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CHAPTER 2 — ARITHMETIC EXPRESSIONS
Class VII Mathematics — NCERT Ganita Prakash 2024
Preeti Kushwah Classes — Unit Test — Set 1 (Foundation)
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
Simplify: 5 + 3 × 2
Q2.1
In the expression 24 ÷ 4 + 2 × 3, which operations are done first according to BODMAS?
Q3.1
Simplify: 10 × [8 − (4 + 2)]
Q4.1
True or False: 8 − 3 − 2 = 8 − (3 − 2). Justify your answer.
Q5.1
Write an arithmetic expression for: “7 more than the product of 4 and 5”
Q6.1
What is the full form of BODMAS? Write each letter and what it stands for.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Simplify step by step: 36 ÷ 4 − 3 + 2 × 5
Q8.2
Simplify: 50 − [23 − {8 × 3 − (4 + 1)}]
Q9.2
Write an expression for the following statement and then evaluate it:
“Subtract 12 from the sum of 45 and 27, then multiply the result by 3.”
“Subtract 12 from the sum of 45 and 27, then multiply the result by 3.”
Q10.2
Using the numbers 4, 5, 6 (each used exactly once) with the operations + and ×:
(a) Write one expression without brackets and evaluate it.
(b) Write a different expression with brackets that gives a different value. Evaluate it too.
(a) Write one expression without brackets and evaluate it.
(b) Write a different expression with brackets that gives a different value. Evaluate it too.
Q11.2
Riya has ₹150. She buys 3 pens at ₹12 each and 2 notebooks at ₹25 each.
Write a single expression for the money left and evaluate it.
Write a single expression for the money left and evaluate it.
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Simplify step by step (show every step clearly):
4 + 3 × [15 − {10 − (4 − 2)}]
4 + 3 × [15 − {10 − (4 − 2)}]
Q13.3
Evaluate the expression 5 × (a + 3) − 4 when a = 7.
Also verify your answer using the Distributive Property of multiplication over addition.
Also verify your answer using the Distributive Property of multiplication over addition.
Q14.3
A school canteen sells 4 plates of rice at ₹35 each and 3 glasses of juice at ₹20 each. A loyalty discount of ₹15 is applied on the total.
(a) Write a single arithmetic expression for the amount to be paid.
(b) Evaluate the expression step by step.
(c) If the same bill is split equally among 5 students, write a new expression and find each student’s share.
(a) Write a single arithmetic expression for the amount to be paid.
(b) Evaluate the expression step by step.
(c) If the same bill is split equally among 5 students, write a new expression and find each student’s share.
Q15.3
Identify and correct all mistakes in the following solution:
“Simplify: 24 ÷ 6 + 3 × 2 − 1
Step 1: 24 ÷ (6 + 3) × 2 − 1 [added 6 and 3 first]
Step 2: 24 ÷ 9 × 2 − 1
Step 3: = 24 ÷ 18 − 1
Step 4: ≈ 2.33 − 1 = 1.33”
Write the fully correct solution.
“Simplify: 24 ÷ 6 + 3 × 2 − 1
Step 1: 24 ÷ (6 + 3) × 2 − 1 [added 6 and 3 first]
Step 2: 24 ÷ 9 × 2 − 1
Step 3: = 24 ÷ 18 − 1
Step 4: ≈ 2.33 − 1 = 1.33”
Write the fully correct solution.
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
A school library has 3 shelves. Each shelf has 8 rows, and each row holds 15 books.
(a) Write one expression and find the total number of books.
(b) During a drive, 42 books are removed and 25 new books are added. Write and evaluate a single expression for the new total.
(c) The library buys 2 more shelves of the same size (same rows and books per row). Write an expression for the grand total of books after the purchase. Evaluate it.
(d) If each book costs ₹48, write a single expression and find the total cost of all books after the purchase in part (c).
(a) Write one expression and find the total number of books.
(b) During a drive, 42 books are removed and 25 new books are added. Write and evaluate a single expression for the new total.
(c) The library buys 2 more shelves of the same size (same rows and books per row). Write an expression for the grand total of books after the purchase. Evaluate it.
(d) If each book costs ₹48, write a single expression and find the total cost of all books after the purchase in part (c).
Q17.5
(a) Simplify step by step:
100 − [40 + {18 − (4 × 3 − 6)} × 2] ÷ 4
(b) Using the numbers 2, 3, 4, 5 (each used exactly once) and the operations + and × (you may use each any number of times), place brackets to get the largest possible value. Show at least three different attempts and identify the largest.
(c) Can you form an expression using 2, 3, 4, 5 (each once) that equals exactly 45? Show your expression and verify.
100 − [40 + {18 − (4 × 3 − 6)} × 2] ÷ 4
(b) Using the numbers 2, 3, 4, 5 (each used exactly once) and the operations + and × (you may use each any number of times), place brackets to get the largest possible value. Show at least three different attempts and identify the largest.
(c) Can you form an expression using 2, 3, 4, 5 (each once) that equals exactly 45? Show your expression and verify.
Bonus Question (Optional) [2 Marks]
Q18.2
★ Find the value of □ in the equation:
(□ + 3) × 4 − 10 = 2 × (□ − 1) + 8
Show all steps clearly.
(□ + 3) × 4 − 10 = 2 × (□ − 1) + 8
Show all steps clearly.
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Answer Key & Detailed Solutions
Q1. [1 Mark]
By BODMAS, multiplication is done before addition.
5 + 3 × 2 = 5 + 6 = 11
5 + 3 × 2 = 5 + 6 = 11
Q2. [1 Mark]
In 24 ÷ 4 + 2 × 3:
Division and Multiplication are done first (left to right), then Addition.
24 ÷ 4 = 6 and 2 × 3 = 6 are done first.
Then: 6 + 6 = 12
Division and Multiplication are done first (left to right), then Addition.
24 ÷ 4 = 6 and 2 × 3 = 6 are done first.
Then: 6 + 6 = 12
Q3. [1 Mark]
Innermost bracket first: (4 + 2) = 6
Then: 10 × [8 − 6] = 10 × 2 = 20
Then: 10 × [8 − 6] = 10 × 2 = 20
Q4. [1 Mark]
False.
LHS: 8 − 3 − 2 = 5 − 2 = 3
RHS: 8 − (3 − 2) = 8 − 1 = 7
3 ≠ 7, so the statement is false.
(Subtraction is not associative — brackets change the meaning.)
LHS: 8 − 3 − 2 = 5 − 2 = 3
RHS: 8 − (3 − 2) = 8 − 1 = 7
3 ≠ 7, so the statement is false.
(Subtraction is not associative — brackets change the meaning.)
Q5. [1 Mark]
“Product of 4 and 5” = 4 × 5
“7 more than” means add 7.
Expression: 4 × 5 + 7
Value: 20 + 7 = 27
“7 more than” means add 7.
Expression: 4 × 5 + 7
Value: 20 + 7 = 27
Q6. [1 Mark]
B — Brackets
O — Orders (powers/roots)
D — Division
M — Multiplication
A — Addition
S — Subtraction
(D & M are done left to right; A & S are done left to right.)
O — Orders (powers/roots)
D — Division
M — Multiplication
A — Addition
S — Subtraction
(D & M are done left to right; A & S are done left to right.)
Q7. [2 Marks]
36 ÷ 4 − 3 + 2 × 5
Step 1 (D and M): 36 ÷ 4 = 9 and 2 × 5 = 10
Expression becomes: 9 − 3 + 10
Step 2 (A and S, left to right): 9 − 3 = 6, then 6 + 10 = 16
Step 1 (D and M): 36 ÷ 4 = 9 and 2 × 5 = 10
Expression becomes: 9 − 3 + 10
Step 2 (A and S, left to right): 9 − 3 = 6, then 6 + 10 = 16
Q8. [2 Marks]
50 − [23 − {8 × 3 − (4 + 1)}]
Step 1 — Round brackets: (4 + 1) = 5
Step 2 — Curly brackets: {8 × 3 − 5} = {24 − 5} = 19
Step 3 — Square brackets: [23 − 19] = 4
Step 4: 50 − 4 = 46
Step 1 — Round brackets: (4 + 1) = 5
Step 2 — Curly brackets: {8 × 3 − 5} = {24 − 5} = 19
Step 3 — Square brackets: [23 − 19] = 4
Step 4: 50 − 4 = 46
Q9. [2 Marks]
Statement: “Subtract 12 from the sum of 45 and 27, then multiply by 3.”
Expression: (45 + 27 − 12) × 3
Step 1: 45 + 27 = 72
Step 2: 72 − 12 = 60
Step 3: 60 × 3 = 180
Expression: (45 + 27 − 12) × 3
Step 1: 45 + 27 = 72
Step 2: 72 − 12 = 60
Step 3: 60 × 3 = 180
Q10. [2 Marks]
(a) Without brackets (BODMAS applies): 4 + 5 × 6 = 4 + 30 = 34
(Multiplication first, then addition)
(b) With brackets (changing the order): (4 + 5) × 6 = 9 × 6 = 54
Different value — brackets changed what was calculated first.
(Multiplication first, then addition)
(b) With brackets (changing the order): (4 + 5) × 6 = 9 × 6 = 54
Different value — brackets changed what was calculated first.
Q11. [2 Marks]
Cost of pens = 3 × ₹12 = ₹36
Cost of notebooks = 2 × ₹25 = ₹50
Expression: 150 − (3 × 12 + 2 × 25)
= 150 − (36 + 50)
= 150 − 86 = ₹64
Cost of notebooks = 2 × ₹25 = ₹50
Expression: 150 − (3 × 12 + 2 × 25)
= 150 − (36 + 50)
= 150 − 86 = ₹64
Q12. [3 Marks]
4 + 3 × [15 − {10 − (4 − 2)}]
Step 1 — Innermost ( ): (4 − 2) = 2
Expression: 4 + 3 × [15 − {10 − 2}]
Step 2 — Curly { }: {10 − 2} = 8
Expression: 4 + 3 × [15 − 8]
Step 3 — Square [ ]: [15 − 8] = 7
Expression: 4 + 3 × 7
Step 4 — Multiplication: 3 × 7 = 21
Step 5 — Addition: 4 + 21 = 25
Step 1 — Innermost ( ): (4 − 2) = 2
Expression: 4 + 3 × [15 − {10 − 2}]
Step 2 — Curly { }: {10 − 2} = 8
Expression: 4 + 3 × [15 − 8]
Step 3 — Square [ ]: [15 − 8] = 7
Expression: 4 + 3 × 7
Step 4 — Multiplication: 3 × 7 = 21
Step 5 — Addition: 4 + 21 = 25
Q13. [3 Marks]
Expression: 5 × (a + 3) − 4, with a = 7
Direct substitution:
= 5 × (7 + 3) − 4
= 5 × 10 − 4
= 50 − 4 = 46
Verification using Distributive Property:
5 × (a + 3) = 5 × a + 5 × 3 = 5 × 7 + 15 = 35 + 15 = 50
50 − 4 = 46 ✓
Direct substitution:
= 5 × (7 + 3) − 4
= 5 × 10 − 4
= 50 − 4 = 46
Verification using Distributive Property:
5 × (a + 3) = 5 × a + 5 × 3 = 5 × 7 + 15 = 35 + 15 = 50
50 − 4 = 46 ✓
Q14. [3 Marks]
(a) Expression: 4 × 35 + 3 × 20 − 15
(b) Step by step:
= 140 + 60 − 15 (multiplication first)
= 200 − 15
= ₹185
(c) Each student’s share: (4 × 35 + 3 × 20 − 15) ÷ 5
= 185 ÷ 5 = ₹37 per student
(b) Step by step:
= 140 + 60 − 15 (multiplication first)
= 200 − 15
= ₹185
(c) Each student’s share: (4 × 35 + 3 × 20 − 15) ÷ 5
= 185 ÷ 5 = ₹37 per student
Q15. [3 Marks]
Mistakes identified:
• Step 1 is wrong: there are NO brackets in the original expression. The student incorrectly grouped 6 + 3 with brackets that don’t exist.
• Rule violated: D and M must be done left to right before A and S — no arbitrary grouping.
Correct Solution:
24 ÷ 6 + 3 × 2 − 1
Step 1 (D, left to right): 24 ÷ 6 = 4
Step 2 (M): 3 × 2 = 6
Expression: 4 + 6 − 1
Step 3 (A & S, left to right): 4 + 6 = 10, then 10 − 1 = 9
• Step 1 is wrong: there are NO brackets in the original expression. The student incorrectly grouped 6 + 3 with brackets that don’t exist.
• Rule violated: D and M must be done left to right before A and S — no arbitrary grouping.
Correct Solution:
24 ÷ 6 + 3 × 2 − 1
Step 1 (D, left to right): 24 ÷ 6 = 4
Step 2 (M): 3 × 2 = 6
Expression: 4 + 6 − 1
Step 3 (A & S, left to right): 4 + 6 = 10, then 10 − 1 = 9
Q16. [5 Marks]
(a) Expression: 3 × 8 × 15
= 24 × 15 = 360 books
(b) 42 books removed, 25 new books added.
Expression: 3 × 8 × 15 − 42 + 25
= 360 − 42 + 25 = 318 + 25 = 343 books
(c) 2 more shelves, same size (8 rows, 15 books each). Total shelves = 3 + 2 = 5.
Expression: 5 × 8 × 15 − 42 + 25
= 600 − 42 + 25 = 558 + 25 = 583 books
(d) Cost of all 583 books at ₹48 each:
Expression: (5 × 8 × 15 − 42 + 25) × 48
= 583 × 48 = ₹27,984
= 24 × 15 = 360 books
(b) 42 books removed, 25 new books added.
Expression: 3 × 8 × 15 − 42 + 25
= 360 − 42 + 25 = 318 + 25 = 343 books
(c) 2 more shelves, same size (8 rows, 15 books each). Total shelves = 3 + 2 = 5.
Expression: 5 × 8 × 15 − 42 + 25
= 600 − 42 + 25 = 558 + 25 = 583 books
(d) Cost of all 583 books at ₹48 each:
Expression: (5 × 8 × 15 − 42 + 25) × 48
= 583 × 48 = ₹27,984
Q17. [5 Marks]
(a) 100 − [40 + {18 − (4 × 3 − 6)} × 2] ÷ 4
Step 1 — Innermost ( ): 4 × 3 = 12, then 12 − 6 = 6
Step 2 — Curly { }: {18 − 6} = 12 → then × 2 = 24
Step 3 — Square [ ]: [40 + 24] = 64
Step 4 — Division (outside brackets): 64 ÷ 4 = 16
Step 5: 100 − 16 = 84
(b) Using 2, 3, 4, 5 (each once) with + and ×:
• 2 + 3 × 4 × 5 = 2 + 60 = 62
• (2 + 3) × 4 × 5 = 5 × 4 × 5 — wait, 5 is already used. So: (2 + 3) × 4 × 5 = 5 × 20 = 100
• 2 × 3 × (4 + 5) = 6 × 9 = 54
Largest value: (2 + 3) × 4 × 5 = 100
(c) Target: 45
Try: (2 + 3) × (4 + 5) = 5 × 9 = 45 ✓
Expression: (2 + 3) × (4 + 5) = 45
Step 1 — Innermost ( ): 4 × 3 = 12, then 12 − 6 = 6
Step 2 — Curly { }: {18 − 6} = 12 → then × 2 = 24
Step 3 — Square [ ]: [40 + 24] = 64
Step 4 — Division (outside brackets): 64 ÷ 4 = 16
Step 5: 100 − 16 = 84
(b) Using 2, 3, 4, 5 (each once) with + and ×:
• 2 + 3 × 4 × 5 = 2 + 60 = 62
• (2 + 3) × 4 × 5 = 5 × 4 × 5 — wait, 5 is already used. So: (2 + 3) × 4 × 5 = 5 × 20 = 100
• 2 × 3 × (4 + 5) = 6 × 9 = 54
Largest value: (2 + 3) × 4 × 5 = 100
(c) Target: 45
Try: (2 + 3) × (4 + 5) = 5 × 9 = 45 ✓
Expression: (2 + 3) × (4 + 5) = 45
Q18. [Bonus — 2 Marks]
(□ + 3) × 4 − 10 = 2 × (□ − 1) + 8
Let □ = x
LHS: (x + 3) × 4 − 10 = 4x + 12 − 10 = 4x + 2
RHS: 2 × (x − 1) + 8 = 2x − 2 + 8 = 2x + 6
Setting LHS = RHS:
4x + 2 = 2x + 6
4x − 2x = 6 − 2
2x = 4
x = 2
Verification: LHS = (2+3)×4−10 = 20−10 = 10 ✓
RHS = 2×(2−1)+8 = 2+8 = 10 ✓
Let □ = x
LHS: (x + 3) × 4 − 10 = 4x + 12 − 10 = 4x + 2
RHS: 2 × (x − 1) + 8 = 2x − 2 + 8 = 2x + 6
Setting LHS = RHS:
4x + 2 = 2x + 6
4x − 2x = 6 − 2
2x = 4
x = 2
Verification: LHS = (2+3)×4−10 = 20−10 = 10 ✓
RHS = 2×(2−1)+8 = 2+8 = 10 ✓