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NCERT Solutions for Class 7th Maths Chapter 4 In-text Questions — Simplification of Algebraic Expressions

Book page 88–90 Updated on2026-09-19

Q1.
Example 5: The price per pencil is c and the price per eraser is d. The money earned by selling pencils on Day 1 is 5c. Similarly, the money earned by selling pencils on Day 2 is _____, and Day 3 is ______.
Answer

Multiply the number sold that day by the price per pencil.

Day 2: 3 pencils → 3c
Day 3: 10 pencils → 10c
Day 1Day 2Day 3
Pencils (price c)5310
Money from pencils5c3c10c
Q2.
If c = ₹50, find the total amount earned by the sale of pencils.
Answer

The total money from pencils is 5c + 3c + 10c, which simplifies to 18c.

5c + 3c + 10c = (5 + 3 + 10) × c = 18c
18c = 18 × ₹50
= ₹900
Why it happens: Adding 5 lots of c, 3 lots of c and 10 lots of c gives 18 lots of c. That is the distributive property at work.
Q3.
Write the expression for the total money earned by selling erasers. Then, simplify the expression.
Answer

Erasers sold: 4 on Day 1, 6 on Day 2 and 1 on Day 3, each priced d.

Total from erasers = 4d + 6d + 1d
= (4 + 6 + 1) × d
= 11d
Tip: 1d is simply written as d. So the shop's three-day earning altogether is 18c + 11d.
Q4.
Can the expression 18c + 11d be simplified further?
Answer

No. It is already in its simplest form.

Why it happens: 18c and 11d contain different letter-numbers — they are unlike terms. c is the price of a pencil and d is the price of an eraser; there is no way to combine ₹-per-pencil with ₹-per-eraser into a single term.
Did you know? Sets like (5c, 3c, 10c) are called like terms and can always be merged into one term. Sets like {18c, 11d} are unlike terms and cannot.
Q5.
Check that both expressions take the same value when c is replaced by different numbers. (5c + 3c + 10c and 18c)
Answer

Try three different values of c.

c5c + 3c + 10c18c
210 + 6 + 20 = 3636
525 + 15 + 50 = 9090
50250 + 150 + 500 = 900900
Why it happens: Simplifying only rewrites an expression using the same rules that hold for numbers. So the two forms must agree for every value of c — that is exactly what ‘equal expressions’ means.
Q6.
As earlier, a big rectangle is split into two smaller rectangles as shown below. Write an expression to find the area of the rectangle AEFD.
n4DFCA12EB
Rectangle ABCD, page 90 — length AB = 12, breadth AD = n. The dashed line FE splits it into AEFD and EBCF, with FC = 4.
Answer

AEFD is what is left of ABCD after the strip EBCF is removed.

Method 1 — use its own sides:
AE = 12 – 4 = 8, AD = n
Area of AEFD = 8 × n = 8n

Method 2 — subtract:
Area of ABCD = 12n, Area of EBCF = 4n
Area of AEFD = 12n – 4n = 8n
A E B D F C n 12 4
Rectangle ABCD of sides 12 and n, split at EF. The shaded strip EBCF has area 4n.
Why it happens: Both routes must agree, and they do: 12n – 4n = (12 – 4)n = 8n. This is the distributive property seen as areas.
Q7.
Example 7: A shop rents out chairs (₹40 each) and tables (₹75 each); on return it pays back ₹6 per chair and ₹10 per table. For x chairs and y tables, describe the procedure to get these amounts.
Answer

Amount paid at the beginning: multiply each rate by how many pieces are taken and add.

Chairs: x × ₹40 = 40x
Tables: y × ₹75 = 75y
Paid at the start = 40x + 75y

Amount returned: the same procedure with the return rates.

Chairs: x × ₹6 = 6x
Tables: y × ₹10 = 10y
Returned = 6x + 10y
So the total amount actually paid = (40x + 75y) – (6x + 10y)
Q8.
Can we simplify this expression? If yes, how? If not, why not? [(40x + 75y) – (6x + 10y)]
Answer

Yes. Open the brackets, then collect like terms.

(40x + 75y) – (6x + 10y)
= 40x + 75y – 6x – 10y
= 40x + (–6x) + 75y + (–10y) (swapping and grouping)
= (40 – 6)x + (75 – 10)y
= 34x + 65y
Why it happens: The minus sign outside the bracket changes the sign of both terms inside. After that, 40x and –6x are like terms, and so are 75y and –10y.
Check it yourself: For x = 2 chairs and y = 1 table: paid ₹155, returned ₹22, so ₹133 is kept. And 34 × 2 + 65 × 1 = 68 + 65 = ₹133. ✔
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