Class 7 Mathematics Chapter 2 Worksheet: Arithmetic Expressions

The chapter 2 of the NCERT class 7 book is all about Arithmetic Expressions. This worksheet is designed for Class 7 students who have completed the chapter.

Class 7 Mathematics – Arithmetic Expressions | Practice Set: Challenging

A. Reading, Building, and Rewriting Expressions

1. Write an arithmetic expression for:
   “Riya buys 6 pens for ₹12 each and then gets ₹25 cashback.”
2. Write two different expressions that both have the value 48.
   Use different operations in each.
3. Without solving fully, rewrite the expression 9 + 17 + 23 as a sum of three terms so that the middle term becomes 40.
4. Insert brackets to show two different meanings for:
   50 – 12 + 8
   (Write two bracketed versions that can give different values.)
5. Choose any number (your favourite), and write five different expressions having that value.
   Use at least one bracket in two of them.

B. Compare Expressions Without Complicated Calculations

6. Compare using >, < or = (avoid full calculation):
   999 + 78 ____ 1000 + 76
7. Compare:
   75 – 18 – 2 ____ 75 – (18 + 2)
8. Compare:
   38 × 25 ____ 19 × 50
9. Compare:
   420 ÷ 7 ____ 400 ÷ 7
10. Without computation, identify which expressions are equal to 84 – (30 + 12):
    • (i) 84 – 30 – 12
    • (ii) 84 – 42
    • (iii) –30 + 84 – 12
    • (iv) 84 – (12 + 30)

    (There can be more than one correct option.)

C. Brackets, Terms, and Simplification

11. Remove the brackets and write an expression with the same value:
    18 + (25 – 7)
12. Remove the brackets and write an expression with the same value:
    18 – (25 – 7)
13. Remove the brackets and write an expression with the same value:
    40 – (12 + 9)
14. Fill in the blanks so both sides are equal:
    26 + (9 – 4) = 26 + 9 ____ 4
15. Fill in the blanks so both sides are equal:
    52 – (11 + 6) = 52 ____ 11 ____ 6
16. Two expressions are given:
    • (a) (8 + 15) – 6
    • (b) 8 + (15 – 6)

    Are they always equal? Write Yes/No and give a one-line reason.

17. Add brackets at suitable places so the expression becomes true:
    64 – 18 + 6 = 40

D. Distributive Property and Creating Expressions

18. Use the distributive property to simplify (do not multiply fully first):
    7 × (100 + 23)
19. Simplify using distributive property:
    12 × (50 – 3)
20. Create four different expressions using exactly the numbers 2, 3, 5 once each,
    using only +, –, and brackets, so that you get four different values.
21. “Shortcut Strategy”:
    Arun says, “To subtract 19 from a number, I subtract 20 and then add 1.”
    • (a) Is Arun always correct? (Yes/No)
    • (b) Show with one example using an expression.

Answer Key with Hints

1. • Answer: 6 × 12 + 25
   • Hint: “6 pens at ₹12 each” becomes a product, then add cashback.
2. • Answer: Examples: (6 × 8) and (60 – 12)
   • Hint: Same value can come from different operations. Keep it simple but different.
3. • Answer: 9 + 40 + 0 (or 9 + 40 + 0 by regrouping 17 + 23)
   • Hint: Combine 17 and 23 first to make 40, then keep 9 as the first term.
4. • Answer: (50 – 12) + 8 and 50 – (12 + 8)
   • Hint: Brackets change which operation happens first, especially around subtraction.
5. • Answer: Many possible. Example for 24: 12 + 12, 6 × 4, 48 ÷ 2, 30 – 6, (5 × 6) – 6
   • Hint: Target the same value using different “routes”: +, –, ×, ÷, and brackets.
6. • Answer: <
   • Hint: Left has 999, right has 1000 (already 1 more). Compare the added parts: 78 vs 76.
7. • Answer: =
   • Hint: “–18 –2” is the same as subtracting (18 + 2) when written carefully.
8. • Answer: =
   • Hint: Double-halves idea: 38×25 = (2×19)×25 = 19×50.
9. • Answer: >
   • Hint: Same divisor 7. Since 420 > 400, the quotient is also greater.
10. • Answer: (i), (ii), (iii), (iv)
    • Hint: (i) is removing brackets, (ii) is simplified inside brackets, (iii) is rearranging terms, (iv) order inside addition doesn’t matter.
11. • Answer: 18 + 25 – 7
    • Hint: Brackets after a plus sign can be removed without changing signs.
12. • Answer: 18 – 25 + 7
    • Hint: Brackets after a minus sign flip the signs of terms inside: –(25 – 7) = –25 + 7.
13. • Answer: 40 – 12 – 9
    • Hint: Minus before brackets changes +9 into –9.
14. • Answer: –
    • Hint: (9 – 4) becomes +9 – 4 once brackets are removed.
15. • Answer: – , –
    • Hint: 52 – (11 + 6) turns into 52 – 11 – 6 because both are being subtracted.
16. • Answer: Yes
    • Hint: (8 + 15) – 6 and 8 + (15 – 6) are equal due to how subtraction works as adding a negative: both become 8 + 15 – 6.
17. • Answer: 64 – (18 + 6) = 40
    • Hint: Without brackets, you get 64 – 18 + 6. To reduce more, group the subtractions together.
18. • Answer: 7×100 + 7×23 = 700 + 161 = 861
    • Hint: Distribute: a×(b + c) = a×b + a×c.
19. • Answer: 12×50 – 12×3 = 600 – 36 = 564
    • Hint: Distribute across subtraction: a×(b – c) = a×b – a×c.
20. • Answer: Many possible. Example set:
      
      2 + 3 + 5 = 10,
      2 – 3 + 5 = 4,
      3 – (5 – 2) = 0,
      5 – (3 – 2) = 4 (choose another distinct value instead, e.g. (5 + 3) – 2 = 6)
    • Hint: Brackets can completely change subtraction. Aim for variety, not just one pattern.
21. • Answer:
      • (a) Yes
      • (b) Example: 86 – 19 = 86 – 20 + 1
    • Hint: Because 19 = 20 – 1, subtracting 19 is same as subtract 20 then add 1 back.

Other Class 7 Maths worksheet

• Class 7 Maths Chapter 1 Worksheet: Large Numbers Around Us
• Class 7 Maths Chapter 3 Worksheet: A Peek Beyond the Point
• Class 7 Maths Chapter 4 Worksheet: Another Peek Beyond the Point
• Class 7 Maths Chapter 6 Worksheet: Number Play
• Class 7 Chapter 7 Maths Worksheet: Finding the Unknown
• Class 7 Maths Chapter 8 Worksheet: Working with Fractions