Teachers can assign these Ganita Prakash Class 7 Worksheet and Class 7 Maths Chapter 4 Expressions using Letter Numbers Worksheet with Answers Pdf Download for daily practice.
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
Multiple Choice Questions
Choose the correct option.
Question 1.
Symbol used as number-letter represents tkat it can take
(a) different values
(b) a fixed value
(c) only two values
(d) only three values
Answer:
(a) different values
Question 2.
The expression obtained when x is multiplied by 2 and then subtracted from 3 is
(a) 2x – 3
(b) 2x + 3
(c) 3 – 2x
(d) 3x – 2
Answer:
(c) 3 – 2x
Question 3.
In algebra, a x b means ab; in arithmetic 4 x 6 is
(a) 46
(b) 64
(c) 24
(d) 10
Answer:
(c) 24
Question 4.
One plate of Samosa-chat costs ?40 and one plate of Pani-puri costs ?20. If x plates of Samosa-chat and y plates of Pani-puri were ordered in a day, which expression(s) describe the total amount in rupees earned that day by the shopkeeper?
(a) 40x + 20y
(b) (40 + 20) x (x + y)
(c) 20x + 40y
(d) 40x – 20y
Answer:
(a) 40x + 20y
Question 5.
Rohit sells two types of sweets on a festival: laddus and barfis. ‘p’ customers bought only laddus,’q’ customers bought only barfis and V customers bought both laddus and barfis. Rohit gave a coupon to every customer. How many coupons does Rohit distribute?
(a) p + q + r + 2
(b) p + g + r
(c) 2(p + q + r)
(d) p + q + r + r
Answer:
(b) p + g + r
Question 6.
The simplest form of 8 – (2 – x + y) is
(a) x + y – 6
(b) x + y + 10
(c) x – y – 6
(d) x – y + 6
Answer:
(d) x – y + 6
Question 7.
The value of (4a – 8b – 6) + (8a – 4b – 7a + 2) is
(a) 5a – 12b – 4
(b) 5a – 12b + 4
(c) 12a – 12b – 4
(d) 12a + 12b – 4
Answer:
(a) 5a – 12b – 4
Question 8.
Find the colour at position 99, if the colours change in a traffic signal as follows:
(a) Red
(b) Green
(c) Yellow
(d) Can’t determine
Answer:
(b) Green
Assertion and Reason-based Questions.
Directions.: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
Question 1.
Assertion (A): If f = 3, g = 1, then 3f – 3g – 3 = 0.
Reason (R): When the letter-numbers are replaced by the numbers, we get the value of the expression.
Answer:
(d) Assertion (A) is false but Reason (R) is true.
Question 2.
Assertion (A): 6 x (5 x a) = 30a.
Reason (R): In algebra, a x b = ab, but in arithmetic 3 × 5 = 15.
Answer:
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Fill in the blanks.
1. An auto rickshaw charges ₹ 25 for the first kilometre, then ₹ 12 for each subsequent kilometre. The total charge (in ₹) for d kilometres is ________.
Answer:
25 + 12(d – 1)
2. If the present age of Raman is x years, then his age after 7 years will be ________.
Answer:
x + 7
3. 42 + 12 – (8 -7) = ________.
Answer:
53
4. If a = 7, then 3 (a + 1) = ________.
Answer:
24
5. The value of (8x + 4y) – (7x – 4y) is ________.
Answer:
x + 8y
True or False
Write true or false for the following.
1. Expressions 7k – 7 is equal to 7(k – 1).
Answer:
True
2. Three times a number added to itself gives 8 can be expressed as 3x + y = 8.
Answer:
False
3. If a = -5, then 10 – a = 15.
Answer:
True
4. (50x – 40y) + (-20x + 40y) = 30x.
Answer:
True
5. The perimeter of a regular octagon of side length 4a is 32a.
Answer:
True
Match the following:
Question 1.
| Column I | Column II |
| 1. The difference of 3 and a number | (a) 2 (a + 6) |
| 2. 5 less than twice a number | (b) 5 – 3a |
| 3. Five minus thrice a number | (c) 2a – 5 |
| 4. Seven times the sum of a number and 1 | (d) 3 – a |
| 5. 2 times the sum of a number and 6 | (e) 7(a + 1) |
Answer:
| Column I | Column II |
| 1. The difference of 3 and a number | (d) 3 – a |
| 2. 5 less than twice a number | (c) 2a – 5 |
| 3. Five minus thrice a number | (b) 5 – 3a |
| 4. Seven times the sum of a number and 1 | (e) 7(a + 1) |
| 5. 2 times the sum of a number and 6 | (a) 2 (a + 6) |
Solve the following:
Question 1.
Write formulas for the perimeter of the following if the sidelength = a :
(a) an equilateral triangle
(b) a regular pentagon
(c) a regular heptagon
Answer:
(a) 3a
(b) 5a
(c) 7a
Question 2.
Write a situation corresponding to the following algebraic expressions:
(a) 11 × x + 5 × y
(b) 13 × x – 2 × y
Answer:
Do it yourself
Question 3.
At a concert, there were x men and twice the number of women. During the interval, 5 men and 7 women left the concert.
(a) How many people left during the interval?
(b) How many people were there at the concert after the interval?
(c) If x = 700, how many people were there at the concert after the interval?
Answer:
(a) 12 people
(b) 3x – 12
(c) 2088
Question 4.
Subtract 7x + 2y from the sum of (x – 2xy + 2y) and (4x + 2xy – 2y).
Answer:
(-2x – 2y)
Case-Based Question
Question 1.
Two students Anaya and Kabir brought gardening supplies. They brought some packets of seeds and some pairs of gloves from different stores.
They wrote their supplies in the form of expressions: ‘
Anaya wrote: 7x + 2y, and Kabir wrote: 3x + 5y, where:
- x = packets of seeds
- y = pairs of gloves
Based on the above information, answer the following question:
(a) Find the total gardening supplies brought.
(b) If each seed packet costs ₹ 15 and each pair of gloves costs ₹ 30, find the total cost of the combined list.
Answer:
(a) 10x + 7y
(b) ₹ 360
THE NOTION OF LETTER-NUMBERS
Srieha and her family are sitting in the living room, spending quality time.
Sneha’s brother: Papa! I want to distribute some stationery items to an orphanage on my birthday.
Papa: That’s great!
Sneha’s mother: You should buy some notebooks and 8 more pencils than the double of notebooks.
Sneha: You mean, if we buy Y notebooks, then we should buy (2x + 8) pencils to distribute.
Sneha’s brother: What is this V?
Mother: If we have unknown quantities or numbers, then we use letter-numbers to represent unknown quantities or numbers. They are denoted by the small letters: a, b, c, x, y, z, …, and so on.
So, the letter Y represents the unknown quantity of notebooks, and the expression 2x + 8 is an the algebraic expression, like an arithmetical expression that shows the total pencils to be bought for distribution.
Question 1.
Four children, Ananya, Shubham, Harsh, and Shruti are playing luha-chipi. Let the age of Harsh be 10 years. Now, Jind the ages of other children, ij:
(a) Shubham is 2 years younger than Harsh, then Shubham’s age is _____________.
(b) Ananya is 2 years older than Harsh, then Ananya’s age is _____________.
(c) Shruti is 2 years younger than Shubham, then Shruti’s age is _____________.
(d) Harsh’s age is x years, then Shruti’s age is _____________.
Answer:
(a) 8 years
(b) 12 years
(c) 6 years
(d) (x – 4) years
Question 2.
Toshl and AkasKi have a matchbox, and they try to make some interesting patterns using the matchsticks.
(a) Observe the given pattern and fill in the blank space of the following table:
Answer:
(b) How many matchsticks are needed to make 20 Ls?
Answer:
40 Matchsticks
(c) How many matchsticks are needed to make 50 Ls?
Answer:
100 Matchsticks
(d) Write an algebraic expression for the number of matchsticks to be used to make x Ls.
Answer:
2 × x, where x is number of Ls.
Question 3.
Toshi asked Akashi to use the above matchstick patterns (forming Ls) and form a pattern of Hs by adding rnatchsticks. Help Akashi compLeting the tabLe that shows the number of matchsticks
required to make a pattern of Hs, as,
Answer:
(a) Using the letter n, write the rule by that will give the number of matchsticks required for forming any number of Hs.
______________________________________________________
______________________________________________________
______________________________________________________
Answer:
Rule = 3n + 2
(b) Choose any five letters or shapes that can be made using matchsticks and write the rules for making matchstick patterns.
______________________________________________________
______________________________________________________
______________________________________________________
Answer:
Do it yourself
Question 4.
Raman, Sara and Manoj want to buy notebooks and pens from the school bookstore. The price of one notebook is ₹ 16 and that of one pen Is ₹ 6. How. much- money should each of them should carry when:
(a) Raman wants to buy 5 notebooks and 2 pens?
(b) Sara wants to buy 6 notebooks and 1 pen?
(c) Manoj wants to buy 4 notebooks and 4 pens?
(d) They together buy n notebooks and p pens?
Answer:
(a) ₹ 92
(b) ₹ 102
(c) ₹ 88
(d) 16n + 6p, where n represents number of notebooks and p represents number of pens
Question 5.
Write the formulas for the following:
(a) The perimeter of the an isosceles triangle with equal side x and base y is _____________.
(b) The perimeter of a square having each side x is _____________.
(c) The perimeter of an octagon having each side x is _____________.
(d) The perimeter of a rectangle of length x and breadth y is _____________.
Answer:
(a) x + x + y
(b) 4x
(c) 8x
(d) 2(x + y)
Question 6.
If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)
Answer:
50b
Question 7.
Find the total amount with Harsh if he has the following number of ₹ 500, ₹ 200, ₹ 100, ₹ 50 and ₹ 10 notes. Complete the table given below:
Answer:
Question 8.
Sneha scored 85 marks in Maths, x marks in Science and y marks in English. If she got a total of 350 marks in four subjects, including Hindi, then how many marks did she get in Hindi?
Answer:
265 – x – y
Question 9.
Write an algebraic expression by using a letter-number of your choice for the following:
(a) 5 more than a number
(b) 3 less than a number
(c) the product of 4 and a number
(d) 11 is subtracted from twelve times a number
(e) the product of any two numbers divided by the sum of another two numbers
Answer:
(a) x + 5
(b) y – 3
(c) 4Z
(d) 12a – 11
(e) \(\frac{a \times b}{p+q}\)
Question 10.
Describe situations corresponding to the following algebraic expressions:
(a) 2x + 2y
______________________________________________________
Answer:
Pranav bought x number of lollipops and y number of candies. What is the total amount he has to pay to the shopkeeper, if the cost of each lollipop is ₹ 2 and the cost of each candy is ₹ 2.
(b) 4x – 6y
______________________________________________________
Answer:
Do it yourself
Question 11.
In a calendar month, September 20XX
- Dates increase by 1 from left to right across the week.
- Dates increase by 7 from top to bottom (each row = a week).
(a) If the bottom last cell contains the date labelled ‘w’, write algebraic expressions for the other five dates in the grid, in terms of w.
(b) Using your expressions, find the actual dates in the grid if w = 15.
Answer:
Question 12.
By using swapping, grouping and distributive property find the^value of the following expressions:
(a) 56 – 5 × 10
(b) 45 + 24 – 20 + 32
(c) 56 + 15 – ( 8 – 7)
(d) 5 × 4 + 6 × 5
(e) 12 + 32 – (8 × 8)
(f) 25 + 5 x (15 – 5)
Answer:
(a) 6
(b) 81
(c) 70
(d) 50
(e) -20
(f) 75
Omission of the Multiplication Symbol in Algebraic Expressions
Question 13.
NCC cadets are marching in a parade on Annual Day and there are 6 cadets in a row.
(a) How many cadets are in 5 rows and 12 rows?
Answer:
30 cadets, 72 cadets
(b) What is the rule that gives the number of cadets, in n rows?
Answer:
Number of cadets = 6n
Question 14.
Uma is drawing a beautiful Rangoli pattern on Ganesh Chaturthi by joining dots through lines. She has 9 dots in a row.
(a) How many dots are there if there are 8 rows and 10 rows?
(b) How many dots wilt her Rangoli have for x rows?
Answer:
(a) 72 dots, 90 dots
(b) number of dots = 9x
Mind the Mistake, Mend the mistake
Question 15.
Observe each of the sentence. If you think there is a mistake, try to explain what might have gone wrong. Then, correct it and give the value of the expression. ,
(a) If x = 5, then 10 + x = 15.
(b) If a = -6, then 3a -12 = 6
(c) If t = 5, b = 3, then 2t + b = 25.
(d) If b = 6, n = 8, then h – (3 – n) = 4.
Answer:
(a) No mistake
(b) 3a – 12 = -30
(c) 2t + b = 13
(d) h -(3 – n) = 11
Simplification of Algebraic Expressions
Question 16.
If the length of a rectangle Is 4 times its breadth b, find the perimeter of this rectangle.
Answer:
10b
Question 17.
Shubham, Harsh and Shruti are climbing the steps to a hilltop. Shubham is at the step p. Harsh is 10 steps ahead and Shruti is 6 steps behind Shubham.
(a) Where are Harsh and Shruti?
Answer:
Harsh is at (p + 10), Shruti is at (p – 6)
(b) The total number of steps to the hilltop is 3 steps less than 8 times what Shubham has reached. Express the total number of steps using p.
Answer:
Total Steps = 8p – 3
Question 18.
A sports shop rents out cricket bats and footballs for tournaments.
- The initial rent per bat is ₹ 80, and per football is ₹ 50.
- After the event, ₹ 30 is refundedfor each bat and ₹20 for eachfootball returned in good condition. If b bats and f footballs are rented, write an expression for:
(a) The total amount paid initially.
(b) The total amount refunded after returning the equipment.
(c) The final amount collected.
Answer:
(a) Total initial payment = 80b + 50f
(b) Total refund = 30b + 20f
(c) Final amount spent = ₹(50b + 30f)
Question 19.
In a science quiz, Priya’s scores In three sections are as follows:
- Section A: 6p – 4q
- Section B: 9p – 5q
- Section C: 3p – 2q
Here, p Is the points for a correct answer and q Is the penalty for a wrong answer,
(a) Find an expression for the combined score of all three sections.
(b) Find the average score per section.
(c) What is her total score if p = 2 and q = 0?
Answer:
(a) 18p – 11q
(b) \(\frac{18 p-11 q}{3}\)
(c) 36
Question 20.
Simplify the expression: 5(x + y) – 2(x – y) + y
Answer:
3x + 8y
Question 21.
Is the expression 10(x + y) = 10xy? Justify your answer.
Answer:
No
Question 22.
Is the expression 6(xy + yx) = 12xy? Justify your answer.
Answer:
Yes
Question 23.
Add the following expressions and simplify the result.
(a) x + x + x + x, x + x + y, x + y + x – y
(b) x – y + x – y, x – x + y
(c) p + q – (p + q), p – q – (p – q)
(d) 2x – y – (x – y), – 2(x – y) – z
Answer:
(a) 8x + y
(b) 2x – y
(c) 0
(d) – x + 2y – z
Mind the Mistake, Mend the mistake
Question 24.
Observe each of the following and see if there is a mistake. If you think there is a mistake, try to explain what might have gone wrong. Then, simplify it correctly.
(a) Is expression x – y is the simplest form of expression 6(x + y) – 5(x + y)?
Answer:
No
(b) Is expression 14a is the simplest form of expression 8(a + b) – 3 (a + b) + 9a – 5b?
Answer:
Yes
(c) Is expression -20 — 8r — 12s is the simplest form of expression -4(2r + 3s + 5)?
Answer:
Yes
(d) Is expression 5(x + 2y + 3z + 4) is the simplest form of expression 5x + 10y + 15z + 20?
Answer:
Yes
(e) Is there any relation between the number of terms and the number of letter-numbers in the simplified expressions? Explain.
Answer:
Yes
PICK PATTERNS AND REVEAL RELATIONSHIPS
Formula Detective
Look at the adjoining number machine. It takes in two numbers, A and B as inputs and performs some operations and produces the result as output C.
For example, if input A = 4 and input B = 6, then output C = 20.
Here, we see that (4 + 6) × 2 = 20
Rule obtained: Twice the sum of two numbers taken in.
Question 25.
Now, look at the Input-Output table:
(a) Can you guess the rule? If yes, then write it.
(b) What would the output be for inputs 6 and 7?
Answer:
(a) Rule: A + B = C
(b) 13
Algebraic Expressions to Describe Patterns
Question 26.
A table both border has a repeating sequence of designs of: Sun (S), Moon (M), and Star (T) as follows:
Find the following:
(a) The expression for the nth occurrence of the Sun design.
Answer:
3n – 2
(b) The expression for the nth occurrence of the Moon design.
Answer:
3n – 1
(c) The expression for the nth occurrence of the Star design.
Answer:
3n
(d) Complete the table below to show the design at each position.
| Position number | Quotient | Remainder | Design |
| 14 | |||
| 29 | |||
| 45 | |||
| 61 |
Answer:
| Position number | Quotient | Remainder | Design |
| 14 | 4 | 2 | Moon |
| 29 | 9 | 2 | Moon |
| 45 | 15 | 0 | Star |
| 61 | 20 | 1 | Sun |
Patterns In a Calendar
Take a calendar for November 20XX. Extend the numbers in the calendar beyond 30, creating endless rows. Based on this answer the following:
Question 27.
Take the 2 × 2 square starting at 25, like
| 25 | 26 |
| 32 | 33 |
(a) Find the sums of the diagonals. What do you observe?
(b) Write the general rule for each date if we take the last corner date 33 as d.
| ________ | _______ |
| ________ | d |
(c) Without calculating, predict the diagonal sums for the 2 × 2 square end at 47.
Answer:
(a) 58
(b) General rule =
| d – 8 | d – 7 |
| d – 1 | d |
(c) 86
Question 28.
Consider a set of numbers from the calendar, like
| 11 | ||
| 17 | 18 | 19 |
| 25 |
(a) Write expressions for all the numbers in terms of the centre number ‘a’.
| ________ | _____ | _______ |
| _______ | a | _______ |
| _______ | _____ | _____ |
Answer:
| a – 7 | ||
| a – 1 | a | a + 1 |
| a + 7 |
(b) Find the total sum of all the numbers.
Answer:
90
(c) Show that the total sum is always 5 times the centre number.
Answer:
Do it yourself
Think and Answer
Find a 3 x 3 grid on the calendar for which the total sum is always 9 times the centre number. Describe and explain your reasoning.
Matchstick Patterns
Question 29.
Look at the matchstick pattern below and complete the table:
Answer:
| a – 8 | a – 7 | a – 6 |
| a – 1 | a | a + 1 |
| a + 6 | a + 7 | a + 8 |
The post Expressions using Letter Numbers Class 7 Worksheet with Answers Maths Chapter 4 appeared first on Learn CBSE.
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