CBSE Important Questions Class 7 Maths Chapter 4 Expressions using Letter-Numbers

CBSE Important Questions Class 7 Maths Chapter 4 – Expressions using Letter-Numbers

Class 7 Maths Chapter 4 Expressions using Letter-Numbers is a chapter of the new NCERT (National Council of Educational Research and Training) textbook Ganita Prakash. In this chapter, letters such as x, y, a and n stand for numbers that can change. Students learn to write real-life situations as algebraic expressions, to add and simplify expressions, to find the value of an expression for a given number, and to see patterns using letter-numbers.

These CBSE important questions for Class 7 Maths Chapter 4 include multiple choice questions, an assertion-reason question, and word problems on canteen revenue, savings plans, perimeter of shapes, garden patterns, bank balance and game scores. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them in class. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 7 Maths Chapter 4 Expressions using Letter-Numbers

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Find the formulas of the number machines below and write the expression for each set of inputs.

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​In the following figure, observe how the expression w + 2 becomes 4w + 20 along one path. Fill in the missing blanks on the remaining paths. The ovals contain expressions and the boxes contain operations.

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Have you noticed how the colours change in a traffic signal? The sequence of colour changes is shown below. Find the colour at positions 90, 190, and 343. Write expressions to describe the positions for each colour.

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. If the rope is folded once and then cut as shown, we get 3 pieces. Observe the pattern and find the number of pieces if the rope is folded 10 times and cut. What is the expression for the number of pieces when the rope is folded r times and cut?

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Describe situations corresponding to the following algebraic expressions:
(a) 8x + 3y
(b) 15x – 2x

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Subtract the expressions given below:
(a) 9a – 6b + 14 from 6a + 9b – 18
(b) –15x + 13 – 9y from 7y – 10 + 3x
(c) 17g + 9 – 7h from 11 – 10g + 3h
(d) 9a – 6b + 14 from 6a – (9b + 18)
(e) 10x + 2 + 10y from –3y + 8 – 3x
(f) 8g + 4h – 10 from 7h – 8g + 20

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Add the expressions given below:
(a) 4d – 7c + 9 and 8c – 11 + 9d
(b) –6f + 19 – 8s and –23 + 13f + 12s
(c) 8d – 14c + 9 and 16c – (11 + 9d)
(d) 6f – 20 + 8s and 23 – 13f – 12s
(e) 13m – 12n and 12n – 13m
(f) –26m + 24n and 26m – 24n

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Simplify the following expressions:
(a) 3a + 9b – 6 + 8a – 4b – 7a + 16
(b) 3(3a – 3b) – 8a – 4b – 16
(c) 2(2x – 3) + 8x + 12
(d) 8x – (2x – 3) + 12
(e) 8h – (5 + 7h) + 9
(f) 23 + 4(6m – 3n) – 8n – 3m – 18

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time taken in minutes to travel from one station to the next station is the same and is denoted by t. The train stops for 2 minutes at each of the three stations.
(a) If t = 4, what is the time taken to travel from Yahapur to Vahapur?
(b) What is the algebraic expression for the time taken to travel from Yahapur to Vahapur? [Hint: Draw a rough diagram to visualise the situation]

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Radha is preparing for a cycling race and practices daily. The first week she cycles 5 km every day. Every week she increases the daily distance cycled by ‘z’ km. How many kilometers would Radha have cycled after 3 weeks?

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Given a position number can we find out the design that appears there? Which Design appears at Position 122? (Position at which the design A, B and C appears for nth time are 3n-2, 3n-1 and 3n)​

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

A snail is trying to climb along the wall of a deep well. During the day it climbs up ‘u’ cm and during the night it slowly slips down ‘d’ cm. This happens for 10 days and 10 nights.
(a) Write an expression describing how far away the snail is from its starting position.
(b) What can we say about the snail’s movement if d > u?

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Pushpita sells two types of flowers on Independence day: champak and marigold. ‘p’ customers only bought champak, ‘q’ customers only bought marigold, and ‘r’ customers bought both. On the same day, she gave away a tiny national flag to every customer. How many flags did she give away that day?
(a) p + q + r
(b) p + q + 2r
(c) 2 × (p + q + r)
(d) p + q + r + 2
(e) p + q + r + 1
(f) 2 × (p + q)

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

One plate of Jowar roti costs ₹30 and one plate of Pulao costs ₹20. If x plates of Jowar roti and y plates of pulao were ordered in a day, which expression(s) describe the total amount in rupees earned that day?
(a) 30x + 20y
(b) (30 + 20) × (x + y)
(c) 20x + 30y
(d) (30+20) × x + y
(e) 30x – 20y

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​How does the number of matchsticks change in each orientation as the steps increase? Write an expression for the number of matchsticks at Step ‘y’ in each orientation. Do the two expressions add up to 2y + 1?​

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

Does the above expression also give the number of matchsticks at each step correctly? Are these expressions the same? [Expression: 3 + 2 × (y – 1) and 2y + 1]

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​How many matchsticks will there be in Step 33, Step 84, and Step 108? Of course, we can draw and count, but is there a quicker way to find the answers using the pattern present here?​

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Verify this expression for diagonal sums by considering any 2 × 2 square and taking its top left number to be ‘a’.​

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Can the remainder obtained by dividing the position number by 3 be used for this? Observe the table below.

Position	Quotient on division by 3	Remainder
99	33	0
122	40	2
148	49	1

View Solution

Expressions using Letter-Numbers (New NCERT)

Medium

Q.

​Observe the pattern below. How many squares will be there in Step 4, Step 10, Step 50? Write a general formula. How would the formula change if we want to count the number of vertices of all the squares?

View Solution

Q1. Read the following statements and choose the correct option from the choices given below:
Assertion (A): A linear equation in one variable can be represented in the standard form by the expression ax + b = 0, where a ≠ 0.
Reason (R): In a linear equation ax + b = 0 in one variable, x is a variable and a, b are constants.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation for A.
(c) A is true, but R is false.
(d) A is false, but R is true.

Answer: (b) Both A and R are true, but R is not the correct explanation for A.
Assertion (A) is true: the standard form of a linear equation in one variable is ax + b = 0, and a must not be 0, otherwise the x term disappears. Reason (R) is also true: x is the variable and a, b are constants. But R only tells us what x, a and b are; it does not explain why a ≠ 0 is needed. So R is not the correct explanation of A.

Q2. The school canteen sells sandwiches for ₹(2x + 15) each and juice boxes for ₹(x + 10) each, where x represents a cost that changes daily based on ingredient prices.
Daily Sales Data:
Monday: 25 sandwiches, 40 juice boxes
Tuesday: 30 sandwiches, 35 juice boxes
Wednesday: 20 sandwiches, 45 juice boxes
(a) Write expressions for the total revenue on each day.
(b) Find the expression for the total revenue over the three days.

Answer: (a) Monday Revenue = 25 × (2x + 15) + 40 × (x + 10) = 50x + 375 + 40x + 400 = 90x + 775
Tuesday Revenue = 30 × (2x + 15) + 35 × (x + 10) = 60x + 450 + 35x + 350 = 95x + 800
Wednesday Revenue = 20 × (2x + 15) + 45 × (x + 10) = 40x + 300 + 45x + 450 = 85x + 750
(b) Total Revenue = (90x + 775) + (95x + 800) + (85x + 750)
= (90 + 95 + 85)x + (775 + 800 + 750)
= 270x + 2325
Total revenue over three days = ₹(270x + 2,325)

Q3. The perimeter of a triangle with sides 4m + 1/4, 3/4 m − 1/6 and 5/6 m, where m = 12, is:
(a) 65 + 1/4
(b) 67 + 1/12
(c) 65 + 1/12
(d) 67 + 1/4

Answer: (b) 67 + 1/12
Perimeter of a triangle = sum of all sides.
Put m = 12: (4 × 12 + 1/4) + (3/4 × 12 − 1/6) + (5/6 × 12)
= 48 + 1/4 + 9 − 1/6 + 10
= 67 + (1/4 − 1/6) = 67 + (3/12 − 2/12)
= 67 + 1/12

Q4. Two friends, Amit and Priya, are comparing their savings plans:
Amit's plan: He starts with ₹(3x + 2y) and saves ₹(2x − y) each month.
Priya's plan: She starts with ₹(x + 4y) and saves ₹(3x + y) each month.
(a) Write expressions for each person's total savings after n months.
(b) If x = 100 and y = 50, calculate their savings after 6 months.

Answer: (a) Amit’s savings after n months: A(n) = (3x + 2y) + n(2x − y) = (3 + 2n)x + (2 − n)y
Priya’s savings after n months: P(n) = (x + 4y) + n(3x + y) = (1 + 3n)x + (4 + n)y
(b) With n = 6, x = 100, y = 50:
A(6) = (3 + 12) × 100 + (2 − 6) × 50 = 1500 − 200 = ₹1,300
P(6) = (1 + 18) × 100 + (4 + 6) × 50 = 1900 + 500 = ₹2,400

Q5. If p = 5/2 and q = 1/3, then which of the following options is greater than p + q?
(a) 1
(b) 1/3
(c) 2
(d) 3

Answer: (d) 3
p + q = 5/2 + 1/3 = 15/6 + 2/6 = 17/6 = 2 5/6, which is about 2.83. The only option greater than 2.83 is 3.

Q6. If 3/5 p + 2/3 q = 7/6 and p = 5/4, find the value of q.
(a) 1/2
(b) 1/4
(c) 5/4
(d) 5/8

Answer: (d) 5/8
Substitute p = 5/4: 3/5 × 5/4 + 2/3 q = 7/6, so 3/4 + 2/3 q = 7/6.
2/3 q = 7/6 − 3/4 = 14/12 − 9/12 = 5/12
q = 5/12 × 3/2 = 15/24 = 5/8

Q7. If 2(x + 3y) + 5(2x − y) = px + qy, and 3(x − 2y) + 4(3x + y) = rx + sy, what is the value of p + q + r + s?
(a) 22
(b) 24
(c) 26
(d) 28

Answer: (c) 26
2(x + 3y) + 5(2x − y) = 2x + 6y + 10x − 5y = 12x + y, so p = 12, q = 1.
3(x − 2y) + 4(3x + y) = 3x − 6y + 12x + 4y = 15x − 2y, so r = 15, s = −2.
p + q + r + s = 12 + 1 + 15 + (−2) = 26.

Q8. The perimeter of a triangle with sides (2x + 3), (3x − 1) and (4x + 5) is equal to the perimeter of a rectangle with length (3x + 2) and width (x + 1). Find the value of x.

Answer: Triangle perimeter = (2x + 3) + (3x − 1) + (4x + 5) = 9x + 7
Rectangle perimeter = 2[(3x + 2) + (x + 1)] = 2(4x + 3) = 8x + 6
The perimeters are equal, so 9x + 7 = 8x + 6
9x − 8x = 6 − 7
x = −1

Q9. A sequence of rectangular gardens is designed such that:
1st garden: length = (2a + 1) meters, width = (a + 3) meters
2nd garden: length = (3a + 1) meters, width = (a + 3) meters
3rd garden: length = (4a + 1) meters, width = (a + 3) meters
And so on...
(a) Write the general expression for the length of the nth garden.
(b) Write the expression for the perimeter of the nth garden.
(c) If a = 5 meters, find the dimensions of the 6th garden.

Answer: (a) The coefficient of a is always one more than the garden number: 1st garden (1 + 1)a + 1, 2nd garden (2 + 1)a + 1, 3rd garden (3 + 1)a + 1. So the length of the nth garden = (n + 1)a + 1 metres.
(b) Perimeter = 2(length + width) = 2[(n + 1)a + 1 + a + 3] = 2[(n + 2)a + 4] = [2(n + 2)a + 8] metres.
(c) For the 6th garden, length = 7a + 1 = 7(5) + 1 = 36 metres and width = a + 3 = 5 + 3 = 8 metres.

Q10. A bank account starts with a balance of $200. Each week, the balance changes by $(2x − 15). After 4 weeks, the balance is $140. Find the value of x.
(a) −2
(b) 0
(c) 2
(d) 5

Answer: (b) 0
Total change in 4 weeks = 4(2x − 15) = 8x − 60.
Final balance = starting balance + total change: 140 = 200 + 8x − 60
140 = 140 + 8x, so 8x = 0 and x = 0.

Q11. The expression h = 50 − 5t represents the height of a ball thrown upward, where t is time in seconds and h is height in metres. At what time will the ball be at ground level?
(a) t = 5 seconds
(b) t = 10 seconds
(c) t = 15 seconds
(d) t = 20 seconds

Answer: (b) t = 10 seconds
At ground level the height is 0, so put h = 0: 50 − 5t = 0, which gives 5t = 50 and t = 10 seconds.

Q12. A profit-loss expression is given by 8x − 3y, where x represents sales and y represents expenses (both can be positive or negative integers). If x = −2 and y = −5, what does the result represent?
(a) Profit of 1 unit
(b) Loss of 1 unit
(c) Loss of 31 units
(d) Profit of 31 units

Answer: (b) Loss of 1 unit
Substitute x = −2 and y = −5: 8(−2) − 3(−5) = −16 + 15 = −1. The result is negative, so it represents a loss of 1 unit.

Q13. A game awards points based on the formula p = 15 − 3m, where m is the number of mistakes made. A player's score cannot go below −12 points. What is the maximum number of mistakes a player can make?
(a) 7
(b) 8
(c) 9
(d) 10

Answer: (c) 9
Put p = −12: 15 − 3m = −12, so 3m = 27 and m = 9. If m is less than 9 the score is above −12, and if m is more than 9 the score goes below −12. So the maximum number of mistakes is 9.

Q14. The sum of two consecutive odd primes is 24. If these primes are represented as p and p + d, what is the value of d?
(a) 2
(b) 4
(c) 6
(d) 8

Answer: (a) 2
Check consecutive odd primes: 3 + 5 = 8, 5 + 7 = 12, 7 + 11 = 18, 11 + 13 = 24 ✓. So p = 11 and p + d = 13, which gives d = 2.

Q15. If a and b are consecutive prime numbers greater than 2, what can we say about the expression a + b?
(a) It is always prime
(b) It is always even
(c) It is always odd
(d) It could be either odd or even

Answer: (b) It is always even
All prime numbers greater than 2 are odd. The sum of two odd numbers is always even. For example, 3 + 5 = 8, 5 + 7 = 12, 7 + 11 = 18.

Related Study Material on Extramarks

• CBSE Important Questions Class 7 Maths Chapter 1
• CBSE Important Questions Class 7 Maths Chapter 2
• CBSE Important Questions Class 7 Maths Chapter 3
• CBSE Important Questions Class 7 Maths Chapter 5
• CBSE Important Questions Class 7 Maths Chapter 6
• CBSE Important Questions Class 7 Maths Chapter 7
• CBSE Important Questions Class 7 Maths Chapter 8
• CBSE Important Questions Class 7 Maths Chapter 9
• CBSE Important Questions Class 7 Maths Chapter 10
• CBSE Important Questions Class 7 Maths Chapter 11