CBSE Class 7 Mathematics Expressions using Letter Numbers Practice Paper Assignment Set 03 with Answers

This page gives Class 7 Maths Ganita Prakash Chapter 4 Expressions using Letter-Numbers Practice Paper 12 (40 marks, 20 questions in Sections A to E) together with fully worked answers. The paper focuses on the coefficient of a term, translating phrases like "13 less than 2 times a number", opening brackets with a minus sign, equivalent forms of the rectangle perimeter 2(l + b), describing situations for 8x + 3xy, pencil and eraser prices, and a 2×3 calendar grid built around the date w.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Find the value of the expression h − (3 − n) when h = 5 and n = 6.
Answer:
Substitute h = 5 and n = 6: 5 − (3 − 6).
Work out the bracket first: 3 − 6 = −3.
5 − (−3) = 5 + 3 = 8.
In simple words: The bracket is −3, and 5 − (−3) = 8.

Teacher's Note:
1. Solve the bracket before subtracting.
2. Another way: h − (3 − n) = h − 3 + n = 5 − 3 + 6 = 8.

Question 12. The perimeter of a regular octagon is given by the expression 8s. If its side length is halved, what is the new expression for its perimeter?
Answer:
A regular octagon has 8 equal sides. New side length = \( \frac{s}{2} \).
New perimeter = 8 × \( \frac{s}{2} \) = 4s.
So halving each side halves the perimeter: 8s becomes 4s.
In simple words: Half of each side gives half the perimeter: 4s.

Teacher's Note:
1. Change the side first, then multiply by the number of sides.
2. 8 × s ÷ 2 = 4s.

Question 13. Simplify the expression 5(2w + 3x + 4w) and then check its value for w = 2 and x = 3.
Answer:
Combine like terms inside the bracket: 2w + 4w = 6w, so the expression is 5(6w + 3x).
Distribute: 5 × 6w + 5 × 3x = 30w + 15x.
Value at w = 2, x = 3: 30 × 2 + 15 × 3 = 60 + 45 = 105.
Check with the original: 5(4 + 9 + 8) = 5 × 21 = 105. ✓
In simple words: The expression simplifies to 30w + 15x, which is 105 for w = 2, x = 3.

Teacher's Note:
1. Simplify inside the bracket before distributing.
2. The original and simplified forms must give the same value.

Question 14. Write an algebraic expression for the following situation: A factory produces m toys per hour for 8 hours and n toys per hour for the next 5 hours.
Answer:
Toys made in the first 8 hours = m × 8 = 8m.
Toys made in the next 5 hours = n × 5 = 5n.
Total number of toys = 8m + 5n.
In simple words: Rate × time for each part, then add: 8m + 5n.

Teacher's Note:
1. Number made = number per hour × hours.
2. 8m and 5n are unlike terms, so they stay separate.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Simplify the expression 5 − (2 − 6z) and find its value if z = −1.
Answer:
Open the bracket (the minus sign before it changes both signs): 5 − 2 + 6z.
Simplify the numbers: 3 + 6z. The simplified expression is 3 + 6z.
Put z = −1: 3 + 6 × (−1) = 3 − 6 = −3.
Check with the original: 5 − (2 − 6 × (−1)) = 5 − (2 + 6) = 5 − 8 = −3. ✓
In simple words: 5 − (2 − 6z) = 3 + 6z, which is −3 when z = −1.

Teacher's Note:
1. −(2 − 6z) = −2 + 6z.
2. Use brackets when substituting a negative value.

Question 16. A number machine takes in three numbers, a, b, and c. The output is given by the expression a × b − c. If the output is 15, and the values of a and b are 5 and 4 respectively, find the value of c.
Answer:
Substitute a = 5 and b = 4: 5 × 4 − c = 20 − c.
The output is 15, so 20 − c = 15.
The number taken from 20 to leave 15 is 20 − 15 = 5, so c = 5.
Check: 5 × 4 − 5 = 20 − 5 = 15. ✓
In simple words: 5 × 4 = 20, and 20 − c = 15 means c = 5.

Teacher's Note:
1. Multiply first, then subtract.
2. Ask: what must be taken from 20 to leave 15?

Question 17. Describe a situation corresponding to the algebraic expression 8x + 3xy.
Answer:
8x + 3xy has two terms: 8 × x and 3 × x × y.
Situation: A school buys x art kits. Each kit has a sketchbook costing ₹8 and 3 brushes costing ₹y each.
Cost of sketchbooks = 8 × x = 8x. Number of brushes = 3 × x = 3x, so their cost = 3x × y = 3xy.
Total cost = ₹(8x + 3xy).
For example, with x = 10 kits and brushes at ₹5: 8 × 10 + 3 × 10 × 5 = 80 + 150 = ₹230.
In simple words: 8x + 3xy can be the cost of x kits, each with an ₹8 item and 3 items of ₹y.

Teacher's Note:
1. The term 3xy needs three numbers multiplied: 3, x and y.
2. Check your story by putting numbers in.

Section D: Long Answer Question (5 Marks)

Question 18. Simplify the expression 2d − d − d − d and then check if it's equal to 2d − (d − d) − c when d = 5 and c = 10.
Answer:
First expression: 2d − d − d − d = (2 − 1 − 1 − 1)d = −1d = −d.
Second expression: the bracket d − d = 0, so 2d − (d − d) − c = 2d − 0 − c = 2d − c.
Values at d = 5, c = 10:
First expression: −d = −5. (Directly: 10 − 5 − 5 − 5 = −5.)
Second expression: 2d − c = 2 × 5 − 10 = 10 − 10 = 0. (Directly: 10 − (5 − 5) − 10 = 0.)
Since −5 ≠ 0, the two expressions are not equal for d = 5 and c = 10.
Note: the brackets change the meaning. In the second expression the last two d's are grouped, so they cancel each other instead of both being subtracted.
In simple words: The first is −d = −5 and the second is 2d − c = 0, so they are not equal.

Teacher's Note:
1. Brackets change which terms are subtracted.
2. The second expression also contains a new letter-number, c.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: A dedicated shopkeeper offers stationery to her customers, pricing her products based on a simple system. Pencils are sold for ₹c each, while erasers cost ₹d each. A student, for example, might buy a certain number of pencils and erasers. This straightforward pricing model allows the shopkeeper to easily calculate the total cost for any combination of items a customer purchases.
(a) The shopkeeper earns a total of ₹18c from selling pencils over three days. What could be the number of pencils sold on each of the three days? Give three possible combinations. (2 marks)
(b) If the shopkeeper sells 10 pencils and 1 eraser on Day 3, and the total earnings for Day 3 is ₹150, write an equation and find the value of c if d = 20. (2 marks)
Answer:
(a) Each pencil earns ₹c, so ₹18c means 18 pencils were sold in all.
We need three numbers that add up to 18. Three possible combinations: (6, 6, 6), (5, 5, 8) and (10, 4, 4).
For example, 5c + 5c + 8c = 18c. (Other answers such as (9, 6, 3) are also correct.)
(b) Day 3 earnings = 10 × c + 1 × d = 10c + d.
Equation: 10c + d = 150. With d = 20: 10c + 20 = 150.
10c = 150 − 20 = 130, so c = 13. A pencil costs ₹13.
Check: 10 × 13 + 20 = 130 + 20 = 150. ✓
In simple words: 18c means 18 pencils in all; and 10c + 20 = 150 gives c = 13.

Teacher's Note:
1. The coefficient of c counts the pencils.
2. Undo + 20 first, then divide by 10.

Teacher's Note:
1. Up one row means 7 less; right one cell means 1 more.
2. The +1 and −1 in the bottom row cancel each other.