Algebraic Expressions — Questions and Answers
Welcome to HSLC Guru. This page gives complete, step-by-step solutions to every “Work it Out” box (4.1–4.8) and Exercise 4 of ASSEB Class 7 New Mathematics Chapter 4, Algebraic Expressions, along with extra practice questions and a key-terms glossary.
Summary
Instead of repeating the name of an object, a relationship can be written briefly using letters. Such letters (like x, s, p, n) are called letter-numbers, and an expression built from them is an algebraic expression (for example s + 5 or 3x + 100). In algebraic expressions the multiplication sign (×) is usually dropped — 3 × x is written as 3x.
If the values of the letter-numbers are given, we can find the value of the expression; when a letter-number changes, the value changes too. The parts of an expression separated by the ‘+’ sign are called terms. Terms with the same letter-number are like terms (2x, 5x) and terms with different letter-numbers are unlike terms (2x, 3y). Only like terms can be added or subtracted to simplify an expression.
Number and shape patterns can also be written as algebraic expressions — for example 2, 4, 6, 8, … is 2n and 3, 6, 9, 12, … is 3n. From the expression we can find the number (or shape) at any position, and conversely.
Summary: This ASSEB Class 7 New Mathematics Chapter 4 (Algebraic Expressions) solution explains letter-numbers (variables), forming algebraic expressions, removing the multiplication sign, finding the value of an expression, identifying like and unlike terms, simplifying expressions, and writing algebraic expressions for number and shape patterns. Every Work it Out (4.1–4.8) box and Exercise 4 is solved step by step, with extra MCQs, fill-in-the-blanks, true/false, short answers and a key-terms glossary.
Textbook Questions and Answers
Work it Out 4.1
1. Uttam reads h hours daily. Express the total number of hours he reads in a week in an algebraic expression.
Answer: A week has 7 days. Reading h hours each day, total hours = 7 × h = 7h hours.
2. Liza bought 15 balloons and 30 chocolates for her birthday. If a balloon costs ₹x and a chocolate costs ₹y, express the total cost in an algebraic expression.
Answer: Cost of 15 balloons = 15 × x = 15x; cost of 30 chocolates = 30 × y = 30y. Total cost = 15x + 30y.
Work it Out 4.2
1. Write the following algebraic expressions by removing the multiplication symbol:
Answer:
(a) 5 × x = 5x
(b) a × 5 = 5a
(c) 2 × m + n = 2m + n
(d) 7 × p − q = 7p − q
(e) m × 2 + 7 = 2m + 7
(f) 10 − t × 5 = 10 − 5t
2. Determine the value [values of letter-numbers are given]:
Answer:
(a) 2x + 3, x = 0 → 2 × 0 + 3 = 3
(b) 4q + 3 + 2p, p = −2, q = 5 → 4 × 5 + 3 + 2 × (−2) = 20 + 3 − 4 = 19
(c) 17u + 5v, u = 6, v = 5 → 17 × 6 + 5 × 5 = 102 + 25 = 127
(d) 9l, l = 6 → 9 × 6 = 54
(e) 10 − b, b = −4 → 10 − (−4) = 10 + 4 = 14
(f) $\frac{j+1}{3}$, j = 10 → $\frac{10+1}{3} = \frac{11}{3}$.
3. Write true or false:
Answer:
(a) 5f − 5g = 5, if f = 1, g = 0 → 5 × 1 − 5 × 0 = 5. True.
(b) 4h + 3 = 25, if h = −7 → 4 × (−7) + 3 = −28 + 3 = −25 ≠ 25. False.
(c) 3q + 4 = 7, if q = 1 → 3 × 1 + 4 = 7. True.
(d) 3a = 2a + 2, if a = 1 → left 3 × 1 = 3; right 2 × 1 + 2 = 4; 3 ≠ 4. False.
(e) 6(m − 9) = 0, if m = 9 → 6 × (9 − 9) = 0. True.
Think about it: If a = 4 and b = 6, will the value of 3a + b be 18? → 3 × 4 + 6 = 12 + 6 = 18. Yes, the value is 18.
Work it Out 4.3
1. Observe the block patterns of the table below. Count how many blue and red blocks there are, write it as an algebraic expression, and also simplify the expression. (Consider the blue block as ‘x’ and the red block as ‘y’.)
Answer: In each pattern, take the number of blue blocks as x and red blocks as y, first write every block as a sum, then add the like terms (x with x, y with y) to get the simplified form — as in the given row (a):
| Sl. no. | Blue (x) and red (y) blocks | Algebraic Expression | Simplified form |
|---|---|---|---|
| (a) | 2 blue, 3 red | x + x + y + y + y | 2x + 3y |
| (b) | Count the blue and red blocks | Write each as x and y in a sum | Add like terms |
| (c) | Count the blue and red blocks | Write each as x and y in a sum | Add like terms |
| (d) | Count the blue and red blocks | Write each as x and y in a sum | Add like terms |
For example, a pattern with 3 blue and 2 red blocks gives the expression x + x + x + y + y, whose simplified form is 3x + 2y.
Work it Out 4.4
1. Write the like terms together from the following expressions:
5x, 19y, 2, 7y, 3x, −11x, −17y, x, 25x, 100, z
Answer: Terms with the same letter-number are like terms —
- x terms: 5x, 3x, −11x, x, 25x
- y terms: 19y, 7y, −17y
- z term: z
- constants (no letter-number): 2, 100
2. Complete the following table by giving appropriate reasons:
Answer:
| Terms | Like / Unlike | Reason |
|---|---|---|
| 12m, 7y | Unlike | Different letter-numbers (m and y) |
| 2x, −8x | Like | Same letter-number x |
| 11n, n | Like | Same letter-number n |
| 2, 3n | Unlike | 2 is a constant, 3n has the letter-number n |
Work it Out 4.5
1. Two statements and four options (A), (B), (C), (D) are given. Find the correct answer.
Statement 1: If the price of a pen is ₹a and the price of a notebook is ₹b, then the mathematical expression of the total price of 5 pens and 3 notebooks is 5a + 3b.
Statement 2: Gita has a number of ₹100 notes and b number of ₹50 notes. The mathematical expression of her total money is 50a + 100b.
(A) Both statements are true. (B) Both statements are false. (C) Statement 1 is true but statement 2 is false. (D) Statement 1 is false but statement 2 is true.
Answer: (C) Statement 1 is true but statement 2 is false. Price of 5 pens = 5a, price of 3 notebooks = 3b, total = 5a + 3b, so Statement 1 is true. But a notes of ₹100 = 100a and b notes of ₹50 = 50b, so the total is 100a + 50b (not 50a + 100b); hence Statement 2 is false.
2. Simplify:
Answer:
(a) (15x + 7y) − 2x − 5y = 15x − 2x + 7y − 5y = 13x + 2y
(b) 4p + 2q − 6(3p + q) = 4p + 2q − 18p − 6q = (4p − 18p) + (2q − 6q) = −14p − 4q
Work it Out 4.6
1. Match Column A with Column B by arrow.
Answer: Simplify each expression to find its match —
(a)
7x + 4y − 5x = 2x + 4y
−3x + 4y + x = −2x + 4y
2x + y − 5y = 2x − 4y
5x − 2y − 7x − 2y = −2x − 4y
(b)
4m + 3n + m − n = 5m + 2n
5p + 2q + 3p = 8p + 2q
a + a + a + a + a = 5a
3(l + b) = 3l + 3b
2x + 3y + 5x − 2y = 7x + y
2. Add the terms in the small boxes in the figure and write the sum of the algebraic terms in the coloured area.
Answer: In each figure, add the like terms separately and write the sum in the coloured area —
(a) 2p + 6p − 5k + 7k + 10 − 7 = (2p + 6p) + (−5k + 7k) + (10 − 7) = 8p + 2k + 3
(b) 4m − 2m + m − 2n + 10n + 3n + 6 − 5 = (4m − 2m + m) + (−2n + 10n + 3n) + (6 − 5) = 3m + 11n + 1
(c) 2x + 4x + 4y + 5y + 3a + 11a = (2x + 4x) + (4y + 5y) + (3a + 11a) = 6x + 9y + 14a
3. Each question has an Assertion (A) and a Reason (R). Find the correct answer.
Assertion (A): An algebraic expression can be expressed in letter-numbers.
Reason (R): Addition and subtraction can only be done among like terms.
Answer: (b) Both (A) and (R) are true, but (R) is not the correct explanation of (A). Both statements are true, yet the rule that only like terms can be added/subtracted does not explain why an expression can be written using letter-numbers.
4. Write the following algebraic expressions in simplified form:
Answer:
(a) 2x + y + 3x + 4y = 5x + 5y
(b) b + b + c + c + a + a = 2a + 2b + 2c
(c) 7m − 2m + 5n − 3n = 5m + 2n
(d) 4a + 5b + 6c + a + b + c = 5a + 6b + 7c
(e) u + u − u + v − v = u
(f) 6x + 3y + x + 2y = 7x + 5y
(g) 3s + 4t − s + 2t = 2s + 6t
(h) 5x − (2x − 2y) = 5x − 2x + 2y = 3x + 2y
(i) 9p − p + 6q − 3q = 8p + 3q
(j) 8(2w + 3x + 4w) = 8(6w + 3x) = 48w + 24x
5. Fill in the blanks:
Answer:
(i) 6a + 7a + 5b = 13a + 5b
(ii) 8a + 7b + 2a + 5b = 10a + 12b
(iii) 7x + 4y + 3x + y = 10x + 5y
(iv) 10a − 4a + 6b = 6a + 6b
(v) 8m − 3m + 2n + n = 5m + 3n
6. If m = 5, n = 3, check whether the values of the two algebraic expressions 5m + 3n and m + m + n + m + n + m + m + n are equal.
Answer: First expression: 5m + 3n = 5 × 5 + 3 × 3 = 25 + 9 = 34. The second expression has 5 m’s and 3 n’s, so m + m + n + m + n + m + m + n = 5m + 3n = 25 + 9 = 34. Both values are 34, so they are equal.
7. Pallavi bought 5 kg of apples and 3 dozen oranges. If the price of apples is ₹x per kg and oranges is ₹y per dozen, express the total price as an algebraic expression. If apples cost ₹200 per kg and oranges ₹100 per dozen, how much is spent in total?
Answer: Price of 5 kg apples = 5x, price of 3 dozen oranges = 3y. Total price = 5x + 3y. With x = 200 and y = 100, total = 5 × 200 + 3 × 100 = 1000 + 300 = ₹1300.
Work it Out 4.7
From the star patterns we get: n → 1, 2, 3, …; 2n → 2, 4, 6, …; 2n − 1 → 1, 3, 5, …; 2n + 1 → 3, 5, 7, …; 3n → 3, 6, 9, …; 3n − 1 → 2, 5, 8, …. Using this idea:
1. Express the following patterns of numbers in algebraic expression:
Answer: (here n = 1, 2, 3, …)
| Pattern of numbers | Algebraic Expression |
|---|---|
| (a) 4, 6, 8, 10, 12, 14 | 2n + 2 |
| (b) 4, 7, 10, 13, 16, 19 | 3n + 1 |
| (c) 1, 4, 7, 10, 13, 16 | 3n − 2 |
| (d) 4, 8, 12, 16, 20, 24 | 4n |
| (e) 3, 7, 11, 15, 19, 23 | 4n − 1 |
| (f) 2, 6, 10, 14, 18, 22 | 4n − 2 |
For instance, in (a) the difference is 2 and the first term is 4, so the expression is 2n + 2 (n = 1 gives 2 × 1 + 2 = 4). In (d) the numbers are multiples of 4, so 4n.
Fill in the blanks (flower pattern): position of blue flowers = 4n, pink = 4n − 1, yellow = 4n − 2 and red = 4n − 3. Using these —
| Position | Expressing in pattern | Algebraic expression | Colour of flower |
|---|---|---|---|
| 51 | 4 × 13 − 1 | 4n − 1 | Pink |
| 62 | 4 × 16 − 2 | 4n − 2 | Yellow |
| 77 | 4 × 20 − 3 | 4n − 3 | Red |
| 98 | 4 × 25 − 2 | 4n − 2 | Yellow |
| 27 | 4 × 7 − 1 | 4n − 1 | Pink |
| 88 | 4 × 22 | 4n | Blue |
Work it Out 4.8
1. As in the example above, find the algebraic expression by which the number in Column B is derived from the two numbers in Column A. (Take the first number as x and the second as y.)
Answer (a): Algebraic expression = 3x − 2y. Check: (1, 4) → 3 × 1 − 2 × 4 = −5; (15, 2) → 45 − 4 = 41; (3, 12) → 9 − 24 = −15; (4, 4) → 12 − 8 = 4; (2, 1) → 6 − 2 = 4; (10, 11) → 30 − 22 = 8. All match.
(b) Algebraic expression = x + 5y. Check: (2, 3) → 2 + 15 = 17; (3, 2) → 3 + 10 = 13; (10, 3) → 10 + 15 = 25; (5, 15) → 5 + 75 = 80; (15, 11) → 15 + 55 = 70; (4, 4) → 4 + 20 = 24. All match.
About the 2 × 2 square: If the number in the first cell of any 2 × 2 square of the table is a, the other three cells are a + 1, a + 10 and a + 11. The two diagonal sums are equal: a + (a + 11) = 2a + 11 and (a + 1) + (a + 10) = 2a + 11.
Exercise 4
1. Find the sum of the following algebraic expressions:
Answer: (add like terms together)
(a) 2a − 3b − c and −a + 5b − 2c → (2a − a) + (−3b + 5b) + (−c − 2c) = a + 2b − 3c
(b) x + y + z and 2x − y + 3z → (x + 2x) + (y − y) + (z + 3z) = 3x + 4z
(c) −30a + 20b + 10c and 45a − 15b + 25c → 15a + 5b + 35c
(d) 12x − 9y + 15z and −8x + 11y − 7z → 4x + 2y + 8z
(e) 25m + 18n − 10p and −15m + 22n + 5p → 10m + 40n − 5p
(f) 15p + 6q and −10p + 4q → 5p + 10q
2. Subtract the second from the first of the following algebraic expressions:
Answer:
(a) (6x − 7y) − (−11x + 2y) = 6x − 7y + 11x − 2y = 17x − 9y
(b) (−10p + 12q) − (15p + 6q) = −10p + 12q − 15p − 6q = −25p + 6q
(c) (25m + 8n) − (18m − 7n) = 25m + 8n − 18m + 7n = 7m + 15n
(d) (4m − 3n − 5p) − (m + n + p) = 4m − 3n − 5p − m − n − p = 3m − 4n − 6p
(e) (5x + 6y + 4z) − (−x + y − 2z) = 5x + 6y + 4z + x − y + 2z = 6x + 5y + 6z
(f) (9a − 2b − 4c) − (6a − 3b − 8c) = 9a − 2b − 4c − 6a + 3b + 8c = 3a + b + 4c
3. Simplify the following algebraic expressions:
Answer:
(a) 8a + 3b − 2a + b = (8a − 2a) + (3b + b) = 6a + 4b
(b) 12m − 4n + 3m + 9n = (12m + 3m) + (−4n + 9n) = 15m + 5n
(c) 15p − 7p + 4q − 2q + 3p = (15p − 7p + 3p) + (4q − 2q) = 11p + 2q
(d) 4(5q + 2) − 3 + 2q = 20q + 8 − 3 + 2q = 22q + 5
(e) (x + y) − (y + z) − (z + x) = x + y − y − z − z − x = −2z
(f) 6m + (3m − 2n) − (5n − 2m) = 6m + 3m − 2n − 5n + 2m = 11m − 7n
4. Observe the pattern formed by line segments of equal length (first position 6, second 11, third 16, …):
Answer: The difference is 5 and the first term is 6.
(i) Fourth position = 6, 11, 16, 21 → 21 line segments are required.
(ii) Number of line segments for the nth position = 6 + (n − 1) × 5 = 5n + 1 (n = 1 gives 6, n = 2 gives 11, n = 3 gives 16).
5. Observe the green and white tile patterns and answer:
Answer: In each figure the green tiles form a cross (+) and there are white tiles at the four corners. Figure 1 has 5 green + 4 white = 9 tiles; each later figure extends the four arms by one tile (4 more green tiles each time).
(a) Figures 4 and 5: continue the same rule, extending each arm of the cross by one tile — Figure 4 has 4 green tiles on each arm and Figure 5 has 5 green tiles on each arm.
(b) At the nth position, green tiles = 4n + 1 (5, 9, 13, …) and total tiles = 4n + 5 (9, 13, 17, …; the 4 white corner tiles stay constant).
6. Observe the pattern of geometrical figures (triangle △, circle ○, square □, triangle, circle, square … repeating):
Answer: The pattern repeats in groups of three.
(a) Position of triangle (△) = 3n − 2 (1, 4, 7, …); circle (○) = 3n − 1 (2, 5, 8, …); square (□) = 3n (3, 6, 9, …).
(b) 60 = 3 × 20 → 3n pattern → square (□); 125 = 3 × 42 − 1 → 3n − 1 pattern → circle (○); 278 = 3 × 93 − 1 → 3n − 1 pattern → circle (○).
7. Two statements and four options (A), (B), (C), (D) are given; choose the correct option.
Statement (1): Every pattern of numbers has an algebraic expression.
Statement (2): The algebraic expression for the number pattern 3, 8, 13, 18, … is 5n − 2.
Answer: (A) Both statement (1) and statement (2) are true. Every regular number pattern has an algebraic expression (Statement 1 true). For 3, 8, 13, 18, … the difference is 5 and the first term is 3, so the expression is 5n − 2 (n = 1 gives 5 × 1 − 2 = 3); hence Statement 2 is also true.
Additional Questions and Answers
Multiple Choice Questions (MCQ)
1. Removing the multiplication sign, 3 × x is written as —
(a) 3 + x (b) 3x (c) x3 (d) 3 ÷ x
Answer: (b) 3x
2. If m = 4, the value of 8m is —
(a) 12 (b) 84 (c) 32 (d) 48
Answer: (c) 32 (8 × 4 = 32)
3. 2x and 5x are —
(a) like terms (b) unlike terms (c) constants (d) patterns
Answer: (a) like terms
4. Which of the following is a pair of unlike terms?
(a) 3a, 7a (b) 2y, 9y (c) 4x, 5y (d) n, 6n
Answer: (c) 4x, 5y
5. The simplified form of 2x + 5x is —
(a) 7x (b) 10x (c) 10 (d) 7
Answer: (a) 7x
6. The algebraic expression for the pattern 2, 4, 6, 8, … is —
(a) n (b) 2n (c) 2n − 1 (d) n + 2
Answer: (b) 2n
7. If x = 2, the value of 7 + x is —
(a) 14 (b) 9 (c) 5 (d) 72
Answer: (b) 9
8. Each part of an algebraic expression separated by the ‘+’ sign is called a —
(a) term (b) value (c) pattern (d) perimeter
Answer: (a) term
9. The simplified form of 5x − 4y − 2x is —
(a) 3x − 4y (b) 7x − 4y (c) x − 4y (d) 3x + 4y
Answer: (a) 3x − 4y
10. The algebraic expression for the pattern 3, 6, 9, 12, … is —
(a) 3n (b) n + 3 (c) 3n − 1 (d) 2n + 1
Answer: (a) 3n
Fill in the Blanks
1. a × 5 is written briefly as ______. — 5a
2. Terms with the same ______ are called like terms. — letter-number
3. If n = 5, the value of 2n is ______. — 10
4. 7x + 2x = ______. — 9x
5. The algebraic expression for the pattern 4, 8, 12, 16, … is ______. — 4n
True or False
1. 4x and 4y are like terms. — False (different letter-numbers)
2. 3 × y can be written as 3y. — True
3. A letter-number has no fixed value. — True
4. Only like terms can be added; unlike terms cannot. — True
5. If x = 3, the value of 5x is 8. — False (5 × 3 = 15)
Short Answer Questions
1. What is an algebraic expression? Explain with examples.
Answer: An expression formed by connecting letter-numbers and numbers using operations such as addition, subtraction and multiplication is called an algebraic expression. Examples: s + 5, 3x + 100, 2x + 3y.
2. Distinguish between like terms and unlike terms.
Answer: Terms having the same letter-number are like terms (e.g. 2x, 5x); terms with different letter-numbers are unlike terms (e.g. 2x, 3y). Only like terms can be added or subtracted.
3. Simplify 6x + 3y + x + 2y.
Answer: 6x + x + 3y + 2y = 7x + 5y.
4. If a = 4 and b = 6, find the value of 3a + b.
Answer: 3a + b = 3 × 4 + 6 = 12 + 6 = 18.
Key Terms
| Term | Meaning |
|---|---|
| Algebraic expression | An expression built from letter-numbers and numbers using addition, subtraction and multiplication |
| Letter-number (variable) | A letter used to represent an unknown number (e.g. x, a, n) |
| Term | Each part of an expression separated by the ‘+’ sign |
| Like terms | Terms with the same letter-number (e.g. 2x, 5x) |
| Unlike terms | Terms with different letter-numbers (e.g. 2x, 3y) |
| Simplification | Adding/subtracting like terms to write an expression in short form |
| Value of an expression | The number obtained by substituting values of the letter-numbers |
| Pattern | A sequence of numbers or shapes arranged by a rule |
| Constant | A term with a fixed value and no letter-number |
| Perimeter | The total length around a figure |
| Multiplication sign (×) | The sign for multiplication, usually dropped in algebra |