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CBSE · Class 7 · Mathematics

Chapter 2: Arithmetic Expressions

5 concepts · 40 practice questions with answers · Free to read

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Expressions, terms and value

From daily life

At a canteen you buy 3 samosas at ₹12 each and get ₹5 off: 3 × 12 – 5. This phrase is an expression, and the money you pay is its value: ₹31.

Simple definition

An arithmetic expression is a phrase of numbers and operations (+, –, ×, ÷). Its value is the number it works out to. We read an expression as a sum of terms: a – b means a + (–b), and a part with × or ÷ inside is one single term.

23 – 10 × 223term 1+(–10 × 2)term 2= 23 + (–20) = 3

In the figure: 23 – 10 × 2 has two terms: 23 and (–10 × 2). The second term is –20, so the value is 23 + (–20) = 3.

Rule 1: Find the value — Work out each term first, then add the terms.

  • Easy: 13 + 2 = 15.
  • Medium: 6 × 5 + 4 × 3 = 30 + 12 = 42.
  • Exam-type: 100 – 4 × 15 = 100 + (–60) = 40.

Rule 2: Pick out the terms — Split at each + or – sign; the sign stays with the number after it.

  • Easy: 83 – 14 has terms 83 and –14.
  • Medium: 7 × 4 + 9 × 6 has terms 7 × 4 and 9 × 6.
  • Exam-type: 50 – 6 × 3 + 2 has three terms: 50, –6 × 3 and 2; value 50 – 18 + 2 = 34.

Rule 3: Read it in words — Say what each term does: "times" for ×, "more" for +, "less" for –.

  • Easy: 12 × 5 = 12 multiplied by 5.
  • Medium: 20 – 4 = 4 less than 20.
  • Exam-type: 3 × 8 – 2 = 2 less than 3 times 8.
Remember

A sign belongs to the number that follows it: in 83 – 14 the term is –14.

Common mistake

Reading 30 – 4 × 5 as (30 – 4) × 5 = 130. The right way is 30 – 20 = 10.

Shortcut

Split at + and –; do × and ÷ inside each term first. Memory clue: "Plus and minus split, times and divide stay inside."

Spot the difference

PointTermExpression
Meaningone part between + signswhole phrase
Example6 × 56 × 5 + 4 × 3
Value3042

Practice questions

Easy
  1. 1Find the value of 18 + 7 – 5.
  2. 2Write the terms of 83 – 14.
  3. 3Find the value of 6 × 4 + 5 × 3.
Medium
  1. 4Find the value of 100 – 4 × 15.
  2. 5Write "9 less than 7 times 6" as an expression and find its value.
  3. 6Write the terms of 50 – 6 × 3 + 2 and find its value.
Challenging
  1. 7Find the value of 8 × 7 – 3 × 9 + 11.
  2. 8Which is greater: 45 – 6 × 5 or 6 × 5 – 20?
Show answers (try them yourself first)
  1. 120
  2. 283 and –14
  3. 339 (24 + 15)
  4. 440 (100 – 60)
  5. 57 × 6 – 9 = 33
  6. 650, –6 × 3, 2; value 34
  7. 740 (56 – 27 + 11)
  8. 845 – 6 × 5 = 15 is greater than 6 × 5 – 20 = 10

Order of operations and brackets

From daily life

Ana buys 2 pens at ₹10 and pays with ₹50: 50 – 2 × 10. If she wrongly does (50 – 2) × 10 she gets 480. The correct change is ₹30.

Simple definition

Order: 1) brackets, 2) × and ÷ inside each term, 3) + and – from left to right. A bracket with a minus sign outside flips the sign of every term inside.

50 – 2 × 10×50 – 20–3068 – (18 + 13)68 – 31 = 3768 – 18 – 13 = 37

In the figure: Top: 50 – 2 × 10 → 50 – 20 → 30. Bottom: 68 – (18 + 13) = 68 – 31 = 37, the same as 68 – 18 – 13.

Rule 1: × and ÷ before + and – — Without brackets, finish multiplication and division inside each term first.

  • Easy: 5 + 4 × 3 = 5 + 12 = 17.
  • Medium: 30 – 6 × 4 + 2 = 30 – 24 + 2 = 8.
  • Exam-type: 100 – 24 ÷ 4 × 3 = 100 – 6 × 3 = 100 – 18 = 82.

Rule 2: Brackets first — Work out the inside of the bracket, then continue.

  • Easy: (7 + 3) × 4 = 10 × 4 = 40.
  • Medium: 20 + 8 × (16 – 6) = 20 + 80 = 100.
  • Exam-type: 5 × (12 – 3 × 2) = 5 × 6 = 30.

Rule 3: Minus sign before a bracket — a – (b + c) = a – b – c and a – (b – c) = a – b + c. Or just work out the bracket first.

  • Easy: 15 – (4 + 3) = 15 – 7 = 8.
  • Medium: 42 + 15 – (8 – 7) = 57 – 1 = 56.
  • Exam-type: 100 – (45 – 20) – 10 = 100 – 25 – 10 = 65.
Remember

For + and – alone, go from left to right.

Common mistake

Doing 20 – (5 – 2) as 20 – 5 – 2 = 13. The signs inside must flip: 20 – 5 + 2 = 17.

Shortcut

Not sure about the signs? Solve the bracket first. Memory clue: "Brackets are the Boss; Multiply before you Add; a minus flips the pack."

Spot the difference

PointPlus before bracketMinus before bracket
Rulesigns inside staysigns inside flip
Example10 + (4 – 1) = 10 + 4 – 110 – (4 – 1) = 10 – 4 + 1
Value137

Practice questions

Easy
  1. 1Find 12 + 3 × 5.
  2. 2Find (12 + 3) × 5.
  3. 3Find 40 – (15 + 5).
Medium
  1. 4Find 30 – 6 × 4 + 2.
  2. 5Find 20 – (5 – 2).
  3. 6Find 100 – 24 ÷ 4 × 3.
Challenging
  1. 7Find 5 × (12 – 3 × 2).
  2. 8Put brackets in 8 + 6 × 2 so that its value is 28.
Show answers (try them yourself first)
  1. 127
  2. 275
  3. 320
  4. 48
  5. 517
  6. 682
  7. 730
  8. 8(8 + 6) × 2 = 14 × 2 = 28
Live figure

Order of operations and brackets

In the app you can move this figure with your finger.

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Swapping and grouping terms

From daily life

You add a bill: 28 + 19 + 12 + 21. Smart shoppers pair 28 + 12 = 40 and 19 + 21 = 40, so the bill is 80 in seconds.

Simple definition

Swapping: a + b = b + a. Grouping: (a + b) + c = a + (b + c). In a sum of terms any order or grouping gives the same value, as long as each term keeps its own sign. Subtraction itself cannot be swapped.

2819122128 + 12 = 4019 + 21 = 4040 + 40 = 80

In the figure: Pair 28 with 12 and 19 with 21: 40 + 40 = 80.

Rule 1: Swap the terms — Move a term together with its sign.

  • Easy: 9 + 14 = 14 + 9 = 23.
  • Medium: 83 – 14 = –14 + 83 = 69.
  • Exam-type: 25 – 18 + 5 = 25 + 5 – 18 = 30 – 18 = 12.

Rule 2: Group for round numbers — Look for terms that add to 10, 100 or 1000 and add them first.

  • Easy: 47 + 3 + 20 = 50 + 20 = 70.
  • Medium: 28 + 19 + 12 + 21 = 40 + 40 = 80.
  • Exam-type: 236 + 375 – 136 + 25 = (236 – 136) + (375 + 25) = 100 + 400 = 500.

Rule 3: Subtraction cannot be swapped — a – b and b – a are different. Also (a – b) – c and a – (b – c) are different.

  • Easy: 8 – 3 = 5 but 3 – 8 = –5.
  • Medium: 20 – 15 = 5 but 15 – 20 = –5.
  • Exam-type: (50 – 20) – 5 = 25 but 50 – (20 – 5) = 35.
Remember

The sign sticks to the number after it, so –14 moves as a whole.

Common mistake

Swapping only the numbers: 50 – 20 + 10 = 40, but 50 – 10 + 20 = 60. Move the sign with the number.

Shortcut

Pair up numbers that make 10, 100 or 1000 before anything else. Memory clue: "Friends of ten": 1-9, 2-8, 3-7, 4-6, 5-5. Make friends first!

Spot the difference

PointSwappingGrouping
Rulea + b = b + a(a + b) + c = a + (b + c)
What changesthe orderthe pairing
Example9 + 14 = 14 + 9(7 + 3) + 5 = 7 + (3 + 5)

Practice questions

Easy
  1. 1Fill in: 37 + 18 = 18 + ___.
  2. 2Find 25 + 17 + 5 by grouping.
  3. 3Rewrite 40 – 15 by swapping its terms and find the value.
Medium
  1. 4Find 47 + 36 + 53 + 64 smartly.
  2. 5Find 125 + 78 + 75 + 22 smartly.
  3. 6Is 30 – 12 equal to 12 – 30? Give both values.
Challenging
  1. 7Find 99 + 98 + 97 – 96 – 95 – 94 by grouping.
  2. 8Find 1 + 2 + 3 + … + 10 by pairing.
Show answers (try them yourself first)
  1. 137
  2. 247
  3. 3–15 + 40 = 25
  4. 4200 ((47 + 53) + (36 + 64))
  5. 5300 ((125 + 75) + (78 + 22))
  6. 6No: 30 – 12 = 18 but 12 – 30 = –18
  7. 79 ((99 – 96) + (98 – 95) + (97 – 94))
  8. 855 (five pairs of 11)

Distributive property

From daily life

A hall has 8 rows; each row has 5 chairs on the left and 3 on the right. Chairs: 8 × (5 + 3) = 8 × 5 + 8 × 3 = 64.

Simple definition

a × (b + c) = a × b + a × c and a × (b – c) = a × b – a × c. The multiplier outside is shared with every term inside. Read backwards, it lets us take out a common factor.

7 × 30 = 2102830477 × (30 + 4) = 7 × 30 + 7 × 4= 210 + 28 = 238

In the figure: A rectangle 7 high and 34 wide is split into 30 + 4: 7 × 34 = 210 + 28 = 238.

Rule 1: Split a number — Break one number into easy parts (like 50 + 2 or 100 – 2) and share the multiplier.

  • Easy: 6 × 52 = 6 × 50 + 6 × 2 = 312.
  • Medium: 7 × 98 = 7 × 100 – 7 × 2 = 686.
  • Exam-type: 25 × 104 = 25 × 100 + 25 × 4 = 2,600.

Rule 2: Take out the common factor — a × b + a × c = a × (b + c): add the other numbers first, then multiply once.

  • Easy: 4 × 13 + 4 × 7 = 4 × 20 = 80.
  • Medium: 98 × 14 + 2 × 14 = 100 × 14 = 1,400.
  • Exam-type: 63 × 46 – 63 × 36 = 63 × 10 = 630.

Rule 3: Near-100 numbers — For numbers like 19, 98, 99, 101 use 20 – 1, 100 – 2, 100 – 1, 100 + 1.

  • Easy: 3 × (10 – 2) = 30 – 6 = 24.
  • Medium: 12 × 19 = 12 × 20 – 12 = 228.
  • Exam-type: 15 × 98 = 15 × 100 – 15 × 2 = 1,470.
Remember

The number outside multiplies every term inside the bracket.

Common mistake

3 × (4 + 5) = 3 × 4 + 5 = 17. Both terms must be multiplied: 12 + 15 = 27.

Shortcut

For 99, 98, 101 and 19 think "round number ± small number". Memory clue: "Give every term a gift": the multiplier is the gift.

Spot the difference

PointExpandFactorise
Rulea(b + c) → ab + acab + ac → a(b + c)
Example3 × (4 + 5) → 12 + 1512 + 15 → 3 × (4 + 5)
Usesplit a big numberadd first, multiply once

Practice questions

Easy
  1. 1Find 3 × (4 + 5).
  2. 2Find 6 × 52 by splitting 52.
  3. 3Find 12 × 19 using 19 = 20 – 1.
Medium
  1. 4Find 7 × 98.
  2. 5Find 4 × 13 + 4 × 7.
  3. 6Find 98 × 14 + 2 × 14.
Challenging
  1. 7Find 63 × 46 – 63 × 36.
  2. 8Find 15 × 98.
Show answers (try them yourself first)
  1. 127
  2. 2312
  3. 3228
  4. 4686
  5. 580
  6. 61,400
  7. 7630
  8. 81,470

Forming and comparing expressions

From daily life

Rohan buys 3 notebooks at ₹25 each and 2 pens at ₹8 each. The bill is 3 × 25 + 2 × 8 = 91. Two bills can also be compared without calculating.

Simple definition

To write an expression from a story: equal groups → ×, joining → +, taking away → –. To compare two expressions, cancel the terms that are the same on both sides and compare what is left.

13×5 + 413×5 + 74 < 7 ⇒ 13×5 + 4 < 13×5 + 7

In the figure: Both sides have 13 × 5. So only 4 and 7 matter: the right side is heavier.

Rule 1: Write from a story — Find the equal groups, the joins and the takings away, then write the terms.

  • Easy: 4 packets of 6 biscuits and 3 loose: 4 × 6 + 3 = 27.
  • Medium: ₹100 note, 3 items at ₹15: 100 – 3 × 15 = 55.
  • Exam-type: 2 boxes of 12 and 3 boxes of 8, 5 broken: 2 × 12 + 3 × 8 – 5 = 43.

Rule 2: Compare without calculating — Cancel the same terms on both sides; the bigger leftover wins (for a minus term, the smaller one wins).

  • Easy: 15 + 9 < 15 + 12.
  • Medium: 7 × 8 – 5 > 7 × 8 – 9 (less is taken away).
  • Exam-type: 25 × 4 + 18 = 4 × 25 + 18 (just swapped).

Rule 3: Fill in the missing number — Undo the last step: move the known part to the other side with the opposite operation.

  • Easy: 12 + __ = 20 → 20 – 12 = 8.
  • Medium: 5 × __ + 3 = 38 → 35 ÷ 5 = 7.
  • Exam-type: 100 – __ × 6 = 52 → __ × 6 = 48 → 8.
Remember

Equal terms on both sides can be cancelled; no need to find the full value.

Common mistake

Calculating both sides completely and making a slip. Cancelling first is safer and quicker.

Shortcut

Scan for the common term first. Memory clue: "Cancel the twins, compare the rest."

Spot the difference

PointEvaluateCompare by cancelling
Workfull calculationlook at leftovers only
Speedslowerfaster

Practice questions

Easy
  1. 1Write an expression for 5 bags of 8 apples and 3 extra apples.
  2. 2Which is greater: 20 + 17 or 20 + 19?
  3. 3Fill in: 30 + ___ = 45.
Medium
  1. 4Neha has ₹200. She buys a book for ₹45 and a pen for ₹30. How much is left?
  2. 5Without calculating, compare 9 × 11 – 4 and 9 × 11 – 7.
  3. 6Fill in: 5 × ___ + 3 = 38.
Challenging
  1. 7Fill in: 100 – ___ × 6 = 52.
  2. 8Are 6 × 14 + 5 and 5 + 14 × 6 equal? Why?
Show answers (try them yourself first)
  1. 15 × 8 + 3
  2. 220 + 19 is greater
  3. 315
  4. 4200 – 45 – 30 = ₹125
  5. 59 × 11 – 4 is greater (less is taken away)
  6. 67
  7. 78
  8. 8Yes: swapping the terms and the factors does not change the value