NCERT Solutions for Class 7 Maths Chapter 4 Expressions Using Letter Numbers (PDF) – 2027

Shabnam is always 3 years older, so add 3 to Aftab’s age.

Add 3 to Aftab’s age.

Yes. Give Aftab’s age a short name and the rule becomes one line.

Replace a by 23 in the expression a + 3.

Aftab is 3 years younger, so subtract 3.

Replace s by 20.

Every L uses exactly 2 matchsticks, so the count is always double the number of Ls.

In words: Number of matchsticks = 2 × Number of L’s. Taking n for the number of Ls, the expression is

Find the two costs separately and add them.

Find the two costs and add them.

Let c be the number of coconuts and j the number of kilograms of jaggery.

Put c = 7 and j = 4.

Put q = 7 in 4 × q.

In each case the perimeter is the sidelength added as many times as there are sides. Let the sidelength be a units.

Joining two pipes end to end adds their lengths.

Each row follows the same rule: (number of ₹100 notes × 100) + (number of ₹20 notes × 20) + (number of ₹5 notes × 5).

The answer is (d) 10 + 8 × y.

Let the number be n.

(a) 8 × x + 3 × y

A stationery shop sells a pen for ₹x and a notebook for ₹y. Abha buys 8 pens and 3 notebooks. Her bill is 8x + 3y rupees.

(b) 15 × j – 2 × k

A carpenter makes 15 stools every day and works for j days, so he makes 15j stools. On k of those days, 2 stools got damaged. The number of good stools left is 15j – 2k.

In a calendar, moving one step right adds 1 and moving one step up subtracts 7. Starting from w in the bottom-middle cell:

Write each expression as a sum of terms, turn each term into a number, then add.

These are the multiples of 4 in increasing order, so the term at position n is 4 times n.

Remember 7k means 7 × k and 5m means 5 × m.

Mistake. The negative sign of a was ignored.

Mistake. 3d means 3 × d. The 3 and the 6 were written side by side as “36”.

Mistake. The 2 was subtracted before multiplying.

Mistake. The 2 and the 8 were written side by side as 28.

No mistake. This one is correct.

Mistake. Only m was multiplied by 3 (not the 1), and the minus sign of m was dropped: 3 × 6 + 1 = 19.

Mistake. 2f and 2g were read as the two-digit numbers 23 and 21, and 23 – 21 = 2.

Mistake. The + was treated as a ×.

Mistake. The bracket was handled wrongly.

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

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

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

No. It is already in its simplest form.

Try three different values of c.

Area of the bigger rectangle = 7v square units.

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

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

Amount returned: the same procedure with the return rates.

Yes. Open the brackets, then collect like terms.

Yes. Subtracting an expression is the same as adding its opposite.

Use p = 4 and q = 1 in each expression.

No penalty means nothing is taken away for a wrong answer.

Add the three round scores and simplify.

Split 23 into three parts and 7 into three parts.

Krishita scored more.

No. They describe two different operations.

The two columns never match, so 5u ≠ 5 + u.

10y – 3 means ‘3 less than 10 times y’, while 10(y – 3) means ‘10 times (3 less than y)’.

No, the two expressions are not equal.

The sum is 2r + 2s + 24. Three ways of adding:

Picture (i) — two rows: 5y, –6, x and x, 2, 5y.

Picture (ii) — 2p and 3q appear 4 times each; the number tiles are –2, 3, 3, –2.

Picture (iii) — the four corners are –5g and every other circle is 5k (12 of them).

Mistake. Unlike terms were added.

No mistake.

Mistake. The 6 multiplied p, but it was added to the 2 (6 + 2 = 8) instead of multiplying it.

Mistake. 3y – 4y was worked out as 4y – 3y = y; the minus sign before the bracket was not applied to 4y.

Mistake. Only the first term inside the bracket had its sign changed.

Mistake. The + before the bracket was treated as ×, and the sign of 3 was also changed: 2(x – 3) = 2x – 6.

Mistake. The signs inside were flipped even though the bracket has a plus in front.

Mistake. The – p was left out.

Mistake. The distribution was done correctly, but like terms were not collected — so it is not the simplest form.

Mistake. The answer is correct as an equal expression, but it is not in simplest form because the bracket is still there.

Mistake. Every term was given a minus sign, though there is no minus anywhere.

Yes. In every row, the number of letter-numbers is never more than the number of terms:

The formula is “two times the first number minus the second number”, that is 2a – b.

Machine 1 — “add the two numbers, then subtract 2”, that is a + b – 2.

Machine 2 — “multiply the two numbers, then add 1”, that is ab + 1.

Here is one you can use. Formula: 3a – 2b — “three times the first number minus twice the second”.

The border repeats in blocks of three: A, B, C, A, B, C, …

Design C first appears at position 3, then 6, then 9 — the multiples of 3.

B occurs at 2, 5, 8, 11, 14, … — always one less than a multiple of 3.

Yes, and the design at position 122 is Design B.

Yes. The remainder alone decides the design.

Both diagonals add up to the same number.

Yes — but checking examples can never make us sure, because there are unlimited 2 × 2 squares.

Describe them in words first, then in symbols.

• the number to the right of a is 1 more than it
• the number below a is 7 more than it
• the number diagonal to a is 8 more than it

Take the square with top-left number 25 (so a = 25): the square is 25, 26 over 32, 33.

Now take a = 40: the square is 40, 41 over 47, 48.

Another plus shape, centred at 26: the numbers are 19 / 25, 26, 27 / 33.

Observation: the total is always 5 times the number in the centre.

Yes, always. Let the centre be a.

Any shape that is symmetric about one cell works. Taking the centre as a:

Each step adds one more triangle to the row, using only 2 extra matchsticks each time, because the new triangle shares one side with the previous one.

Step 4 uses 9 matchsticks, and every step adds 2.

Yes — count how many 2s are added. Step 1 starts with 3, and each later step adds one more 2.

Step 33 needs 67 matchsticks.

Step y has one 3 and (y – 1) twos.

Noticing that the first step also contains a 2 (since 3 = 1 + 2) gives a second form:

Yes to both. Simplify the first expression and it turns into the second.

Horizontal sticks go 1, 2, 3, 4, … and diagonal sticks go 2, 3, 4, 5, … Each set grows by exactly 1 per step.

The correct expression is (a) 30x + 20y.

The correct expression is (a) p + q + r.

(a) In one full day-and-night the snail gains (u – d) cm. This repeats 10 times.

(b) If d > u, then u – d is negative.

It slips down more each night than it climbs during the day, so it keeps losing ground and will never reach the top.

Work out each week separately — a week has 7 days.

Follow each arrow away from the centre oval w + 2, applying one box at a time.

Three stations lie between the two towns, so the journey is cut into 4 stretches, with 3 halts.

“Subtract A from B” means work out B – A. Change the sign of every term of A, then add.

(a) 8x + 3y

A fruit seller sells mangoes at ₹x each and bananas at ₹y each. A customer buys 8 mangoes and 3 bananas, so the bill is 8x + 3y rupees.

(b) 15x – 2x

A shopkeeper has a packet of 15 pencils, each costing ₹x. Two of them are damaged and cannot be sold. The money received for the packet is 15x – 2x = 13x rupees.

Each extra fold gives one extra piece.

The first square needs 4 matchsticks; every square after that shares one side, so it needs only 3 more.

The printed sequence is red, yellow, green, yellow, red, … so the block red – yellow – green – yellow repeats every 4 positions.

Expressions for the positions:

Each step is an X with one centre square and four arms. Step 1 has arms of length 1, Step 2 arms of length 2, and so on.

Counting vertices: every square has 4 corners, so

(This counts 4 corners for every square. Neighbouring squares touch at one corner; if each shared corner point is counted only once, there are 4n fewer: 16n + 4 – 4n = 12n + 4.)

(a) Column expressions (with r the row number):

(b) Divide by 4: the remainder is the column (remainder 0 means column 4).

(c) The number in row r and column c is

(d) Multiples of 3. Their columns run 3, 2, 1, 4, 3, 2, 1, 4, … repeating.

Other patterns:

• Every number in column 4 is a multiple of 4.
• Even numbers appear only in columns 2 and 4; odd numbers only in columns 1 and 3.
• Going down any column, the numbers rise by 4 each time.
• Along a row the numbers rise by 1; along a downward diagonal they rise by 5.