NCERT Solutions for Class 7 Maths Chapter 2 Arithmetic Expressions (PDF) – 2027

Let us choose 24. Using two numbers and any one of +, –, × and ÷ we can write many expressions whose value is 24.

First find each value.

Now put the values in increasing order: 40 < 47 < 48 < 55 < 60.

Compare the two sides part by part, the way we compared Raja’s and Joy’s marbles.

Take a few pairs and compare the two values.

In every case both forms give the same value.

In the Token Model, one (+) token and one (–) token together make a zero pair (value 0).

Removing 3 positive tokens and adding 3 negative tokens leave the same result, so subtracting 3 is the same as adding its inverse: 5 – 3 = 5 + (–3).

Turn every subtraction into “add the inverse”, then read off the terms.

Their values are 17, 23, 10, 31 and 39 respectively.

No. The value stays the same however we order the terms.

Yes. Swapping two terms keeps the sum even when the terms are negative.

Swapping two terms does not change the value because the tokens on the table do not change — only the order in which we put them down changes.

Take 6 + (–4). Put down 6 positive tokens, then 4 negative tokens. Four zero-pairs cancel, leaving 2 positives, i.e. 2.

Take (–4) + 6. Put down 4 negative tokens first, then 6 positive tokens. The same four zero-pairs cancel, leaving 2 positives, i.e. 2.

Yes. Grouping the terms in either way gives the same value, even with negative terms.

Take (–7) + 10 + (–11) as tokens: 7 negatives, 10 positives, 11 negatives — that is 18 negatives and 10 positives in all.

Group the first two first: (–7) + 10 gives 3 positives; then 3 positives with 11 negatives leaves 8 negatives.
Group the last two first: 10 + (–11) gives 1 negative; then 7 negatives with 1 negative gives 8 negatives.

Yes. Any order and any grouping gives the same value.

Three terms: 9 + 4 + 6

Four terms (one negative): 15 + (–8) + 5 + 12

Write every term as a pile of tokens and push all the piles onto one table.

For 15 + (–8) + 5 + 12 the table holds 15 + 5 + 12 = 32 positive tokens and 8 negative tokens.

No, she does not. She only has to add the missing number to the total she already has.

It does not matter — she can wear the hat first and then the shoes, or the shoes first and then the hat. Manasa will look exactly the same either way.

But if her mother says “Wear your socks and shoes!”, the order does matter. Socks must go on before shoes.

Seven friends order one dosa each at ₹23, and the tip stays ₹5.

Terms: 7 × 23 and 5 — two terms.

There were 33 students playing. When the teacher called out ‘5’, the children formed groups of 5.

The terms are 6 × 5 and 3.

There are 33 students playing, so we split 33 into complete groups plus those left out.

For your own class: suppose 40 children are playing.

Each product is a single term, because none of them contains a ‘+’ sign.

Each expression has four terms.

Yes — many. Here are four more, using ₹100, ₹50, ₹20, ₹10 notes and ₹5, ₹1 coins.

Check the second one: 200 + 200 + 20 + 10 + 2 = 432 ✓

The right-hand picture has two identical columns. Each column is made of 5 yellow squares on top and 3 blue squares below.

The same arrangement can also be described as

(a) Story: A school library had 89 books on its shelves. The librarian bought 21 new books. Later, 10 books were issued to students. How many books are left on the shelves?

(b) Story: Ravi buys 5 boxes of mangoes with 12 mangoes in each box. On the way home 6 mangoes get spoilt. How many good mangoes does he have?

(c) Story: In a rangoli, Meena uses 4 rows of 9 yellow dots and 2 rows of 6 red dots. How many dots are there in all?

(a) Elsa doubled her 100 coins → 2 × 100. Anna has half of her 100 coins → 100 ⁄ 2.
(c) From the picture: 2 borders of 3 cm, 6 grill bars of 2 cm and 7 gaps of 5 cm.

Change one term by a little and the value changes by exactly the same little amount.

A bracket with a plus before it keeps the signs inside; a bracket with a minus before it flips them.

When are the two expressions equal? They are equal exactly when, after removing the brackets, both expressions become the same list of terms with the same signs.

(a) Write each as a sum of terms:

319 – 537 and –537 + 319 have the same value — the same two terms, only swapped.

(b) Again compare the terms:

So the three copies of 87 + 46 – 109 are equal to one another, and 87 – 46 + 109 = (87 – 46) + 109. The odd one out is 87 – (46 + 109).

Use each of 2, 3 and 5 once. Here are all the different values that can be reached.

So we get six different values: –6, –4, 0, 4, 6 and 10.

(a) Yes, she always gets the correct answer.

(b) Other strategies of the same kind:

Remove every bracket first, then compare the terms.

No. Lhamo and Norbu each ordered one vegetable cutlet (₹43) and one rasgulla (₹24), so each share is 43 + 24 and the total is double the whole share.

Now three friends each have a cutlet (₹43) and a rasgulla (₹24).

In 5 × 4 + 3 the terms are 5 × 4 and 3, so only the 4 is multiplied by 5. In 5 × (4 + 3) the bracket makes 4 + 3 one quantity, so both 4 and 3 are multiplied by 5.

Yes — all three are equal, because 4 + 3 = 3 + 4 and 5 × 7 = 7 × 5.

Yes, it is quicker — each product becomes one easy multiplication by a round number plus one easy addition or subtraction, with no carrying.

Any product where one number sits just above or just below a round number — a multiple of 10, 50, 100 or 1000.

Multiply the outside number into every term inside the bracket, keeping each sign.

Split 14 as a product first, then split one factor as a sum.

More answers: 1 × (7 + 7), 2 × (6 + 1), 7 × (0 + 2).

Picture (I) — five 4s (squares) and four 8s (circles).

Picture (II) — eight 5s (blue) and eight 6s (red).

Melvin reads on 7 – 2 = 5 days a week, one story each of those days.

The expressions that describe the scenario are (b) and (g).

(a) 83 – 37 – 12 has terms 83, –37, –12.

So (i) and (iv) are equal to 83 – 37 – 12 (all three have value 34; (ii) is 35 and (iii) is 32).

(b) 93 + 37 × 44 + 76 has terms 93, 37 × 44, 76.

So only (iv) is equal to 93 + 37 × 44 + 76 (both are 1797).

Let us choose 36.

Use exactly four 4s each time, with +, –, ×, ÷, brackets and the two-digit number 44.

Using only +, –, ×, ÷, brackets and 44, the values 11, 13, 14, 18 and 19 cannot be made with exactly four 4s (checking every possible expression shows this). They can be made if the decimal .4 (four tenths) is allowed; note that 4 ÷ .4 = 10, since ten 0.4s make 4:

Use each of 1, 2, 3, 4, 5 once, with +, –, ×, ÷ and brackets. Every whole number from –10 to 10 can be reached.

Here is one neat solution using each of 0, 1, 2, …, 9 exactly once.

— puzzles of the same family:

• Using three 5s and any operations, make every value from 1 to 10.
• Using four 2s exactly once each, which numbers from 1 to 15 can you make?
• Using the digits of the current year (for example 2, 0, 2 and 6) once each, make the numbers 1 to 12 — one for each month.
• Using 1, 2, 3, 4 exactly once each, what is the largest value you can make? And the smallest?