Each of our Ganita Prakash Class 7 Worksheet and Class 7 Maths Chapter 4 Expressions using Letter Numbers Worksheet with Answers Pdf focuses on conceptual clarity.
Class 7 Maths Chapter 4 Expressions using Letter Numbers Worksheet with Answers Pdf
Expressions using Letter Numbers Class 7 Maths Worksheet
Class 7 Maths Chapter 4 Worksheet with Answers – Class 7 Expressions using Letter Numbers Worksheet
Tick (✓) for the correct option
Question 1.
‘x added to lo’ is written as
(a) 10 + x
(b) 10x
(c) 10 – x
(d) x – 10
Question 2.
‘3 more than y’ is written as
(a) 3y
(b) y + 3
(c) y – 3
(d) y + 3
Question 3.
‘5 increased by m’ is written as
(a) 5 + m
(b) m + 5
(c) 5m
(d) 5 ÷ m
Question 4.
‘7 less than’ is written as
(a) 7 – z
(b) z – 7
(c) 7z
(d) z ÷ 7
Question 5.
‘4 times x’ is written as
(a) 4 + x
(b) x – 4
(b) 4x
(d) x + 4
Question 6.
‘5 reduced by y’ is written as
(a) 5 – y
(b) y – 5
(c) 5z
(d) y + 5
Question 7.
‘3 less than twice of n’ is written as
(a) 3 – 2n
(b) 2n – 3
(c) 2n × 3
(d) 3 + 2n
Question 8.
‘6 times xadded toy’ is written as
(a) 6xy
(b) 6 + xy
(c) y + 6x
(d) x + 6y
Question 9.
‘7 times m subtracted from n’ is written as
(a) 7m – n
(b) 7n – m
(e) n – 7m
(d) m – 7n
Question 10.
‘3 times y added to 2 times x’ is written as
(a) 6xy
(b) 6 + xy
(c) 2x + 3y
(d) 3x + 2y
Question 11.
If the length of each side of a regular hexagon is x metres, then the perimeter of given hexagon is
(a) (x + 6) metres
(b) (x + 6) metres
(c) (x – 6) metres
(d) (6 x x) metres a
Question 12.
‘Four times a number x added to 5’ is
(a) 4 + x
(b) 4x + 5
(c) 5x + 3
(d) 15x a
Question 13.
82 equals
(a) 8 + z
(b) 8 – z
(c) 8 × z
(d) 8 ÷ z
Question 14.
‘y is subtracted from the sum of x and 9’ is written as
(a) (x + 9) -y
(6) y – (x + 9)
(c) y – (x – 9)
(d) y + (x + 9)
Question 15.
Pooja earns ₹ a per month and saves ₹ b per month. Her monthly expenditure (in ₹) is
(a) a + b
(b) a + b
(c) a × b
(d) a – b
Question 16.
Ravi drives a km in one hour. How much distance does he cover in 3 hours 40 minutes?
(a) 3a + 23
(b) 23a + 3
(c) 113a
(d) 113 + a
Assertion-Reason Questions
In questions 1 to 3, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
Question 1.
Assertion (A) : For a number sequence 3, 5, 7, 9, 11, The mth term is 2m + 1.
Reason (R) : 2 + m is written as 2m.
(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 of (A).
(c) (A) is true, but (R) is false.
(id) (A) is false, but (R) is true.
Question 2.
Assertion (A) : If x = 5 and y = 6, then x – (3 – y) = 4
Reason (R) 😡 – (3 – y) = x – 3 + y
(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 of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.
Question 3.
Assertion (A) :3 + 2 × (y – 1)is simplified as 2y +1.
Reason (R) :2 × (y – 1) = 2y – 1
(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 of (A).
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is true.
Fill in the blanks
1. ‘Half of x and 5 is doubled’ is written as ____________
2. ‘ 5 times y to which 3 is subtracted ’ is written as ____________.
3. ‘ Half of x and 5 is doubled ’ is written as ____________.
4. ‘ 6 added to thrice a number x is 45 ’ is written as ____________.
5. ‘two-thirds of a number y is 12’ is written as ____________.
6. ‘x exceeds by 8’ can be expressed as ____________.
7. The simplest form of 3x + 4y – 7 + x – -2y is ____________
8. The 11th term in the sequence 4, 8, 12, 16, 20, … is ____________.
9. The sum of (- 6f + 17 – 4g) and (-7 + 11f + 7g) i is ____________.
10. Expression for total cost “if a pencil costs ₹ x and a pen costs ₹ 5x” is ____________
Write (T) for True or (F) for False for the given statements
1. If a book costs ₹ 24, then the cost of x such books is ₹ (24 + x).
2. If length of an edge of a square is l cm, then the area of the square is 4Z sq. cm.
3. In a 2-digit number, if the ones and tens digits are a and b respectively, then the number is a +b.
4. There are 35 students in a class. If another x students join the class, the total number of students in the class is 35 + x.
5. If the side of an equilateral triangle is s, then its perimeter is (3 + s).
6. The expression obtained when x is multiplied by 2 and then subtracted from 3 is 3 – 2;
7. Savita has p pencils in her box. She puts q more pencils in the box. The total number of pencils with her is p + q.
8. ‘One-fourth of a number x added to one-third of the four times of x’ is written as x3 + x4.
9. The letter-number in the expression 2p + 3 is 2 and 3.
Match the Following
If Sapna’s present age is x years. Match the following statements with their corresponding expressions.
| Situation | Expression |
| (a) Her brother is 5 years younger than her. | (i) x + 26 |
| (b) Her father’s age exceeds her age by 25 years. | (ii) 8x |
| (c) Mother’s age is 4 years less than that of her father. | (iii) 8x – 5 |
| (d) Her grandfather’s age is 8 times of her age. | (iv) x + 25 |
| (e) Her grandmother’s age is 5 years less than her grandfather. | (v) x – 5 |
Very Short Answer Type Questions
Question 1.
Write the following, using numbers, letter-numbers and signs of operations
(i) Twice the sum of x andy
(ii) 2 more than the quotient of m by n.
Solution:
__________________________________
__________________________________
Question 2.
Write the following, using numbers, letter-numbers and signs of operations
(i) 3 is added to the sum of p and 5
(ii) twice a number y decreased by 7
Solution:
__________________________________
__________________________________
Question 3.
Write the algebraic expression for the
(i) perimeter of an equilateral triangle of side length ‘s’ cm
(ii) perimeter of a square of side length ‘y’ cm.
Solution:
__________________________________
__________________________________
Question 4.
If a bird flies 2 km in one minute, then how much distance is covered by the bird in
(i) t minutes
(ii) (p + 2) minutes.
Solution:
__________________________________
__________________________________
Question 5.
For the following number sequence, 5, 10, 15, 20, …………. write
(i) nth term
(ii) (p +2)‘h term
Solution:
__________________________________
__________________________________
Question 6.
For the following number sequence, 6, 11, 16, 21, ………. write
(i) (n – 1)th term
(ii) (p + 1)th term
Solution:
__________________________________
__________________________________
Question 7.
For each of the two statements
(i) one-fourth of a number x is added to one – third of four times the same number.
(ii) 3 is added to twice a number m and the sum is divided by 4.
Solution:
__________________________________
__________________________________
Question 8.
Think of a number x. Multiply it by 3, add 5 to the product and subtract y subsequently. Find the resulting number.
Solution:
___________________________
___________________________
Question 9.
Find the number of days in (i) 3 weeks (ii) 10 weeks (Hi) p weeks.
Solution:
___________________________
___________________________
Question 10.
Write an algebraic expression for the statement “The selling price (S) of an article is equal to the sum of its cost price (C) and the profit (P) earned.”
Solution:
___________________________
___________________________
Question 11.
The time taken by an aeroplane to travel from City A to City B is 10 minutes more than one- eighth of the time taken by a train.
Find the time taken by the aeroplane if the time taken by the train is (i) 12 hours (ii) t hours.
Solution:
___________________________
___________________________
Question 12.
Write algebraic expression using letter number of your choice:
(i) 12 more than a number
(ii) 5 less than a number
(iii) 3 more than twice a number
(iv) 4 less than 5 times a number.
Solution:
___________________________
___________________________
Question 13.
Express the following word statements algebraically:
(i) 10 more than the number x
(ii) 5 less than twice the number y
(iii) 4 more than the sum of x and y
(iv) 2 less than the quotient of 3a by 7.
Solution:
___________________________
___________________________
Question 14.
The mass of Book A is 760 g and the mass of Book B is 550 g. Find the total mass of
(i) 3 copies of Book A and 5 copies of Book B.
(ii) m copies of Book A and n copies of Book B.
Solution:
___________________________
___________________________
Question 15.
Describe a real-life situation that could be represented by the algebraic expression
(i) 2x + 3
(ii) 4m + 3n
Solution:
___________________________
___________________________
Question 16.
What does the following represent?
(i) 3x + 4y
(ii) (x + 2y) × 4
(iii) (a – 36) ÷ 2
(iv) \(\frac{t}{8}-\frac{1}{6}\)
Solution:
___________________________
___________________________
Question 17.
Some simplifications are shown below where the letter-numbers are replaced by numbers and the value of the expression is obtained. Observe each of them and identify the wrong ones. For each wrong ones, find the correct value of the expression.
(i) If x = 3, then x + 3 = 6
(ii) If m = 5, then 3 – m = 2
(iii) If t = 6, then \(\frac{3}{t}\) = 2
(iv) If p = 10, then 5p – 2 = 13
(v) If x = 3 and y = 1, then x + 2y = 5
(vi) If p = 10 and q = 5, then 5pq + 1 = 21
Solution:
___________________________
___________________________
Short Answer Type Questions
Question 1.
If x = 4, find the value of
(i) 3x – 7
(ii) 6 – 4x
Solution:
___________________________
___________________________
Question 2.
If p = 5 , q = – 2, find the value of
(i) p-(q + 7)
(ii) pq – 1
Solution:
___________________________
___________________________
Question 3.
If x = 3 , y = 2 and 2 = 0, find the value of
(i) x – (y + z)
(ii) x(y – z)
(iii)(x + y)z
Solution:
___________________________
___________________________
Question 4.
If p = 2 , q = 3 and r = 6, find the value of
(i) 2p(3q – r)
(ii) 2p + 3qr
(iii) \(\frac{p r-q}{q-p}\)
Solution:
___________________________
___________________________
Question 5.
If a pencil costs ₹ m and an eraser costs ₹ n, then find the cost of 3 pencils and 2 erasers 7 erasers and 2 pencils.
Solution:
___________________________
___________________________
Question 6.
(i) Think of a number p. Multiply it by 3, add 5 to the product and subtract q subsequently. Write the number so obtained.
(ii) Think of a number x. Add 3 to it, multiply the sum by 6 and subtract y subsequently. Write the number so obtained.
Solution:
___________________________
___________________________
Question 7.
Compare and examine the difference between each of the following pair of expressions , by taking any one value of n.
(i) 2n and 2 + n
(ii) 2n – 1 and 2 (n – 1)
(iii) 3n – 5 and 5 – 3n
Solution:
___________________________
___________________________
Question 8.
The number of classrooms on the ground floor of a public school is 5 less than twice the number of rooms on the first floor. If the number of rooms on the first floor isy, then find the number of rooms on the ground floor.
Solution:
___________________________
___________________________
Long Answer Type Questions
Question 1.
Amrita starts in her car from Amritsar at 8 : 00 a.m. for Delhi. She is driving her car at a uniform speed of x km/h. At 12:00 noon, she finds that she is still 50 km away from Delhi. Find the distance between Amritsar and Delhi.
Solution:
___________________________
___________________________
Question 2.
The length of a rectangular hall is 4 metres less than 3 times the breadth of the hall. Write the length of the hall, if the breadth is b metres.
Solution:
___________________________
___________________________
Question 3.
A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.
Solution:
___________________________
___________________________
Question 4.
Add the expressions given below:
(i) 6m – 10 n + 6,23 -2m + 5 n and In -10 -m
(ii) 5x-8- 12y , 6x + 8y + 6 and 7 – 3x + 4y
Solution:
___________________________
___________________________
Question 5.
Subtract the expression given below:
(i) 4f- 7g – 23 from 14-5f + 7g
(ii) 8m + 4n – 12 from 3n – 5m + 11
Solution:
___________________________
___________________________
Question 6.
Simplify the expression given below:
(i) 7x – (3x + 14) – 5
(ii) 13 + An – 2 (m – 2n) + 1
Solution:
___________________________
___________________________
Question 7.
Describe the situations for the following algebraic expressions:
(i) 3a + 5b
(ii) 4x – 7b
(iii) 2 (p + q)
(iv) – 1
Solution:
___________________________
___________________________
Question 8.
Anju is 12p years old. Her son was born when she was 9p years old. Find :
(i) Anju’s age 5 years later
(ii) the sum of their ages 5 years later
Solution:
___________________________
___________________________
Question 9.
Raman is preparing for a cycle race and practicing daily. The first week he cycles 8 km every day. Every week he increases the daily distance cycled by y km. Write the distance cycled by him in 5th week.
Solution:
___________________________
___________________________
Question 10.
Write expression for the following: Take Ruhi’s present age to be x years.
(a) What will be her age after 5 years from now?
(b) What was her age 3 years ago?
(c) Ruhi’s grandfather’s age is 6 times her age. What is the age of her grandfather? id) Grandmother is 2 years younger than grandfather. What is grandmother’s age?
(e) Ruhi’s father’s age is 5 years more than 3 times Ruhi’s age. What is her father’s age?
Solution:
___________________________
___________________________
Question 11.
Look at the questions below and write an expression for each,
(a) What is the length of the knife?
Solution:
___________________________
___________________________
(b) What is length of the handle of the screwdriver?
Solution:
___________________________
___________________________
(c) What is perimeter of the notebook?
Solution:
___________________________
___________________________
(d) If there are x apples and y bananas in the baskets. What is the total cost of the fruits altogether?
Solution:
___________________________
___________________________
Question 12.
Study the given pattern and complete the table that follows:
Question 13.
Identify the following shape sequence. Identify the number pattern involved in it. Write it. And, extend the pattern by drawing next two shapes.
Solution:
___________________________
___________________________
Case-Based Questions
Shalini is organizing a school fair. She is in charge of budgeting for various stalls. She notes the following expenses:
- The cost of each food stall is ₹ a.
- The cost of each game stall is ₹ b.
- She plans to have 4 food stalls and 3 game stalls.
- There is a fixed decoration cost of ₹ 1000.
Based on the above information, answer the following questions:
Question 1.
Write an expression for the total cost to organize the school fair.
Solution:
___________________________
___________________________
Question 2.
What does the term 4a represent?
Solution:
___________________________
___________________________
Question 3.
If the cost of each food stall is ₹ 200 and each game stall is ₹ 150, what will be the total cost?
Solution:
___________________________
___________________________
Crossword Puzzle
Complete the crossword puzzle using the given directions:
Directions:
Across:
1. If F represents your current age, express the total age of you and your three siblings (all the same age) using F.
2. If 3x + 1 = 13, What is the value of x?
3. If 2y + 3 = 17, find y.
4. Mary is twice as old as her brother. If her brother is x years old and Mary is 18, what is x?
Down:
5. Your age is such that twice your age equals 30. What is your age?
6. Jayant is 3 years older than Lalita. Lalita is 8 years old. How old is Jayant?
7. A number E is divided by 3. Write the expression.
