3 + 5 × 2 − 8 ÷ 4 + (6 − 2) × 3
Step 1: Brackets — (6 − 2) = 4 [1 mark]
= 3 + 5 × 2 − 8 ÷ 4 + 4 × 3
Step 2: Division — 8 ÷ 4 = 2 [1 mark]
= 3 + 5 × 2 − 2 + 4 × 3
Step 3: Multiplication — 5 × 2 = 10, then 4 × 3 = 12 [1 mark]
= 3 + 10 − 2 + 12
Step 4: Addition & Subtraction left to right: [1 mark]
3 + 10 = 13 → 13 − 2 = 11 → 11 + 12 = 23
Answer = 23 [1 mark]
Step 1: Brackets — (6 − 2) = 4 [1 mark]
= 3 + 5 × 2 − 8 ÷ 4 + 4 × 3
Step 2: Division — 8 ÷ 4 = 2 [1 mark]
= 3 + 5 × 2 − 2 + 4 × 3
Step 3: Multiplication — 5 × 2 = 10, then 4 × 3 = 12 [1 mark]
= 3 + 10 − 2 + 12
Step 4: Addition & Subtraction left to right: [1 mark]
3 + 10 = 13 → 13 − 2 = 11 → 11 + 12 = 23
Answer = 23 [1 mark]
Q18. Bonus [2 Marks]
Verification with a = 7, b = 15, c = 8:
Left side: a × (b − c) = 7 × (15 − 8) = 7 × 7 = 49 [1 mark]
Right side: a × b − a × c = 7 × 15 − 7 × 8 = 105 − 56 = 49 [1 mark]
Both sides equal 49. ✓
This property is called the Distributive Property of Multiplication over Subtraction.
Left side: a × (b − c) = 7 × (15 − 8) = 7 × 7 = 49 [1 mark]
Right side: a × b − a × c = 7 × 15 − 7 × 8 = 105 − 56 = 49 [1 mark]
Both sides equal 49. ✓
This property is called the Distributive Property of Multiplication over Subtraction.