Expressions Using Letter Numbers — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Expressions Using Letter Numbers" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Expressions Using Letter Numbers" — 8 important questions with detailed answers for…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 7 Mathematics — Expressions Using Letter Numbers. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Expressions Using Letter Numbers — All 8 Questions Solved
Q1. Write an algebraic expression for: A number multiplied by 5 and then increased by 3.
Step 1: Let the number be x
Step 2: "Multiplied by 5" means: 5x
Step 3: "Increased by 3" means add 3: 5x + 3
Answer: 5x + 3
Q2. Identify the terms and coefficients in: 3a + 2b - 5
Step 1: Rewrite to see all terms clearly:
3a + 2b + (-5)
Step 2: Identify the terms:
Terms are: 3a, 2b, and -5
Step 3: Identify coefficients:
Coefficient of a = 3
Coefficient of b = 2
Constant term = -5
Answer: Terms: 3a, 2b, -5. Coefficients: 3 (for a), 2 (for b). Constant: -5
Q3. Simplify: 4x + 2y - x + y
Step 1: Group like terms:
(4x - x) + (2y + y)
Step 2: Combine x terms:
4x - x = 3x
Step 3: Combine y terms:
2y + y = 3y
Step 4: Write the simplified expression:
3x + 3y
Answer: 3x + 3y
Q4. Find the value of 2a + 5 when a = 3
Step 1: Substitute a = 3 into the expression 2a + 5
Step 2: Calculate:
2(3) + 5
= 6 + 5
= 11
Answer: 11
Q5. Write an expression for: The perimeter of a rectangle with length l and width w
Step 1: Perimeter = sum of all four sides
Step 2: A rectangle has 2 lengths and 2 widths:
Perimeter = l + w + l + w
Step 3: Combine like terms:
Perimeter = 2l + 2w
Or: P = 2(l + w)
Answer: 2l + 2w or 2(l + w)
Q6. Find the value of 5b - 3 when b = 2
Step 1: Substitute b = 2 into the expression 5b - 3
Step 2: Calculate:
5(2) - 3
= 10 - 3
= 7
Answer: 7
Q7. Solve: x + 7 = 12
Step 1: Isolate x by subtracting 7 from both sides:
x + 7 - 7 = 12 - 7
Step 2: Simplify:
x = 5
Step 3: Verify:
5 + 7 = 12 ✓
Answer: x = 5
Q8. Solve: 3y = 15
Step 1: Isolate y by dividing both sides by 3:
3y ÷ 3 = 15 ÷ 3
Step 2: Simplify:
y = 5
Step 3: Verify:
3(5) = 15 ✓
Answer: y = 5
Expressions Using Letter Numbers — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. In the expression `3x + 5`, what does 'x' represent?
- A. A fixed value
- B. A variable
- C. A constant
- D. A coefficient
Answer: B. A variable — A variable is a letter or symbol that represents an unknown numerical value, which can change.
MCQ 2. Identify the constant term in the expression `7y - 2 + 4z`.
- A. 7y
- B. 4z
- C. -2
- D. 7
Answer: C. -2 — A constant term is a numerical value in an expression that does not change and is not multiplied by any variable.
MCQ 3. Write an algebraic expression for "the sum of p and 8".
- A. p - 8
- B. p * 8
- C. p + 8
- D. p / 8
Answer: C. p + 8 — "Sum" indicates addition, so the expression for the sum of p and 8 is p + 8.
MCQ 4. Write an algebraic expression for "the product of 5 and q".
- A. 5 + q
- B. 5 - q
- C. 5q
- D. 5/q
Answer: C. 5q — "Product" indicates multiplication. When a number is multiplied by a variable, it is written as 5q.
MCQ 5. What is the coefficient of `y` in the expression `12 - 3y + 5z`?
- A. 12
- B. 3
- C. -3
- D. 5
Answer: C. -3 — The coefficient is the numerical factor multiplying the variable. In `-3y`, the coefficient of `y` is -3.
MCQ 6. Form an expression for "7 added to twice the number m".
- A. 7m + 2
- B. 2m + 7
- C. 7 - 2m
- D. m + 14
Answer: B. 2m + 7 — "Twice the number m" means 2 * m or 2m. "7 added to" means we add 7 to this quantity, resulting in 2m + 7.
MCQ 7. How many terms are there in the expression `4x^2 - 3xy + 5y - 8`?
- A. 2
- B. 3
- C. 4
- D. 5
Answer: C. 4 — Terms are parts of an algebraic expression separated by addition or subtraction signs. The terms are `4x^2`, `-3xy`, `5y`, and `-8`.
MCQ 8. Which of the following is a pair of like terms?
- A. 3x, 3y
- B. 5ab, 5a
- C. 7p, -2p
- D. x^2, x
Answer: C. 7p, -2p — Like terms have the same variables raised to the same powers. Both 7p and -2p have the variable 'p' raised to the power of 1.
MCQ 9. Simplify the expression `5a + 3b - 2a + 7b`.
- A. 3a + 10b
- B. 7a + 10b
- C. 3a + 4b
- D. 10a + 10b
Answer: A. 3a + 10b — Combine like terms: `(5a - 2a)` gives `3a`, and `(3b + 7b)` gives `10b`. So, the simplified expression is `3a + 10b`.
MCQ 10. If `x = 3`, what is the value of the expression `4x - 5`?
- A. 7
- B. 12
- C. 17
- D. 1
Answer: A. 7 — Substitute `x = 3` into the expression: `4(3) - 5 = 12 - 5 = 7`.
MCQ 11. The age of Rohit is `y` years. His father is 5 years more than three times Rohit's age. What is the father's age in terms of `y`?
- A. 3y - 5
- B. y + 5
- C. 3y + 5
- D. (y+5)/3
Answer: C. 3y + 5 — Three times Rohit's age is `3y`. 5 years more than that is `3y + 5`.
MCQ 12. Simplify: `(3x + 2y - 4) - (x - 5y + 1)`
- A. 2x - 3y - 3
- B. 2x + 7y - 5
- C. 2x + 7y - 3
- D. 2x - 3y - 5
Answer: B. 2x + 7y - 5 — Distribute the negative sign: `3x + 2y - 4 - x + 5y - 1`. Combine like terms: `(3x - x) + (2y + 5y) + (-4 - 1)` which simplifies to `2x + 7y - 5`.
MCQ 13. If `a = 2` and `b = -1`, find the value of `2a + 3b`.
- A. 1
- B. 7
- C. -1
- D. 5
Answer: A. 1 — Substitute the values: `2(2) + 3(-1) = 4 - 3 = 1`.
MCQ 14. In the expression `p/q`, which letter represents the numerator?
- A. q
- B. p
- C. both p and q
- D. neither
Answer: B. p — In a fraction `p/q`, 'p' is the numerator and 'q' is the denominator.
MCQ 15. A square has a side length of `s` units. What is the expression for its perimeter?
- A. s^2
- B. s + 4
- C. 4s
- D. 2s + 2s
Answer: C. 4s — The perimeter of a square is the sum of its four equal sides. If one side is `s`, the perimeter is `s + s + s + s = 4s`.
MCQ 16. If a pattern starts with `n` and each subsequent term increases by 3, what is the expression for the 5th term? (Assuming `n` is the 1st term)
- A. n + 3
- B. n + 12
- C. n + 15
- D. n + 4*3
Answer: B. n + 12 — The terms are n, n+3, n+3+3, n+3+3+3, n+3+3+3+3. So, the 5th term is n + 4*3 = n + 12.
MCQ 17. Which of the following is NOT a term in the expression `2ab - 3c + 5`?
- A. 2ab
- B. -3c
- C. 5
- D. a
Answer: D. a — The terms are `2ab`, `-3c`, and `5`. 'a' is a factor of the first term, not a term itself.
MCQ 18. If `x = -2`, what is the value of `x^2 + 3x + 1`?
- A. 4
- B. -1
- C. 11
- D. -5
Answer: B. -1 — Substitute `x = -2`: `(-2)^2 + 3(-2) + 1 = 4 - 6 + 1 = -2 + 1 = -1`.
MCQ 19. Write an expression for "One-third of the sum of `a` and `b`, decreased by 10".
- A. (a+b)/3 - 10
- B. 3(a+b) - 10
- C. 10 - (a+b)/3
- D. (a-b)/3 - 10
Answer: A. (a+b)/3 - 10 — The "sum of `a` and `b`" is `a+b`. "One-third of" this sum is `(a+b)/3`. "Decreased by 10" means subtracting 10, so the expression is `(a+b)/3 - 10`.
MCQ 20. Which of the following expressions is equivalent to `5 + x`?
- A. 5x
- B. x - 5
- C. x + 5
- D. 5/x
Answer: C. x + 5 — Addition is commutative, meaning the order of numbers does not change the sum. Therefore, `5 + x` is the same as `x + 5`.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.