Ch 2: Arithmetic Expressions — Class 7 Maths

✎ 1. Simple Expressions

An arithmetic expression is a mathematical phrase that combines numbers with operations. Think of it as a compact way to describe a calculation.

➕ Addition

13 + 2 = 15

➖ Subtraction

20 − 4 = 16

✖ Multiplication

12 × 5 = 60

➗ Division

18 ÷ 3 = 6

Every expression has a value — the number it evaluates to. The = sign shows the relationship between an expression and its value.

💡 Key Idea: Different expressions can have the same value! For example, all of these equal 12:
10 + 2 • 15 − 3 • 3 × 4 • 24 ÷ 2

🎬 Multiple Expressions, One Value

10 + 2

15 − 3

3 × 4

24 ÷ 2

↓

= 12

📖 Example 1: Mallika's Lunch

Mallika spends ₹25 every day for lunch from Monday to Friday.

Expression: 5 × 25 = 125

So Mallika spends ₹125 on lunch in a week.

💡 Remember: An expression is a mathematical phrase, not a sentence. It doesn't have an = sign by itself. When we write "5 × 25 = 125", the left side (5 × 25) is the expression, 125 is its value, and = connects them.

⚖ 2. Comparing Expressions

We can compare expressions using >, <, and = by finding their values first.

📖 Example 2: Raja vs Joy — Marble Challenge

Raja has 1023 + 125 marbles. Joy has 1022 + 128 marbles. Who has more?

Raja: 1023 + 125 = 1148

Joy: 1022 + 128 = 1150

Joy has 2 more marbles! So: 1023 + 125 < 1022 + 128

📊 Marble Comparison

Raja
1023+125

1148

Joy
1022+128

1150

Joy has 2 more marbles!

📖 Example 3: Equal Expressions

Compare: 113 − 25 vs 112 − 24

113 − 25 = 88

112 − 24 = 88

They are equal! So: 113 − 25 = 112 − 24

💡 Quick Trick: Sometimes you can compare without fully computing. If one expression adds more and the other starts higher, think about the net difference. Raja starts 1 higher but adds 3 less, so Joy wins by 2.

✏ Figure it Out 1

Q1. Fill in the blanks:

(a) 13 + 4 = + 6

(b) 22 + = 6 × 5

(c) 8 × = 64 ÷ 2

(d) 34 − = 25

Answers: (a) 11 (b) 8 (c) 4 (d) 9

Q2. Arrange in ascending order (smallest to largest):

67 − 19, 67 − 20, 35 + 25, 5 × 11, 120 ÷ 3

Values: 48, 47, 60, 55, 40

Ascending order: 120 ÷ 3 (=40) < 67−20 (=47) < 67−19 (=48) < 5×11 (=55) < 35+25 (=60)

🔎 3. Reading Complex Expressions

When an expression has more than one operation, things can get confusing — just like ambiguity in language!

💬 Language Analogy: "Shalini sat next to a friend with toys." Does Shalini have toys, or does the friend? The sentence is ambiguous! Similarly, 30 + 5 × 4 can be read in two ways.

📖 Example 4: The Big Debate

Expression: 30 + 5 × 4

👧 Purna says:

"Add first! (30 + 5) × 4 = 35 × 4 = 140"

👦 Mallesh says:

"Multiply first! 30 + (5 × 4) = 30 + 20 = 50"

Who is right? Mallesh is correct! By convention, multiplication is done before addition.

🎬 Two Paths, One Correct

30 + 5 × 4

(30+5) × 4

= 35 × 4

= 140 ✘

30 + (5×4)

= 30 + 20

= 50 ✔

💡 Why We Need Brackets & Rules: Without clear rules or brackets, the same expression could give different answers. That's why we use brackets to make the order clear and we have the convention that multiplication/division is done before addition/subtraction.

📎 4. Brackets in Expressions

Rule: Always evaluate expressions inside brackets first!

📖 Example 5: Irfan's Shopping

Irfan buys biscuits for ₹15 and toor dal for ₹56. He pays ₹100.

Correct: Change = 100 − (15 + 56) = 100 − 71 = ₹29

Wrong way: 100 − 15 + 56 = 85 + 56 = 141 ✘ (Absurd! More than he paid!)

🎬 Bracket Resolver

100 − (15 + 56)

100 − 71

= 29 ✔

💡 Think of brackets as a box: Whatever is inside the box must be solved first before you can use the result in the rest of the expression.

🔥 5. Terms in Expressions

Terms are the parts of an expression separated by the + sign.

Subtracting is the same as adding the inverse:

83 − 14 = 83 + (−14)

So the terms of 83 − 14 are: 83 and −14

➖ Subtraction as Addition

−18 − 3 = (−18) + (−3)

Terms: −18 and −3

✖ Multiplication within a Term

6 × 5 + 3

Terms: 6×5 and 3

6×5 is a single term!

💡 Important: A product like 6 × 5 counts as a single term because there is no + sign inside it. The + sign is what separates terms.

🎬 Term Identifier

23 − 2×4 + 16

📌 Identify the Terms

Click "Reveal" to see the terms for each expression:

Expression	Terms
13 − 2 + 6	13, −2, 6
5 + 6×3	5, 6×3
4 + 15 − 9	4, 15, −9
23 − 2×4 + 16	23, −2×4, 16
28 + 19 − 8	28, 19, −8

🔄 6. Swapping & Grouping

🔁 Commutative Property

Swapping terms doesn't change the sum.

📖 Example 6: Drone Flight

A drone goes 6 m up and then 4 m down.

Expression: 6 + (−4) = 2

Swap the terms: (−4) + 6 = 2

Same result! ✔

🎬 Commutative Swap

6

+

(−4)

=

2

🧰 Associative Property

Grouping terms differently doesn't change the sum.

📖 Example: Different Groupings

Evaluate (−7) + 10 + (−11) in different ways:

Way 1: [(−7) + 10] + (−11) = 3 + (−11) = −8

Way 2: (−7) + [10 + (−11)] = (−7) + (−1) = −8

Way 3: [(−7) + (−11)] + 10 = (−18) + 10 = −8

All give −8!

💡 Key Rule: "In an expression with only additions (remember, subtraction is just adding the inverse), the order of terms doesn't matter."

🔢 Evaluating Expressions with Multiplication

When an expression has multiplication, evaluate each term first, then add.

📖 Example: 30 + 5 × 4

Terms: 30 and 5×4

Step 1: Evaluate 5 × 4 = 20

Step 2: Add: 30 + 20 = 50

💡 Manasa's Problem: Manasa added a long list of numbers and got 11,749. Then she realized she forgot to include 9,055. Does she need to restart? No! She can simply add: 11,749 + 9,055 = 20,804. The associative property saves the day!

🧦 Swapping in Everyday Life: Putting on a hat and shoes — order doesn't matter (commutative!). But putting on socks and then shoes — order matters (not commutative!). In addition, swapping always works.

📖 7. Expressions with Stories

📖 Example 7: Dosa Dinner

A family orders 4 dosas at ₹23 each and gives a ₹5 tip.

Expression: 4 × 23 + 5 = 92 + 5 = ₹97

📖 Example 8: Fire in the Mountain

33 students play "Fire in the Mountain, Run Run Run!" They form groups of 5.

Expression: 6 × 5 + 3 = 30 + 3 = 33

6 complete groups with 3 students left over.

🎬 Fire in the Mountain!

📖 Example 9: Raghu's Packets

Raghu has 4 packets. His mother gives half of 100 more.

Expression: 4 + 100 ÷ 2 = 4 + 50 = 54 packets

📖 Example 10: Kannan's Payment

Kannan pays ₹432 using notes and coins:

Expression: 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1

= 400 + 20 + 10 + 2 = ₹432

📖 Example 11: Grid Arrangements

Which grid matches 5 × 2 + 3?

We need a grid with 5 rows of 2, plus 3 extra = 13 cells

5×2 + 3 = 13 ✔

✏ Figure it Out 2

Q1. Find the values by identifying terms:

(a) 28 − 7 + 8 =

(b) 39 − 2×6 + 11 =

(c) 40 − 10 + 10 + 10 =

(d) 48 − 10×2 + 16÷2 =

(e) 6×3 − 4×8÷5 =

Answers: (a) 29 (b) 38 (c) 50 (d) 36 (e) 11.6

Q2. Write a story for each expression:

(a) 89 + 21 − 10

(b) 5 × 12 − 6

(c) 4 × 9 + 2 × 6

Sample stories:
(a) A shop had 89 items, received 21 more, then sold 10. Total = 100 items.
(b) 5 packets of 12 biscuits, 6 got crushed. Remaining = 54 biscuits.
(c) 4 rows of 9 red chairs + 2 rows of 6 blue chairs = 36 + 12 = 48 chairs.

Q3. Word Problems:

(a) A princess has 5 chests with 20 gold coins each, plus 13 loose coins. How many coins total?

Answer:

(b) A metro ticket costs ₹35. A family of 4 buys tickets but gets ₹10 discount. Total cost?

Answer:

(c) A window is at 12 m height. A ladder reaches 3 m above the window. Ladder length?

Answer: m

Answers: (a) 5×20 + 13 = 113 (b) 4×35 − 10 = 130 (c) 12 + 3 = 15 m

🔓 8. Removing Brackets I

💡 Key Rule: When brackets are preceded by a MINUS sign, the signs of all terms inside CHANGE (+ becomes −, − becomes +). When preceded by a PLUS sign, signs stay the same.

📖 Example 12: Minus Before Bracket

100 − (15 + 56)

= 100 − 15 − 56

= 29

📖 Example 13: Be Careful!

500 − (250 − 100)

= 500 − 250 + 100 (the − flipped to +!)

= 350

NOT 500 − 250 − 100 = 150 ✘

📖 Example 14: Plus Before Bracket

28 + (35 − 10)

= 28 + 35 − 10 (signs stay the same!)

= 53

🎬 Sign Flipper

500 − (+250 −100)

↓ minus flips the signs! ↓

500 −250 +100

= 350

🔧 Tinker the Terms I

How does changing one term affect the value?

If 53 + (−16) = 37, what is 54 + (−16)?

Answer:

38 (one more than 37, because 54 is one more than 53)

If 53 + (−16) = 37, what is 53 + (−17)?

Answer:

36 (one less, because we are subtracting 1 more)

If 53 + (−16) = 37, what is 55 + (−18)?

Answer:

37 (53 increased by 2, 16 increased by 2 — net change is 0!)

✏ Figure it Out 3

Q1. Fill in the blanks:

(a) 38 − (−7) = 38 + =

(b) 17 + (−3) = 17 − =

(c) (−22) + 18 = 18 − =

Answers: (a) 7, 45 (b) 3, 14 (c) 22, −4

Q2. Remove brackets:

(a) 13 − (6 + 3) =

(b) 13 − (6 − 3) =

(c) 13 + (6 + 3) =

(d) 13 + (6 − 3) =

(e) −(18 + 5) =

(f) −(18 − 5) =

Answers: (a) 13−6−3=4 (b) 13−6+3=10 (c) 13+6+3=22 (d) 13+6−3=16 (e) −18−5=−23 (f) −18+5=−13

Q3. Compare each pair:

(a) 43 − (12 + 9) vs 43 − 12 − 9 →

(b) 43 − (12 − 9) vs 43 − 12 − 9 →

Answers: (a) = (both equal 22) (b) > (40 vs 22)

Q5. Add brackets to get the indicated values:

(a) 16 − 4 + 2 = 10 → Write with brackets:

(b) 3 + 2 × 4 = 20 →

Answers: (a) 16 − (4+2) = 16−6 = 10 (b) (3+2) × 4 = 5×4 = 20

Q7. Using 2, 3, and 5 with + and −, how many different values can you make?

Try all combinations: 2+3+5, 2+3−5, 2−3+5, 2−3−5, etc.

Possible values:
+2+3+5 = 10, +2+3−5 = 0, +2−3+5 = 4, +2−3−5 = −6
−2+3+5 = 6, −2+3−5 = −4, −2−3+5 = 0, −2−3−5 = −10
Distinct values: −10, −6, −4, 0, 4, 6, 10 (7 values, but 0 appears twice so 6 distinct values)

Q8. Jasoda's Strategy: To subtract 9, she subtracts 10 then adds 1. Why does this work?

Explanation: n − 9 = n − (10 − 1) = n − 10 + 1.
Subtracting 10 is easy (just decrease the tens digit), then add 1 back. This is the bracket-removal rule in action!

🔮 9. Removing Brackets II — Distributive Property

📖 Example 15: Lhamo & Norbu's Hotel Bill

Lhamo and Norbu each order a meal costing ₹43 for food + ₹24 for drink.

Expression: 2 × (43 + 24) = 2 × 67 = 134

OR: 2 × 43 + 2 × 24 = 86 + 48 = 134

Both ways give the same answer!

📖 Example 16: Republic Day Parade

4 rows of soldiers + 3 rows of soldiers, each row has 5 soldiers.

4 × 5 + 3 × 5 = (4 + 3) × 5 = 7 × 5 = 35

💡 Distributive Property:
a × (b + c) = a × b + a × c
"Multiple of a sum = Sum of the multiples"

🎬 Distributive Property — Area Model

a × (b + c)

a × b

a × c

= a×b + a×c

📖 Example 17: Smart Multiplication

Given that 53 × 18 = 954, find 63 × 18.

63 × 18 = (53 + 10) × 18 = 53×18 + 10×18 = 954 + 180 = 1134

📖 Example 18: Mental Math Magic

Calculate 97 × 25 mentally:

97 × 25 = (100 − 3) × 25 = 100×25 − 3×25 = 2500 − 75 = 2425

💡 Power of Distributive Property: It lets us break "hard" multiplications into "easy" ones. 99 × 7 = (100−1) × 7 = 700 − 7 = 693. No long multiplication needed!

🔧 Tinker the Terms II — Mental Math

Use the distributive property to compute:

(a) 102 × 7 =

(b) 98 × 12 =

(c) 999 × 4 =

(a) (100+2)×7 = 700+14 = 714
(b) (100−2)×12 = 1200−24 = 1176
(c) (1000−1)×4 = 4000−4 = 3996

✏ Figure it Out 4

Q1. Use the distributive property:

(a) 3 × (5 + 2) =

(b) 7 × (8 − 3) =

(c) (10 + 4) × 6 =

(d) (20 − 3) × 5 =

(e) 6 × 12 + 6 × 8 = 6 ×

(f) 5 × 17 − 5 × 7 = 5 ×

(g) 101 × 13 =

(h) 99 × 15 =

(i) 48 × 9 =

(j) 52 × 11 =

(k) 4 × 63 + 4 × 37 =

(l) 7 × 84 − 7 × 34 =

(m) 997 × 5 =

(n) 1005 × 8 =

(o) 12 × 45 + 12 × 55 =

(p) 25 × 88 =

(a) 21 (b) 35 (c) 84 (d) 85 (e) 20 (f) 10 (g) 1313 (h) 1485 (i) 432 (j) 572 (k) 400 (l) 350 (m) 4985 (n) 8040 (o) 1200 (p) 2200

Q2. Compare using <, >, or =

(a) 3×(4+5) vs 3×4+5 →

(b) 8×(7−2) vs 8×7−2 →

(c) 5×9+5×1 vs 5×(9+1) →

(d) 6×(10−3) vs 6×10−3 →

(a) > (27 vs 17) (b) < (40 vs 54) (c) = (50 vs 50) (d) < (42 vs 57)

Q3. Write 14 in the form ___ × ( ___ + ___ )

Answer:

Multiple answers: 2 × (5+2), 2 × (3+4), 7 × (1+1), etc.

Q4. Write the sum of the array in two different ways:

A grid with 3 rows of 4 and 3 rows of 6:

Way 1: 3×4 + 3×6 = 12 + 18 = 30

Way 2: 3×(4+6) = 3×10 = 30

Both ways use the distributive property and give 30.

📝 10. Figure it Out 5 — Final Exercises

✏ Figure it Out 5

Q1. Real-life word problems:

(a) A vendor has 5 baskets with 24 mangoes each, and gives away 18 mangoes. How many left?

Answer:

(b) Binu saves ₹15 daily. After 10 days, he spends ₹50. How much does he have?

Answer:

(c) A snail climbs 3 m up each day and slides 1 m down at night. After 5 days, how high is it?

Answer: m

(a) 5×24 − 18 = 120 − 18 = 102
(b) 15×10 − 50 = 150 − 50 = 100
(c) 5×3 − 5×1 = 15 − 5 = 10 m (or 5×(3−1) = 5×2 = 10)

Q2. Melvin wrote these stories. Which expression matches each?

(a) "I had 20 chocolates, gave 5 to each of 3 friends."
Expression:

(b) "4 packets of 6 pencils plus 2 loose pencils."
Expression:

(a) 20 − 5×3 = 20−15 = 5 (b) 4×6 + 2 = 24+2 = 26

Q3. Evaluate 1−2+3−4+5−6+7−8+9−10 in different ways:

Way 1: Group pairs: (1−2)+(3−4)+(5−6)+(7−8)+(9−10) = (−1)+(−1)+(−1)+(−1)+(−1) = −5

Way 2: Group differently: 1+(−2+3)+(−4+5)+(−6+7)+(−8+9)−10 = 1+1+1+1+1−10 = −5

Way 3: Positives: 1+3+5+7+9 = 25. Negatives: 2+4+6+8+10 = 30. Total: 25−30 = −5

Q4. Compare each pair using <, >, =

(a) 28+32 vs 28+33 →

(b) 45−19 vs 45−20 →

(c) 7×8 vs 7×6+7×2 →

(d) 3×(5+2) vs 3×5+2 →

(e) 100−(30+20) vs 100−30+20 →

(f) 50−(25−10) vs 50−25−10 →

(g) 9×(8+3) vs 9×8+9×3 →

(h) 12×5−4 vs 12×(5−4) →

(a) < (b) > (c) = (d) > (21 vs 17) (e) < (50 vs 90) (f) > (35 vs 15) (g) = (99 vs 99) (h) > (56 vs 12)

Q5. Identify equal expressions (same value):

A: 8×6+8×4 • B: 8×(6+4) • C: 8×10 • D: 80 • E: 8×6+4

A = B = C = D = 80. Expression E = 52 (different because 4 is not multiplied by 8).

Q6. Create 10 different expressions that all equal 24:

Some possibilities:
20+4, 30−6, 12×2, 48÷2, 8×3, 6×4, 25−1, 12+12, 100−76, 3×(5+3)

🚀 11. Expression Engineer

Put your expression skills to the ultimate test!

🏆 Challenge 1: Three 3's

Using exactly three 3's and any operations (+, −, ×, ÷, brackets), make as many different values as possible.

Example: 3 + 3 + 3 = 9, 3 × 3 + 3 = 12, 3 × 3 × 3 = 27, 3 × 3 − 3 = 6, (3 + 3) × 3 = 18

🏆 Challenge 2: Four 4's

Using exactly four 4's and any operations, try to make every number from 1 to 20.

1 = 44 ÷ 44

2 = 4 ÷ 4 + 4 ÷ 4

3 = (4 + 4 + 4) ÷ 4

4 = 4 + 4 × (4 − 4)

5 = (4 × 4 + 4) ÷ 4

6 = 4 + (4 + 4) ÷ 4

7 = 4 + 4 − 4 ÷ 4

8 = 4 + 4 + 4 − 4

9 = 4 + 4 + 4 ÷ 4

10 = (44 − 4) ÷ 4

12 = 4 × (4 − 4 ÷ 4)

15 = 4 × 4 − 4 ÷ 4

16 = 4 × 4 + 4 − 4

17 = 4 × 4 + 4 ÷ 4

20 = 4 × (4 + 4 ÷ 4)

🏆 Challenge 3: Using 1, 2, 3, 4, 5

Using digits 1, 2, 3, 4, 5 exactly once each with +, −, try to get every value from −10 to +10.

🏆 Challenge 4: Century Express

Using digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once each, make an expression that equals 100.

🎯 12. Practice Zone

✅ Multiple Choice Questions

1. What is the value of 5 + 3 × 2?
- 16
- 11
- 13
- 10
✔ Answer: 11 (multiply first: 5 + 6 = 11)
2. What is 100 − (30 + 25)?
- 95
- 55
- 45
- 5
✔ Answer: 45 (bracket first: 100 − 55 = 45)
3. The terms of 8 − 3×2 + 5 are:
- 8, −3×2, 5
- 8, −3, 2, 5
- 8, 3×2, 5
- 8−3, 2+5
✔ Answer: 8, −3×2, 5 (3×2 stays together as one term)
4. Which property says a × (b + c) = a×b + a×c?
- Commutative
- Distributive
- Associative
- Identity
✔ Answer: Distributive Property
5. 50 − (20 − 8) equals:
- 22
- 42
- 58
- 38
✔ Answer: 38 (bracket: 50 − 12 = 38)
6. 99 × 7 using distributive property equals:
- 700 + 7
- 700 − 3
- 700 − 7
- 693 + 7
✔ Answer: 700 − 7 = 693 [(100−1)×7 = 700−7]
7. When a minus sign is before a bracket, the signs inside:
- Change (flip)
- Stay the same
- All become positive
- All become negative
✔ Answer: Change (+ becomes −, − becomes +)
8. Which pair of expressions are equal?
- 3×(4+5) and 3×4+5
- 3×(4+5) and 3×4+3×5
- 3+4×5 and (3+4)×5
- 3−(4+5) and 3−4+5
✔ Answer: 3×(4+5) = 3×4+3×5 = 27 (distributive property)
9. The value of 4 + 100 ÷ 2 is:
- 52
- 202
- 54
- 48
✔ Answer: 54 (divide first: 4 + 50 = 54)
10. 15 + (−8) is the same as:
- 15 + 8
- −15 + 8
- −15 − 8
- 15 − 8
✔ Answer: 15 − 8 = 7

✏ Fill in the Blanks

1. An arithmetic __________ is a mathematical phrase combining numbers and operations.

Answer: expression

2. The parts of an expression separated by + are called __________.

Answer: terms

3. a × (b + c) = a×b + a×c is called the __________ property.

Answer: distributive

4. Swapping terms in addition gives the same result due to the __________ property.

Answer: commutative

5. 83 − 14 can be rewritten as 83 + __________.

Answer: (−14)

6. When brackets are preceded by a minus sign, the signs inside __________.

Answer: change (flip / reverse)

7. In 30 + 5 × 4, the expression __________ is done first.

Answer: 5 × 4 (multiplication)

8. Changing the grouping of terms in addition does not change the result. This is the __________ property.

Answer: associative

✔✘ True or False

1. 5 + 3 × 2 = 16

False. 5 + 3×2 = 5 + 6 = 11 (multiply first)

2. 100 − (30 + 20) = 100 − 30 − 20

True. Minus before bracket: signs change, so −(30+20) = −30 − 20

3. 50 − (20 − 5) = 50 − 20 − 5

False. 50 − (20−5) = 50 − 20 + 5 = 35. But 50−20−5 = 25.

4. The terms of 6×5 + 3 are: 6, 5, and 3.

False. 6×5 is a single term. The terms are 6×5 and 3.

5. 7 × 98 = 7 × 100 − 7 × 2 = 686

True. Distributive property: 700 − 14 = 686

6. In addition, the order of terms does not matter.

True. This is the commutative property of addition.

📝 Short Answer Questions

1. Why do we need brackets in arithmetic expressions?

Answer: Brackets remove ambiguity by making the order of operations clear. Without brackets, expressions like 30 + 5 × 4 could be interpreted in multiple ways. Brackets tell us which operation to do first.
2. Explain with an example how the distributive property helps in mental math.

Answer: To calculate 98 × 6 mentally: 98×6 = (100−2)×6 = 600−12 = 588. The distributive property breaks a hard multiplication into easy ones.
3. What are the terms of the expression 15 − 3×4 + 2×7?

Answer: The terms are: 15, −3×4, and 2×7. Products within a term stay together.
4. Remove brackets: 200 − (75 − 30 + 15)

Answer: 200 − 75 + 30 − 15 = 140. When a minus is before the bracket, all signs inside flip.
5. Give a real-life example that uses the expression 3 × 45 + 2 × 30.

Answer: Example: "3 shirts cost ₹45 each and 2 pants cost ₹30 each. Total cost = 3×45 + 2×30 = 135 + 60 = ₹195."

📜 13. Question Paper Sets

Four full question paper sets covering all topics of Chapter 2. Click any set to expand it. Use "Show Answer" on each question or "Show All Answers" at the bottom of each set.

Class: VII Chapter: 2 — Arithmetic Expressions Max Marks: 25 Time: 30 Minutes Level: Foundation

Section A — Multiple Choice Questions (5 × 1 = 5 Marks)

1. The value of 5 + 3 × 4 is: [1 mark]
- (a) 32
- (b) 17
- (c) 24
- (d) 20
✔ Answer: (b) 17 — Multiply first: 5 + 12 = 17
2. 40 − (12 + 8) = [1 mark]
- (a) 44
- (b) 60
- (c) 20
- (d) 36
✔ Answer: (c) 20 — Bracket first: 40 − 20 = 20
3. The terms of the expression 6 + 3×2 are: [1 mark]
- (a) 6, 3, 2
- (b) 6 and 3×2
- (c) 6×3 and 2
- (d) 6+3 and 2
✔ Answer: (b) 6 and 3×2 — Multiplication stays together as one term
4. The property a + b = b + a is called the: [1 mark]
- (a) Associative
- (b) Distributive
- (c) Commutative
- (d) Identity
✔ Answer: (c) Commutative Property
5. When a + sign is placed before a bracket, the signs inside: [1 mark]
- (a) Flip (change)
- (b) Stay the same
- (c) All become +
- (d) All become −
✔ Answer: (b) Stay the same

Section B — Fill in the Blanks (5 × 1 = 5 Marks)

1. 12 + 3 × 4 = _______ [1 mark]

Answer: 24 (3×4 = 12, then 12+12 = 24)

2. The expression 9 − 4 has _______ terms. [1 mark]

Answer: 2 terms (9 and −4)

3. 5 × (6 + 4) = 5×6 + 5 × _______ [1 mark]

Answer: 4 (Distributive: 5×6 + 5×4 = 30 + 20 = 50)

4. 100 − (30 + 20) = _______ [1 mark]

Answer: 50 (Bracket first: 100 − 50 = 50)

5. The value of 7 × 7 − 7 is _______ [1 mark]

Answer: 42 (49 − 7 = 42)

Section C — True or False (5 × 1 = 5 Marks)

1. 3 + 4 × 2 = 14 [1 mark]

False. Multiply first: 3 + 8 = 11, not 14.

2. (3 + 4) × 2 = 14 [1 mark]

True. Bracket first: 7 × 2 = 14. ✔

3. The expression 5×3 − 2 has 3 terms. [1 mark]

False. It has only 2 terms: 5×3 and −2. (5 and 3 are not separate terms.)

4. 50 + (10 + 20) = 50 + 10 + 20 [1 mark]

True. + before bracket: signs inside stay the same. ✔

5. 4 × (5 + 3) = 4×5 + 4×3 [1 mark]

True. Distributive property: 4×8 = 20 + 12 = 32. ✔

Section D — Evaluate the Expressions (4 × 2 = 8 Marks)

1. Evaluate: 10 + 6 × 5 − 2 [2 marks]

Solution: 10 + 6×5 − 2 = 10 + 30 − 2 = 38
2. Evaluate: 48 ÷ 8 + 3 × 4 [2 marks]

Solution: 48 ÷ 8 + 3×4 = 6 + 12 = 18
3. Remove brackets and simplify: 25 − (8 + 7) [2 marks]

Solution: 25 − 8 − 7 = 10 (minus before bracket: signs inside flip)
4. Find using distributive property: 6 × 15 [2 marks]

Solution: 6 × (10 + 5) = 6×10 + 6×5 = 60 + 30 = 90

Section E — Short Answer (1 × 2 = 2 Marks)

1. Riya has 5 bags, each containing 8 candies. She gives away 14 candies. Write an arithmetic expression for the candies left and find its value. [2 marks]

Expression: 5 × 8 − 14
Value: 40 − 14 = 26 candies

Class: VII Chapter: 2 — Arithmetic Expressions Max Marks: 30 Time: 35 Minutes Level: Intermediate

Section A — Multiple Choice Questions (5 × 1 = 5 Marks)

1. 8 × 99 using distributive property equals: [1 mark]
- (a) 799
- (b) 792
- (c) 800
- (d) 801
✔ Answer: (b) 792 — 8×(100−1) = 800 − 8 = 792
2. 60 − (25 − 10) = [1 mark]
- (a) 25
- (b) 45
- (c) 35
- (d) 55
✔ Answer: (b) 45 — 60 − 15 = 45
3. How many terms does 4×5 − 3×2 + 8 have? [1 mark]
- (a) 5
- (b) 4
- (c) 3
- (d) 2
✔ Answer: (c) 3 terms: 4×5, −3×2, and 8
4. 5 × (a + b − c) = [1 mark]
- (a) 5a + b − c
- (b) 5a + 5b + 5c
- (c) 5a + 5b − 5c
- (d) 5a − 5b − 5c
✔ Answer: (c) 5a + 5b − 5c (Distributive property)
5. The value of 24 ÷ 4 + 3 × 2 is: [1 mark]
- (a) 18
- (b) 15
- (c) 12
- (d) 10
✔ Answer: (c) 12 — Division & multiply first: 6 + 6 = 12

Section B — Fill in the Blanks (5 × 1 = 5 Marks)

1. In 40 − (15 + 8), removing brackets gives 40 − _______ − _______ [1 mark]

Answer: 40 − 15 − 8 = 17

2. 7 × 102 = 7 × (100 + 2) = _______ + _______ = _______ [1 mark]

Answer: 700 + 14 = 714

3. The value of 3 + 5 × 0 = _______ [1 mark]

Answer: 3 (Multiply first: 5×0=0, then 3+0=3)

4. In a×(b + c), if a = 4, b = 5, c = 3, the value is _______ [1 mark]

Answer: 32 (4×8=32, or 4×5+4×3=20+12=32)

5. 100 − (40 + 35) = _______ [1 mark]

Answer: 25 (100 − 75 = 25)

Section C — True or False (5 × 1 = 5 Marks)

1. 100 − (30 + 10) = 100 − 30 + 10 [1 mark]

False. 100−(30+10) = 100−30−10 = 60. Minus before bracket changes all signs inside.

2. 7 × (8 − 3) = 7×8 − 7×3 [1 mark]

True. Distributive property: 56 − 21 = 35 = 7×5. ✔

3. The terms of 10 + 3×4 − 5 are: 10, 3×4, −5 [1 mark]

True. The three terms are 10, +3×4, and −5. ✔

4. 4 × (a + b) = 4a + b [1 mark]

False. Correct form is 4a + 4b (multiply 4 by each term inside the bracket).

5. 6 × 25 + 6 × 75 = 6 × 100 = 600 [1 mark]

True. Distributive in reverse: 6×(25+75) = 6×100 = 600. ✔

Section D — Evaluate (4 × 2 = 8 Marks)

1. Evaluate: 5 × (12 + 8) [2 marks]

Solution: 5 × 20 = 100 (or 5×12 + 5×8 = 60+40 = 100)
2. Simplify: 80 − (30 − 15 + 5) [2 marks]

Solution: 80 − 30 + 15 − 5 = 60 (signs change after −)
3. Using distributive property: 11 × 99 [2 marks]

Solution: 11×(100−1) = 1100 − 11 = 1089
4. Evaluate: 15 + 20 ÷ 4 × 2 [2 marks]

Solution: 15 + (20÷4)×2 = 15 + 5×2 = 15 + 10 = 25 (left-to-right for ÷ and ×)

Section E — Application Problems (2 × 3.5 = 7 Marks)

1. A shopkeeper sold 6 notebooks at ₹35 each and 4 pencil boxes at ₹20 each. Write an arithmetic expression and find the total amount. [3 marks]

Expression: 6×35 + 4×20
Solution: 210 + 80 = ₹290
2. Remove brackets and simplify: 150 − (45 − 20 + 15) [4 marks]

Solution: 150 − 45 + 20 − 15 = 110 (signs inside bracket flip after −)

Class: VII Chapter: 2 — Arithmetic Expressions Max Marks: 35 Time: 40 Minutes Level: Advanced

Section A — Multiple Choice Questions (5 × 1 = 5 Marks)

1. 5 + 2 × {3 + (4 − 1)} = [1 mark]
- (a) 17
- (b) 19
- (c) 11
- (d) 15
✔ Answer: (a) 17 — Inner: 4−1=3; {3+3}=6; 2×6=12; 5+12=17
2. Descending order of 3×15, 50−4, 90÷2, 4×10+8 is: [1 mark]
- (a) 4×10+8, 50−4, 3×15 = 90÷2
- (b) 90÷2, 3×15, 50−4, 4×10+8
- (c) 50−4, 4×10+8, 3×15, 90÷2
- (d) 3×15, 50−4, 4×10+8, 90÷2
✔ Answer: (a) Values: 4×10+8=48 > 50−4=46 > 3×15=45 = 90÷2=45
3. 75 − (30 − 15 + 5) = [1 mark]
- (a) 65
- (b) 55
- (c) 35
- (d) 45
✔ Answer: (b) 55 — 75−30+15−5 = 55 (signs flip after −)
4. Using distributive property, 13 × 8 = [1 mark]
- (a) (10+3)×8 = 10×8 + 3×8 = 104
- (b) (10+3)×8 = 10×8 + 3 = 83
- (c) 13×8 = 13 + 8×8 = 77
- (d) 13×8 = 13×10 − 8 = 122
✔ Answer: (a) 80 + 24 = 104
5. (18 + 6) ÷ (4 + 2) − 1 = [1 mark]
- (a) 3
- (b) 4
- (c) 5
- (d) 6
✔ Answer: (a) 3 — 24÷6 − 1 = 4 − 1 = 3

Section B — Fill in the Blanks (5 × 1 = 5 Marks)

1. 16 × 99 = 16 × (100 − _____) = 1600 − _____ = _____ [1 mark]

Answer: 1, 16, 1584

2. 500 − (200 − 75 + 25) = _____ [1 mark]

Answer: 350 (500−200+75−25 = 350)

3. The expression 10×3 + 4×2 − 6÷3 has _____ terms. [1 mark]

Answer: 3 terms: 10×3, +4×2, −6÷3

4. a × (b − c + d) = a×b − _____ + _____ [1 mark]

Answer: a×c and a×d

5. (50 + 30) ÷ (4 × 2) = _____ [1 mark]

Answer: 10 (80 ÷ 8 = 10)

Section C — True or False (5 × 1 = 5 Marks)

1. 12 × 98 = 12 × 100 − 12 × 2 = 1176 [1 mark]

True. 1200 − 24 = 1176. ✔

2. The terms of 20 − 4×3 + 2×5 are: 20, −4, 3, 2, 5 [1 mark]

False. The terms are 20, −4×3, and +2×5. Products within a term stay together.

3. 200 − (100 − 30 + 20) = 110 [1 mark]

True. 200−100+30−20 = 110. ✔

4. (5 × 6) × 2 = 5 × (6 × 2) [1 mark]

True. Associative property of multiplication. ✔

5. 36 ÷ 4 − 2 × 3 = 3 [1 mark]

True. 9 − 6 = 3. ✔

Section D — Evaluate (4 × 2 = 8 Marks)

1. Using distributive property: 13 × (100 + 5) [2 marks]

Solution: 13×100 + 13×5 = 1300 + 65 = 1365
2. Simplify: 200 − (80 − 20 + 15 − 5) [2 marks]

Solution: 200 − 80 + 20 − 15 + 5 = 130
3. Evaluate: 4 × 3 + 6 × 2 ÷ 4 + 5 [2 marks]

Solution: 12 + (6×2÷4) + 5 = 12 + (12÷4) + 5 = 12 + 3 + 5 = 20
4. Using distributive property: 25 × 36 = 25 × (40 − 4) [2 marks]

Solution: 25×40 − 25×4 = 1000 − 100 = 900

Section E — Word Problems (3 × 4 = 12 Marks)

1. A school bought 8 chairs at ₹450 each and 5 tables at ₹800 each. Write an arithmetic expression and find the total cost. [4 marks]

Expression: 8×450 + 5×800
Solution: 3600 + 4000 = ₹7600
2. Priya had ₹500. She spent ₹(120 + 45) on books and ₹(60 − 15) on stationery. Write an expression for money remaining and simplify. [4 marks]

Expression: 500 − (120+45) − (60−15)
Solution: 500 − 165 − 45 = ₹290
3. Using distributive property, calculate 15 × 98 mentally. Show step-by-step working. [4 marks]

Solution:
15 × 98 = 15 × (100 − 2)
= 15×100 − 15×2
= 1500 − 30
= 1470

Class: VII Chapter: 2 — Arithmetic Expressions Max Marks: 40 Time: 45 Minutes Level: Mixed / Mastery

Section A — Multiple Choice Questions (5 × 1 = 5 Marks)

1. The value of 5 + {2 × (3 + 4)} − 1 is: [1 mark]
- (a) 18
- (b) 28
- (c) 19
- (d) 22
✔ Answer: (a) 18 — Inner: 3+4=7; 2×7=14; 5+14−1 = 18
2. 200 − (50 + 30) − (40 − 10) = [1 mark]
- (a) 60
- (b) 90
- (c) 80
- (d) 110
✔ Answer: (b) 90 — 200−80−30 = 90
3. After removing brackets, 70 − (25 + 5) = [1 mark]
- (a) 70 − 25 − 5 = 40
- (b) 70 − 25 + 5 = 50
- (c) 70 + 25 − 5 = 90
- (d) 70 + 25 + 5 = 100
✔ Answer: (a) 40 — Minus before bracket: both signs inside flip
4. Using distributive property, 15 × 98 = [1 mark]
- (a) 1500 − 30 = 1470
- (b) 1500 + 30 = 1530
- (c) 1500 − 2 = 1498
- (d) 15×100 + 15×2 = 1530
✔ Answer: (a) 1470 — 15×(100−2) = 1500−30
5. The expression 14 + 2×7 − 3×4 + 18÷6 has how many terms? [1 mark]
- (a) 6
- (b) 5
- (c) 4
- (d) 3
✔ Answer: (c) 4 terms: 14, +2×7, −3×4, +18÷6

Section B — Fill in the Blanks (5 × 1 = 5 Marks)

1. 17 × 101 = 17 × (100 + 1) = _______ + _______ = _______ [1 mark]

Answer: 1700 + 17 = 1717

2. 400 − (100 − 40 + 60) = _______ [1 mark]

Answer: 280 (400−100+40−60 = 280)

3. In 6×5 + 3×2 − 18÷6, the three terms are _______, _______, _______ [1 mark]

Answer: 6×5, +3×2, −18÷6

4. a × (b + c − d) = a×b + _______ − _______ [1 mark]

Answer: a×c and a×d

5. (3 + 4 + 5) × 10 = 3×10 + 4×10 + _______ [1 mark]

Answer: 5×10 (= 50); total = 30+40+50 = 120

Section C — True or False (5 × 1 = 5 Marks)

1. 100 − (40 + 20 − 10) = 100 − 40 − 20 + 10 = 50 [1 mark]

True. Both sides equal 50. ✔

2. 18 ÷ 3 × 2 = 3 [1 mark]

False. Operations are done left to right: 18÷3=6, then 6×2=12 (not 3).

3. 4 × (25 + 75) = 4 × 100 = 400 [1 mark]

True. Bracket first: 4×100 = 400. ✔

4. The terms of 3×4 − 2×5 + 10 are: 3×4, −2×5, and 10. [1 mark]

True. Each group separated by + or − is a term. ✔

5. (a − b) × c = a×c + b×c [1 mark]

False. Correct: (a−b)×c = a×c − b×c (not + b×c).

Section D — Evaluate (4 × 2 = 8 Marks)

1. Evaluate: 20 − 4 × 3 + 6 ÷ 2 + 5 [2 marks]

Solution: 20 − 12 + 3 + 5 = 16 (multiply and divide first)
2. Simplify: 300 − (80 − 25 + 15) + 50 [2 marks]

Solution: 300 − 80 + 25 − 15 + 50 = 280
3. Using distributive property: 8 × 125 [2 marks]

Solution: 8×(100+25) = 800 + 200 = 1000
4. Evaluate: 15 + 3 × (8 − 5) − 2 × 4 [2 marks]

Solution: 15 + 3×3 − 8 = 15 + 9 − 8 = 16

Section E — Word Problems (Attempt any 4 out of 5 — 4 × 4 = 16 Marks)

1. A school has 4 sections of Class 7 with 35 students each, and 3 sections of Class 8 with 40 students each. Write an expression for total students and find its value. [4 marks]

Expression: 4×35 + 3×40
Solution: 140 + 120 = 260 students
2. Raju had ₹1000. He bought groceries worth ₹(200 + 50), vegetables worth ₹(80 − 15), and fruits worth ₹75. Write an expression for money remaining and simplify. [4 marks]

Expression: 1000 − (200+50) − (80−15) − 75
Solution: 1000 − 250 − 65 − 75 = ₹610
3. Using distributive property, calculate mentally: (a) 25 × 104 (b) 6 × 98. Show complete working. [4 marks]

(a) 25×104 = 25×(100+4) = 2500+100 = 2600
(b) 6×98 = 6×(100−2) = 600−12 = 588
4. A box has 6 layers. Each layer has 5 rows and 4 columns of chocolates. 18 chocolates are broken and removed. Write an expression and find how many are left. [4 marks]

Expression: 6×(5×4) − 18
Solution: 6×20 − 18 = 120 − 18 = 102 chocolates
5. Compare and fill in >, < or =, giving reason: (a) 1025 + 138 _____ 1024 + 139 (b) 7×99 _____ 6×101 [4 marks]

(a) 1025+138 = 1163; 1024+139 = 1163. Answer: =
(b) 7×99 = 693; 6×101 = 606. Answer: 7×99 > 6×101

Arithmetic Expressions

➕ Addition

➖ Subtraction

✖ Multiplication

➗ Division

🎬 Multiple Expressions, One Value

📊 Marble Comparison

🎬 Two Paths, One Correct

🎬 Bracket Resolver

➖ Subtraction as Addition

✖ Multiplication within a Term

🎬 Term Identifier

🎬 Commutative Swap

🎬 Fire in the Mountain!

🎬 Sign Flipper

🎬 Distributive Property — Area Model

🏆 Challenge 1: Three 3's

🏆 Challenge 2: Four 4's

🏆 Challenge 3: Using 1, 2, 3, 4, 5

🏆 Challenge 4: Century Express

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