Class 7 Maths Chapter 10 Practice Question Answers - Algebraic Expressions

Q1. Which of the following is an algebraic expression?
(a) 2 + 3
(b) 4 - x
(c) 5 × 6
(d) √9
Ans: (b)

Sol: An algebraic expression contains variables, and "4 - x" has the variable 'x.'

Q2. Simplify: 2x + 3x - (4 + x)
(a) 4x - 4
(b) 5x - 2
(c) 2x + 4
(d) 6x - 4
Ans: (a)

Sol: 2x + 3x - (4 + x)           
=5x-4-x. (Distributed the negative sign over parentheses and added the like signs )
= 4x - 4

Q3. Which of the following is equivalent to "2a - 5b + 3a"?
(a) 5ab
(b) 5a - 2b
(c) 5a² - 5b²
(d) 5a - 5b
Ans: (d)

Sol: Combine the 'a' terms and the 'b' terms separately: 2a + 3a = 5a, and -5b remains unchanged.
so answer would be 5a-5b

Q4. The algebraic expression for "twice a number increased by 5" is:
(a) 2x + 5
(b) 2x - 5
(c) 5x + 2
(d) x + 2
Ans: (a)

Sol: The expression "twice a number" is 2x, and "increased by 5" means + 5.

Q5. Simplify: 4(2x + 3) + 2(x - 1)
(a) 10x + 10
(b) 10x - 5
(c) 6x + 2
(d) 8x + 5
Ans: (a)

Sol: 4(2x + 3) + 2(x - 1) 
= 8x + 12 + 2x - 2. 
= 10x + 10.

Q6. The algebraic expression for "one-third of a number" is:
(a) x + 3
(b) x/3
(c) 3x
(d) x - 3
Ans: (b)

Sol: "One-third of a number" is 1/3 multiplied by x = x/3.

Q7. Simplify: 5a - (2b - 3a)
(a) 8a - 2b
(b) 8a + 3b
(c) 3a + 2b
(d) 8a - 3b
Ans: (a)

Sol: Distribute the negative sign inside the parentheses:
5a - (2b - 3a)
= 5a - 2b + 3a
= 8a - 2b.

Q8. The algebraic expression for "the sum of twice x and three times y" is
(a) 2x - 3y
(b) 2x + 3y
(c) 2xy
(d) 2x + y
Ans: (b)

Sol: "Twice x" is 2x, and "three times y" is 3y. The sum is 2x + 3y. 

therefore, the algebric equation becomes 2x + 3y

Q9. Simplify: 3(x + 2) - 2(2x - 1)
(a) x + 8
(b) 3x + 2
(c) -x+8
(d) 5x + 1
Ans: (c)

Sol: 3(x + 2) - 2(2x - 1)   [Distribute the negative sign inside the parentheses]

= 3x + 6 - 4x + 2 

= -x + 8

Q10. The algebraic expression for "one more than the product of x and y" is:
(a) x + y
(b) xy
(c) xy + 1
(d) x - y
Ans: (c)

Sol: "Product of x and y" is xy, and "one more than" means + 1.
therefore, the algebric equation becomes  xy + 1

Q11. Simplify: 4x + 3y - 2x + 5y
(a) 6x + 2y
(b) 2x + 8y
(c) 2x - 2y
(d) 2x + 8y
Ans: (d)

Sol: Combine the 'x' terms and the 'y' terms separately:
4x - 2x = 2x, and 3y + 5y = 8y.
therefore, the algebric equation becomes 2x + 8y

Q12. The algebraic expression for "five times a number decreased by 7" is:
(a) 5x - 7
(b) 7x - 5
(c) 5x + 7
(d) 7 - 5x
Ans: (a)

Sol: "Five times a number" is 5x, and "decreased by 7" means - 7.
therefore, the algebric equation becomes 5x - 7

Q13. Simplify: 3(2x + 4) - 2(3x - 5)
(a) -x + 6
(b) 3x + 2
(c) 22
(d) x + 8
Ans: (c)

Sol: 3(2x + 4) - 2(3x - 5)
= 6x + 12 - 6x + 10
=  22.

Q14. The algebraic expression for "one less than the double of a number" is:
(a) 2x - 1
(b) 2x + 1
(c) x - 2
(d) x + 2
Ans: (a)

Sol: "Double of a number" is 2x, and "one less than" means - 1.
therefore, the algebric equation becomes 2x - 1.

Q15. Simplify: 2(a - 3b) + 3(2b - a)
(a) 2a + 6b
(b) 3a + 2b
(c) -a
(d) 4b - a
Ans: (c)

Sol: 2(a - 3b) + 3(2b - a) 
= 2a - 6b + 6b - 3a
 = -a

Q16. The algebraic expression for "three less than twice a number" is:
(a) 2x - 3
(b) 3 - 2x
(c) 2x + 3
(d) 3x - 2
Ans: (a)

Sol: "Twice a number" is 2x, and "three less than" means - 3.
therefore, the algebric equation becomes 2x - 3

Q17. Simplify: 5(3x - 2) - 2(4 - x)
(a) 13x - 2
(b) 17x -18
(c) 15x - 8
(d) 13x + 8
Ans: (b)

Sol: 5(3x - 2) - 2(4 - x) 
= 15x - 10 - 8 + 2x 
= 17x - 18.

Q18. The algebraic expression for "half of the sum of a number and 8" is:
(a) x + 8
(b) (x + 8)/2
(c) 2x + 8
(d) (x - 8)/2
Ans: (b)

Sol: "Sum of a number and 8" is x + 8, and "half of" means divided by 2.
therefore, the algebric equation becomes (x + 8)/2

Q19. Simplify: 4(2x - 3) + 3(4x + 1)
(a) 20x + 3
(b) 8x - 9
(c)20x-9
(d) 16x - 8
Ans: (c)

Sol: 4(2x - 3) + 3(4x + 1) 
= 8x - 12 + 12x + 3 
= 20x - 9.

Q20. The algebraic expression for "the sum of thrice x and twice y" is:
(a) 5xy
(b) 3x + 2y
(c) 3x - 2y
(d) 2xy + 3
Ans: (b)

Sol: "Thrice x" is 3x, and "twice y" is 2y. The sum is 3x + 2y.
therefore, the algebric equation becomes 3x + 2y

Q21. Simplify: 2(x + 5) - (3x - 2)
(a) 5x + 4
(b) x + 8
(c) 5x - 8
(d) -x +12
Ans: (d)

Sol: 2(x + 5) - (3x - 2) 
= 2x + 10 - 3x + 2 
= -x + 12.

Q22. The algebraic expression for "four times the sum of x and y" is:
(a) 4xy
(b) 4(x + y)
(c) 4x + y
(d) 4x - y
Ans: (b)

Sol: "Sum of x and y" is x + y, and "four times" means 4 multiplied by the sum.
therefore, the algebric equation becomes 4(x + y)

Q23. Simplify: 3(2x - 5) + 4(3x + 1)
(a) 18x - 11
(b) 11x + 1
(c) 9x - 1
(d) 5x + 11
Ans: (a)

Sol: 3(2x - 5) + 4(3x + 1)
= 6x - 15 + 12x + 4
= 18x - 11.

Q24. The algebraic expression for "five more than the double of a number" is:
(a) 2x - 5
(b) 2x + 5
(c) 5 - 2x
(d) 5x + 2
Ans: (b)

Sol: "Double of a number" is 2x, and "five more than" means + 5.
therefore, the algebric equation becomes 2x + 5

Q25. Simplify: 3(a + 2b) - 2(3a - 5b)
(a) -3a + 16b
(b) 5a + b
(c) 9a + 11b
(d) 11a + 2b
Ans: (a)

Sol: 3(a + 2b) - 2(3a - 5b)
= 3a + 6b - 6a + 10b
= -3a + 16b.

Q26. The algebraic expression for "the difference between a number and 5" is:
(a) x - 5
(b) 5 -2 x
(c) 5x
(d) 5 + x
Ans: (a)

Sol: "The difference between a number and 5" is x - 5.
therefore, the algebric equation becomes  x - 5

Q27. Simplify: 4(2a - 3b) - 3(4a + b)
(a) -4a - 11b
(b) -4a -15b
(c) -4a + b
(d) 11a - 4b
Ans: (b)

Sol: 4(2a - 3b) - 3(4a + b)
= 8a - 12b - 12a - 3b
= -4a - 15b.

Q28. The algebraic expression for "half of the difference between x and y" is:
(a) x + y
(b) (x - y)/2
(c) 2xy
(d) x - y
Ans: (b)

Sol: "Difference between x and y" is x - y, and "half of" means divided by 2.
therefore, the algebric equation becomes  (x - y)/2

Q29. Simplify: 3(2x + 4) + 2(3x - 1)
(a) 12x + 10
(b) 8x - 2
(c) 12x + 2
(d) 6x + 10
Ans: (a)

Sol: 3(2x + 4) + 2(3x - 1)
= 6x + 12 + 6x - 2
= 12x + 10.

Q30. The algebraic expression for "the sum of a number and its square" is:
(a) x + 1
(b) x - 1
(c) x² +x
(d) 1 - x
Ans: (c)

Sol: "A number" is x, and "its square" is x². The sum is x² + x.
therefore, the algebric equation becomes x² + x.