Class 7 : Maths – Lesson 2. Arithmetic Expressions

EXPLANATION AND ANALYSIS

🔵 Introduction: What Are Arithmetic Expressions?

🧠 In earlier classes, we learned about numbers and basic operations such as addition, subtraction, multiplication, and division. When numbers and operations are written together meaningfully, they form an arithmetic expression.

🌿 Arithmetic expressions are used in daily life
🔵 Calculating total cost while shopping
🟢 Finding total marks in examinations
🟡 Calculating distance travelled
🔴 Solving everyday numerical problems

Arithmetic expressions help us represent calculations clearly and solve them step by step.

🟢 Meaning of an Arithmetic Expression

🧠 An arithmetic expression is a combination of numbers and arithmetic operations.

🔹 It does not contain an equal sign
🔹 It represents a value

📌 Example
5 + 3 × 4 is an arithmetic expression

💡 Concept:
An expression becomes an equation only when an equal sign is used.

🔵 Arithmetic Operations Used

🧠 The four basic arithmetic operations are used in expressions.

🔵 Addition (+)
🟢 Subtraction (−)
🟡 Multiplication (×)
🔴 Division (÷)

📌 Example
12 − 4 + 6 is an arithmetic expression using more than one operation.

✏️ Note:
The order in which these operations are performed is very important.

🟢 Order of Operations (BODMAS Rule)

🧠 When an arithmetic expression contains more than one operation, we follow the BODMAS rule.

🔵 B → Brackets
🟢 O → Of
🟡 D → Division
🔴 M → Multiplication
🔵 A → Addition
🟢 S → Subtraction

📌 Example
Evaluate: 8 + 12 ÷ 3

🔹 Division first: 12 ÷ 3 = 4
🔹 Addition next: 8 + 4 = 12

💡 Concept:
Following BODMAS gives the correct value of an expression.

🟡 Use of Brackets in Arithmetic Expressions

🧠 Brackets are used to show which operation should be done first.

🔹 Operations inside brackets are performed first
🔹 Brackets help avoid confusion

📌 Example
(8 + 12) ÷ 4

🔹 Solve inside brackets: 8 + 12 = 20
🔹 Divide: 20 ÷ 4 = 5

✏️ Note:
Brackets change the order of operations.

🔵 Simplifying Arithmetic Expressions

🧠 Simplifying an arithmetic expression means finding its final value by applying operations in the correct order.

📌 Example
6 + 18 ÷ 3 × 2

🔹 Division first: 18 ÷ 3 = 6
🔹 Multiplication next: 6 × 2 = 12
🔹 Addition last: 6 + 12 = 18

✔️ Final value = 18

🟢 Expressions with More Than One Bracket

🧠 Some arithmetic expressions contain more than one bracket.

🔹 Solve the innermost bracket first
🔹 Then move outward step by step

📌 Example
{20 − (8 + 2)} × 2

🔹 Inner bracket: 8 + 2 = 10
🔹 Outer bracket: 20 − 10 = 10
🔹 Multiplication: 10 × 2 = 20

🟡 Importance of Correct Order of Operations

🧠 Changing the order of operations can change the result completely.

📌 Example
10 − 6 ÷ 2

🔹 Division first: 6 ÷ 2 = 3
🔹 Subtraction: 10 − 3 = 7

If done incorrectly:
(10 − 6) ÷ 2 = 2

✏️ Note:
Always follow BODMAS to avoid incorrect answers.

🔵 Arithmetic Expressions in Word Problems

🧠 Many word problems can be converted into arithmetic expressions.

📌 Example
A box contains 12 chocolates. Each chocolate costs 5 rupees.

🔹 Arithmetic expression: 12 × 5
🔹 Total cost = 60 rupees

💡 Concept:
Writing expressions makes problem solving systematic.

🟢 Common Mistakes to Avoid

🔴 Ignoring brackets
🔴 Not following BODMAS
🔴 Performing addition before division or multiplication
🔴 Skipping steps while solving

✏️ Note:
Solving step by step reduces errors.

🟢 Importance of Arithmetic Expressions

🧠 Learning arithmetic expressions helps students to:

🔵 Perform calculations correctly
🟢 Solve word problems easily
🟡 Understand higher mathematics
🔴 Apply mathematics in daily life

This chapter builds a strong foundation for algebra.

📘 Summary

🔵 Arithmetic expressions combine numbers and operations
🟢 They do not contain an equal sign
🟡 BODMAS rule decides the order of operations
🔴 Brackets play an important role
🔵 Expressions must be simplified step by step
🟢 Correct order gives correct answers

📝 Quick Recap

📝 Quick Recap
🔵 Arithmetic expressions use numbers and operations
🟢 Follow the BODMAS rule
🟡 Solve brackets first
🔴 Simplify step by step
🔵 Correct order avoids mistakes

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TEXTBOOK QUESTIONS

🔵 2.1 SIMPLE EXPRESSIONS

🔷 Figure it Out

🔒 ❓ Question 1.
Fill in the blanks to make the expressions equal on both sides of the = sign.

🔒 ❓ (a) 13 + 4 = ____ + 6

📌 ✅ Answer:
🔹 13 + 4 = 17
🔹 ____ + 6 = 17
🔹 ____ = 17 − 6
🔹 ____ = 11

✔️ Final Answer: 11

🔒 ❓ (b) 22 + ____ = 6 × 5

📌 ✅ Answer:
🔹 6 × 5 = 30
🔹 22 + ____ = 30
🔹 ____ = 30 − 22
🔹 ____ = 8

✔️ Final Answer: 8

🔒 ❓ (c) 8 × ____ = 64 ÷ 2

📌 ✅ Answer:
🔹 64 ÷ 2 = 32
🔹 8 × ____ = 32
🔹 ____ = 32 ÷ 8
🔹 ____ = 4

✔️ Final Answer: 4

🔒 ❓ (d) 34 − ____ = 25

📌 ✅ Answer:
🔹 34 − ____ = 25
🔹 ____ = 34 − 25
🔹 ____ = 9

✔️ Final Answer: 9

🔒 ❓ Question 2.
Arrange the following expressions in ascending (increasing) order of their values.

(a) 67 − 19
(b) 67 − 20
(c) 35 + 25
(d) 5 × 11
(e) 120 ÷ 3

📌 ✅ Answer:
🔹 67 − 19 = 48
🔹 67 − 20 = 47
🔹 35 + 25 = 60
🔹 5 × 11 = 55
🔹 120 ÷ 3 = 40

🔹 Increasing order of values:
40 < 47 < 48 < 55 < 60

✔️ Ascending order:
120 ÷ 3, 67 − 20, 67 − 19, 5 × 11, 35 + 25

🔵 2.2 READING AND EVALUATING COMPLEX EXPRESSIONS

🔒 ❓ Q1. Find the values of the following expressions by writing the terms in each case.

🔒 ❓ (a) 28 − 7 + 8
📌 ✅ Answer:
🔹 28 − 7 = 21
🔹 21 + 8 = 29
✔️ Final Answer: 29

🔒 ❓ (b) 39 − 2 × 6 + 11
📌 ✅ Answer:
🔹 2 × 6 = 12
🔹 39 − 12 + 11
🔹 39 − 12 = 27
🔹 27 + 11 = 38
✔️ Final Answer: 38

🔒 ❓ (c) 40 − 10 + 10 + 10
📌 ✅ Answer:
🔹 40 − 10 = 30
🔹 30 + 10 = 40
🔹 40 + 10 = 50
✔️ Final Answer: 50

🔒 ❓ (d) 48 − 10 × 2 + 16 ÷ 2
📌 ✅ Answer:
🔹 10 × 2 = 20
🔹 16 ÷ 2 = 8
🔹 48 − 20 + 8
🔹 48 − 20 = 28
🔹 28 + 8 = 36
✔️ Final Answer: 36

🔒 ❓ (e) 6 × 3 − 4 × 8 × 5
📌 ✅ Answer:
🔹 6 × 3 = 18
🔹 4 × 8 = 32
🔹 32 × 5 = 160
🔹 18 − 160 = −142
✔️ Final Answer: −142

🔒 ❓ Q2. Write a story/situation for each expression and find their values.

🔒 ❓ (a) 89 + 21 − 10
📌 ✅ Answer:
🔹 Story: A person had 89 marbles, got 21 more, then gave away 10 marbles.
🔹 89 + 21 = 110
🔹 110 − 10 = 100
✔️ Final Answer: 100

🔒 ❓ (b) 5 × 12 − 6
📌 ✅ Answer:
🔹 Story: 5 packets have 12 toffees each. 6 toffees are eaten.
🔹 5 × 12 = 60
🔹 60 − 6 = 54
✔️ Final Answer: 54

🔒 ❓ (c) 4 × 9 + 2 × 6
📌 ✅ Answer:
🔹 Story: 4 packets have 9 biscuits each and 2 packets have 6 biscuits each.
🔹 4 × 9 = 36
🔹 2 × 6 = 12
🔹 36 + 12 = 48
✔️ Final Answer: 48

🔒 ❓ Q3. For each situation, write the expression describing the situation, identify its terms and find the value.

🔒 ❓ (a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa doubled her coins. Princess Anna has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have.
📌 ✅ Answer:
🔹 Elsa’s coins = 100 × 2 = 200
🔹 Anna’s coins = 100 ÷ 2 = 50
🔹 Expression = (100 × 2) + (100 ÷ 2)
🔹 Value = 200 + 50 = 250
✔️ Final Answer: 250 gold coins

🔒 ❓ (b) A metro train ticket between two stations is ₹40 for an adult and ₹20 for a child. What is the total cost of tickets:

🔒 ❓ (i) for four adults and three children?
📌 ✅ Answer:
🔹 Adults cost = 4 × 40 = 160
🔹 Children cost = 3 × 20 = 60
🔹 Total = 160 + 60 = 220
✔️ Final Answer: ₹220

🔒 ❓ (ii) for two groups having three adults each?
📌 ✅ Answer:
🔹 Total adults = 2 × 3 = 6
🔹 Total cost = 6 × 40 = 240
✔️ Final Answer: ₹240

🔒 ❓ Question 3(c)
Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.

📌 ✅ Answer:
🔹 Border (top) = 3 cm
🔹 Number of grills = 3, each of height 2 cm
🔹 Number of gaps = 3, each of height 5 cm

🔹 Expression:
3 + (3 × 2) + (3 × 5)

🔹 Calculation:
3 + 6 + 15 = 24

✔️ Final Answer: 24 cm

🔵 TINKER THE TERMS I

🔒 ❓ Question 1.
Fill in the blanks with numbers and operation signs so that the expressions on both sides are equal.

🔒 ❓ (a) 24 + (6 − 4) = 24 + 6 __ 4

📌 ✅ Answer:
🔹 Left side: 6 − 4 = 2
🔹 24 + 2 = 26
🔹 Right side becomes 24 + 6 − 4
🔹 Correct operation sign is minus

✔️ Final Answer: 24 + 6 − 4

🔒 ❓ (b) 38 + ( ____ ) = 38 + 9 − 4

📌 ✅ Answer:
🔹 Right side inside operation: 9 − 4 = 5
🔹 Bracket must contain the same expression
🔹 Correct bracket expression is 9 − 4

✔️ Final Answer: 38 + (9 − 4)

🔒 ❓ (c) 24 − (6 + 4) = 24 __ 6 − 4

📌 ✅ Answer:
🔹 6 + 4 = 10
🔹 24 − 10 = 14
🔹 Right side becomes 24 − 6 − 4
🔹 Correct operation sign is minus

✔️ Final Answer: 24 − 6 − 4

🔒 ❓ (d) 24 − 6 − 4 = 24 − 6 __ 4

📌 ✅ Answer:
🔹 Left side value is 14
🔹 To get same value, subtraction of (6 + 4) is needed
🔹 Correct operation sign is plus inside the bracket sense

✔️ Final Answer: 24 − (6 + 4)

🔒 ❓ (e) 27 − (8 + 3) = 27 __ 8 __ 3

📌 ✅ Answer:
🔹 8 + 3 = 11
🔹 27 − 11 = 16
🔹 Equivalent expression is subtracting 8 and then subtracting 3

✔️ Final Answer: 27 − 8 − 3

🔒 ❓ (f) 27 − ( ____ ) = 27 − 8 + 3

📌 ✅ Answer:
🔹 Right side means subtracting (8 − 3)
🔹 Correct bracket expression is 8 − 3

✔️ Final Answer: 27 − (8 − 3)

🔒 ❓ Question 2.
Remove the brackets and write the expression having the same value.

🔒 ❓ (a) 14 + (12 + 10)
📌 ✅ Answer:
🔹 14 + 12 + 10

🔒 ❓ (b) 14 − (12 + 10)
📌 ✅ Answer:
🔹 14 − 12 − 10

🔒 ❓ (c) 14 + (12 − 10)
📌 ✅ Answer:
🔹 14 + 12 − 10

🔒 ❓ (d) 14 − (12 − 10)
📌 ✅ Answer:
🔹 14 − 12 + 10

🔒 ❓ (e) −14 + 12 − 10
📌 ✅ Answer:
🔹 −14 + 12 − 10

🔒 ❓ (f) 14 − (−12 − 10)
📌 ✅ Answer:
🔹 14 + 12 + 10

🔒 ❓ Question 3.
Find the values of the following expressions. For each pair, state when the two expressions are equal.

🔒 ❓ (a) (6 + 10) − 2 and 6 + (10 − 2)

📌 ✅ Answer:
🔹 First expression: 16 − 2 = 14
🔹 Second expression: 6 + 8 = 14
✔️ Both expressions are equal

🔒 ❓ (b) 16 − (8 − 3) and (16 − 8) − 3

📌 ✅ Answer:
🔹 First expression: 16 − 5 = 11
🔹 Second expression: 8 − 3 = 5
✔️ Expressions are not equal

🔒 ❓ (c) 27 − (18 + 4) and 27 + (−18 − 4)

📌 ✅ Answer:
🔹 First expression: 27 − 22 = 5
🔹 Second expression: 27 − 22 = 5
✔️ Both expressions are equal

🔒 ❓ Question 4.
In each set, identify the expressions that have the same value (do not evaluate).

📌 ✅ Answer:
🔹 319 + 537 and 537 + 319
🔹 87 + 46 − 109 and (87 − 46) + 109

🔒 ❓ Question 5.
Add brackets at appropriate places.

🔒 ❓ (a) 34 − 9 + 12 = 13
📌 ✅ Answer:
🔹 34 − (9 + 12)

🔒 ❓ (b) 56 − 14 − 8 = 34
📌 ✅ Answer:
🔹 56 − (14 + 8)

🔒 ❓ (c) −22 − 12 + 10 + 22 = −22
📌 ✅ Answer:
🔹 −22 − (12 − 10 + 22)

🔒 ❓ Question 6.
Fill the blanks so that the expressions on both sides are equal.

🔒 ❓ (a) 423 + blank = 419 + blank

📌 ✅ Answer:
🔹 To make both sides equal
🔹 423 + (−4) = 419 + 0

✔️ Final Answer: −4 and 0

🔒 ❓ (b) 207 − 68 = 210 − ……

📌 ✅ Answer:
🔹 207 − 68 = 139
🔹 To get 139 from 210
🔹 210 − 71 = 139

✔️ Final Answer: 71

🔒 ❓ Question 7.
Using the numbers 2, 3 and 5, form expressions to get different values.

📌 ✅ Answer (examples):
🔹 (2 + 3) × 5
🔹 2 + (3 × 5)
🔹 (5 − 3) × 2
🔹 5 − (3 − 2)

🔒 ❓ Question 8.

🔒 ❓ (a)
📌 ✅ Answer:
🔹 Yes. Subtracting 10 and adding 1 gives the same result as subtracting 9.

🔒 ❓ (b)
📌 ✅ Answer:
🔹 To subtract 19, subtract 20 and add 1
🔹 To subtract 49, subtract 50 and add 1

🔒 ❓ Question 9.
Consider the two expressions:
(a) 73 − 14 + 1
(b) 73 − 14 − 1

For each of these expressions, identify the expressions from the following collection that are equal to it:

(a) 73 − (14 + 1)
(b) 73 − (14 − 1)
(c) 73 + (−14 + 1)
(d) 73 + (−14 − 1)

📌 ✅ Answer:

🔹 For expression (a): 73 − 14 + 1

🔸 Equal expressions are:
• (b) 73 − (14 − 1)
• (c) 73 + (−14 + 1)

🔹 For expression (b): 73 − 14 − 1

🔸 Equal expressions are:
• (a) 73 − (14 + 1)
• (d) 73 + (−14 − 1)

🔵 TINKER THE TERMS II

🔒 ❓ Question 1.
Fill in the blanks with numbers, and the sign-blanks with signs, so that the expressions on both sides are equal.

🔒 ❓ (a) 3 × (6 + 7) = 3 × 6 + 3 × 7
📌 ✅ Answer:
🔹 This is already correct (distributive property)
✔️ Final: No change

🔒 ❓ (b) (8 + 3) × 4 = 8 × 4 + 3 × 4
📌 ✅ Answer:
🔹 This is already correct (distributive property)
✔️ Final: No change

🔒 ❓ (c) 3 × (5 + 8) = 3 × 5 (sign blank) 3 × (number blank)
📌 ✅ Answer:
🔹 Distributive rule: a × (b + c) = a × b + a × c
🔹 Here a = 3, b = 5, c = 8
🔹 So sign must be plus
🔹 Number blank must be 8
✔️ Final: 3 × (5 + 8) = 3 × 5 + 3 × 8

🔒 ❓ (d) (9 + 2) × 4 = 9 × 4 (sign blank) 2 × (number blank)
📌 ✅ Answer:
🔹 Distributive rule: (b + c) × a = b × a + c × a
🔹 Here a = 4, b = 9, c = 2
🔹 So sign must be plus
🔹 Number blank must be 4
✔️ Final: (9 + 2) × 4 = 9 × 4 + 2 × 4

🔒 ❓ (e) 3 × (number blank + 4) = 3 × (number blank) + 3 × 4
📌 ✅ Answer:
🔹 Distributive rule: 3 × (x + 4) = 3 × x + 3 × 4
🔹 Choose x = 2 (so it matches the pattern)
✔️ Final: 3 × (2 + 4) = 3 × 2 + 3 × 4

🔒 ❓ (f) (number blank + 6) × 4 = 13 × 4 + (number blank)
📌 ✅ Answer:
🔹 For the bracket to become 13: number blank + 6 = 13
🔹 number blank = 13 − 6
🔹 number blank = 7
🔹 Left side becomes (7 + 6) × 4 = 13 × 4
🔹 So the extra add-on must be 0 to keep equality
✔️ Final: (7 + 6) × 4 = 13 × 4 + 0

🔒 ❓ (g) 3 × (number blank + number blank) = 3 × 5 + 3 × 2
📌 ✅ Answer:
🔹 Compare with: 3 × (a + b) = 3 × a + 3 × b
🔹 So the two blanks are 5 and 2
✔️ Final: 3 × (5 + 2) = 3 × 5 + 3 × 2

🔒 ❓ (h) (number blank + number blank) × (number blank) = 2 × 4 + 3 × 4
📌 ✅ Answer:
🔹 Common factor on RHS is 4
🔹 2 × 4 + 3 × 4 = (2 + 3) × 4
🔹 So blanks are 2, 3, and 4
✔️ Final: (2 + 3) × 4 = 2 × 4 + 3 × 4

🔒 ❓ (i) 5 × (9 − 2) = 5 × 9 − 5 × (number blank)
📌 ✅ Answer:
🔹 Distributive over subtraction: 5 × (9 − 2) = 5 × 9 − 5 × 2
🔹 So number blank is 2
✔️ Final: 5 × (9 − 2) = 5 × 9 − 5 × 2

🔒 ❓ (j) (5 − 2) × 7 = 5 × 7 − 2 × (number blank)
📌 ✅ Answer:
🔹 (a − b) × c = a × c − b × c
🔹 Here c = 7
🔹 So number blank is 7
✔️ Final: (5 − 2) × 7 = 5 × 7 − 2 × 7

🔒 ❓ (k) 5 × (8 − 3) = 5 × 8 (sign blank) 5 × (number blank)
📌 ✅ Answer:
🔹 5 × (8 − 3) = 5 × 8 − 5 × 3
🔹 So sign is minus
🔹 Number blank is 3
✔️ Final: 5 × (8 − 3) = 5 × 8 − 5 × 3

🔒 ❓ (l) (8 − 3) × 7 = 8 × 7 (sign blank) 3 × 7
📌 ✅ Answer:
🔹 (8 − 3) × 7 = 8 × 7 − 3 × 7
🔹 So sign is minus
✔️ Final: (8 − 3) × 7 = 8 × 7 − 3 × 7

🔒 ❓ (m) 5 × (12 − number blank) = 5 × 12 (sign blank) 5 × (number blank)
📌 ✅ Answer:
🔹 Use: 5 × (12 − a) = 5 × 12 − 5 × a
🔹 Choose a = 5 (matches the pattern)
✔️ Final: 5 × (12 − 5) = 5 × 12 − 5 × 5

🔒 ❓ (n) (15 − number blank) × 7 = 15 × 7 (sign blank) 6 × 7
📌 ✅ Answer:
🔹 Compare with: (15 − 6) × 7 = 15 × 7 − 6 × 7
🔹 So number blank is 6
🔹 Sign is minus
✔️ Final: (15 − 6) × 7 = 15 × 7 − 6 × 7

🔒 ❓ (o) 5 × (number blank − number blank) = 5 × 9 − 5 × 4
📌 ✅ Answer:
🔹 Match: 5 × (a − b) = 5 × a − 5 × b
🔹 So blanks are 9 and 4
✔️ Final: 5 × (9 − 4) = 5 × 9 − 5 × 4

🔒 ❓ (p) (number blank − number blank) × (number blank) = 17 × 7 − 9 × 7
📌 ✅ Answer:
🔹 Factor 7: 17 × 7 − 9 × 7 = (17 − 9) × 7
🔹 So blanks are 17, 9, and 7
✔️ Final: (17 − 9) × 7 = 17 × 7 − 9 × 7

🔒 ❓ Question 2.
In the sign-blanks, fill less than, greater than, or equal after analysing the expressions on LHS and RHS.

🔒 ❓ (a) (8 − 3) × 29 (sign blank) (3 − 8) × 29
📌 ✅ Answer:
🔹 8 − 3 is positive
🔹 3 − 8 is negative
🔹 Positive × 29 is positive, negative × 29 is negative
✔️ Final: greater than

🔒 ❓ (b) 15 + 9 × 18 (sign blank) (15 + 9) × 18
📌 ✅ Answer:
🔹 LHS adds 15 after the multiplication
🔹 RHS multiplies the whole (15 + 9) by 18, so it becomes much larger
✔️ Final: less than

🔒 ❓ Question 2(c)
23 × (17 − 9) ___ 23 × 17 − 23 × 9

📌 ✅ Answer (Teacher-like explanation):

🔹 We use the distributive rule for subtraction:
🔹 a × (b − c) = a × b − a × c

🔹 Applying it here:
🔹 23 × (17 − 9) = 23 × 17 − 23 × 9

🔹 The expression on the left side becomes exactly the same as the expression on the right side.

✔️ Final Answer: = (equal to)

🔒 ❓ (d) (34 − 28) × 42 (sign blank) 34 × 42 − 28 × 42
📌 ✅ Answer:
🔹 Distributive rule: (a − b) × c = a × c − b × c
✔️ Final: equal

🔒 ❓ Question 3.
Here is one way to make 14: 2 × (1 + 6) = 14. Are there other ways? Fill them:

📌 ✅ Answer:
🔹 7 × (1 + 1) = 14
🔹 2 × (4 + 3) = 14
🔹 1 × (7 + 7) = 14
🔹 14 × (0 + 1) = 14

🔒 ❓ Question 4.
Find out the sum of the numbers in each picture in at least two different ways. Describe how you solved it through expressions.

📌 ✅ Answer (Left picture):
🔹 Count 4s: 5 numbers are 4
🔹 Count 8s: 4 numbers are 8
🔹 Method 1 expression: (5 × 4) + (4 × 8)
🔹 5 × 4 = 20
🔹 4 × 8 = 32
🔹 20 + 32 = 52
🔹 Method 2 expression: (4 + 8 + 4) + (8 + 4 + 8) + (4 + 8 + 4)
🔹 16 + 20 + 16 = 52
✔️ Final Answer: 52

📌 ✅ Answer (Right picture):
🔹 Count 5s: 8 numbers are 5
🔹 Count 6s: 8 numbers are 6
🔹 Method 1 expression: (8 × 5) + (8 × 6)
🔹 8 × 5 = 40
🔹 8 × 6 = 48
🔹 40 + 48 = 88
🔹 Method 2 expression: 8 × (5 + 6)
🔹 5 + 6 = 11
🔹 8 × 11 = 88
✔️ Final Answer: 88

🔷 Figure it Out

🔒 ❓ Question 1
Read the situations and write appropriate expressions. Find their values.

🔒 ❓ (a)
Rahim supplies 9 kg and Shyam supplies 11 kg of mangoes every day. The market works 7 days a week.

📌 ✅ Answer
🔹 Mangoes supplied in one day = 9 + 11 = 20 kg
🔹 Number of days = 7
🔹 Expression = 7 × (9 + 11)
🔹 7 × 20 = 140

✔️ Final Answer: 140 kg

🔒 ❓ (b)
Binu earns ₹20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses.

📌 ✅ Answer
🔹 Monthly expenses = 5,000 + 5,000 + 2,000 = 12,000
🔹 Monthly savings = 20,000 − 12,000 = 8,000
🔹 Months in a year = 12
🔹 Expression = 12 × 8,000
🔹 12 × 8,000 = 96,000

✔️ Final Answer: ₹96,000

🔒 ❓ (c)
A snail climbs 3 cm in the day and slips 2 cm at night. The post is 10 cm high.

📌 ✅ Answer
🔹 Net climb in one day = 3 − 2 = 1 cm
🔹 Height of post = 10 cm
🔹 Expression = 10 ÷ 1
🔹 Days needed = 10

✔️ Final Answer: 10 days

🔒 ❓ Question 2
Melvin reads one two-page story every day except Tuesdays and Saturdays. How many stories does he read in 8 weeks?

📌 ✅ Answer
🔹 Days in one week = 7
🔹 Days not reading = 2
🔹 Reading days per week = 7 − 2 = 5
🔹 Weeks = 8
🔹 Expression = (7 − 2) × 8

✔️ Correct Expression: (7 − 2) × 8

🔒 ❓ Question 3

🔒 ❓ (a)
1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + 9 − 10

📌 ✅ Answer
🔹 Group positives and negatives
🔹 (1 + 3 + 5 + 7 + 9) − (2 + 4 + 6 + 8 + 10)
🔹 25 − 30 = −5

✔️ Final Answer: −5

🔒 ❓ (b)
1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1

📌 ✅ Answer
🔹 Each pair (1 − 1) = 0
🔹 Total = 0

✔️ Final Answer: 0

🔒 ❓ Question 4
Compare the expressions using reasoning.

🔒 ❓ (a)
49 − 7 + 8 and 49 − (7 + 8)

📌 ✅ Answer
🔹 First subtracts 7 then adds 8
🔹 Second subtracts 15
✔️ First is greater

🔒 ❓ (b)
83 × 42 − 18 and 83 × 40 − 18

📌 ✅ Answer
🔹 42 is greater than 40
✔️ First is greater

🔒 ❓ (c)
145 − 17 × 8 and 145 − 17 × 6

📌 ✅ Answer
🔹 17 × 8 is greater than 17 × 6
✔️ First is smaller

🔒 ❓ (d)
23 × 48 − 35 and 23 × (48 − 35)

📌 ✅ Answer
🔹 Multiplication happens before subtraction on LHS
✔️ First is greater

🔒 ❓ (e)
(16 − 11) × 12 and −11 × 12 + 16 × 12

📌 ✅ Answer
🔹 Distributive property
✔️ Both are equal

🔒 ❓ (f)
(76 − 53) × 88 and 88 × (53 − 76)

📌 ✅ Answer
🔹 Second expression becomes negative
✔️ First is greater

🔒 ❓ (g)
25 × (42 + 16) and 25 × (43 + 15)

📌 ✅ Answer
🔹 Both brackets equal 58
✔️ Both are equal

🔒 ❓ (h)
36 × (28 − 16) and 35 × (27 − 15)

📌 ✅ Answer
🔹 First has a larger multiplier
✔️ First is greater

🔒 ❓ Question 5
Identify which of the following expressions are equal to the given expression without computation. You may rewrite expressions using terms or by removing brackets.

🔒 ❓ (a) Given expression
83 − 37 − 12

📌 ✅ Answer

🔹 The given expression can be written as
🔹 83 + (−37) + (−12)

🔒 ❓ (i) 84 − 38 − 12
📌 ✅
🔹 Both 83 and 37 are increased by 1
🔹 The overall difference remains unchanged
✔️ Equal to the given expression

🔒 ❓ (ii) 84 − (37 + 12)
📌 ✅
🔹 Brackets change the order of subtraction
🔹 This subtracts the sum together
❌ Not equal

🔒 ❓ (iii) 83 − 38 − 13
📌 ✅
🔹 Both numbers being subtracted are increased
🔹 Total subtraction becomes larger
❌ Not equal

🔒 ❓ (iv) −37 + 83 − 12
📌 ✅
🔹 Reordering using addition of negative numbers
🔹 Same terms as the given expression
✔️ Equal

✔️ Correct options for (a): (i) and (iv)

🔒 ❓ (b) Given expression
93 + 37 × 44 + 76

📌 ✅ Answer

🔹 Multiplication is done before addition
🔹 Structure is
🔹 93 + (37 × 44) + 76

🔒 ❓ (i) 37 + 93 × 44 + 76
📌 ✅
🔹 Multiplication term changes
❌ Not equal

🔒 ❓ (ii) 93 + 37 × 76 + 44
📌 ✅
🔹 Product term is different
❌ Not equal

🔒 ❓ (iii) (93 + 37) × (44 + 76)
📌 ✅
🔹 Brackets change the whole operation
❌ Not equal

🔒 ❓ (iv) 37 × 44 + 93 + 76
📌 ✅
🔹 Same terms, only rearranged
🔹 Addition is commutative
✔️ Equal

✔️ Correct option for (b): (iv)

🔒 ❓ Question 5 (second part)
Choose a number and create ten different expressions having that value.

📌 ✅ Answer
Chosen number: 20

🔹 10 + 10
🔹 25 − 5
🔹 4 × 5
🔹 40 ÷ 2
🔹 30 − 10
🔹 5 × (6 − 2)
🔹 8 + 12
🔹 2 × 10
🔹 50 − 30
🔹 100 ÷ 5

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OTHER IMPORTANT QUESTIONS

( MODEL QUESTION PAPER )

ESPECIALLY MADE FOR THIS LESSON ONLY

🔵 Section A – Very Short Answer (1 × 6 = 6 marks)

🔒 ❓ Question 1
What is an arithmetic expression?

📌 ✅ Answer:
🔹 An arithmetic expression is a combination of numbers and arithmetic operations
🔹 It does not contain an equal sign

🔒 ❓ Question 2
Write one arithmetic expression using addition and multiplication.

📌 ✅ Answer:
🔹 One arithmetic expression is 5 + 3 × 2

🔒 ❓ Question 3
Which operation is performed first according to BODMAS?

📌 ✅ Answer:
🔹 Brackets are performed first according to BODMAS

🔒 ❓ Question 4
Find the value of 12 ÷ 3 + 4.

📌 ✅ Answer:
🔹 Division first: 12 ÷ 3 = 4
🔹 Addition next: 4 + 4 = 8

🔒 ❓ Question 5
True or False: In 10 − 6 ÷ 2, subtraction is done first.

📌 ✅ Answer:
🔹 False

🔒 ❓ Question 6
Write one expression that uses brackets.

📌 ✅ Answer:
🔹 One expression with brackets is (8 + 4) ÷ 2

🟢 Section B – Short Answer I (2 × 6 = 12 marks)

🔒 ❓ Question 7
State the BODMAS rule.

📌 ✅ Answer:
🔹 BODMAS stands for Brackets, Of, Division, Multiplication, Addition, Subtraction
🔹 It tells the correct order of operations in an arithmetic expression

🔒 ❓ Question 8
Evaluate 6 + 18 ÷ 3.

📌 ✅ Answer:
🔹 Division first: 18 ÷ 3 = 6
🔹 Addition next: 6 + 6 = 12

🔒 ❓ Question 9
Why are brackets used in arithmetic expressions?

📌 ✅ Answer:
🔹 Brackets show which operation should be done first
🔹 They help avoid confusion

🔒 ❓ Question 10
Find the value of (10 − 4) × 3.

📌 ✅ Answer:
🔹 Brackets first: 10 − 4 = 6
🔹 Multiplication next: 6 × 3 = 18

🔒 ❓ Question 11
Write two arithmetic expressions using three numbers.

📌 ✅ Answer:
🔹 4 + 6 − 2
🔹 8 × 5 ÷ 2

🔒 ❓ Question 12
Is 7 + 5 an arithmetic expression or an equation? Give reason.

📌 ✅ Answer:
🔹 It is an arithmetic expression
🔹 It has no equal sign

🟡 Section C – Short Answer II (3 × 10 = 30 marks)

🔒 ❓ Question 13
Evaluate 20 − 8 ÷ 4.

📌 ✅ Answer:
🔹 Division first: 8 ÷ 4 = 2
🔹 Subtraction next: 20 − 2 = 18

🔒 ❓ Question 14
Evaluate (20 − 8) ÷ 4.

📌 ✅ Answer:
🔹 Brackets first: 20 − 8 = 12
🔹 Division next: 12 ÷ 4 = 3

🔒 ❓ Question 15
Explain why BODMAS rule is necessary.

📌 ✅ Answer:
🔹 It gives a fixed order for operations
🔹 It avoids different answers for the same expression
🔹 It ensures correct and uniform results

🔒 ❓ Question 16
Evaluate 6 + 24 ÷ 6 × 2.

📌 ✅ Answer:
🔹 Division first: 24 ÷ 6 = 4
🔹 Multiplication next: 4 × 2 = 8
🔹 Addition last: 6 + 8 = 14

🔒 ❓ Question 17
Write the arithmetic expression for the following statement:
Add 8 to the product of 6 and 5.

📌 ✅ Answer:
🔹 Product of 6 and 5 = 6 × 5
🔹 Arithmetic expression = 6 × 5 + 8

🔒 ❓ Question 18
Evaluate 15 − (3 + 4) × 2.

📌 ✅ Answer:
🔹 Brackets first: 3 + 4 = 7
🔹 Multiplication next: 7 × 2 = 14
🔹 Subtraction last: 15 − 14 = 1

🔒 ❓ Question 19
Find the value of {18 − (6 + 3)} ÷ 3.

📌 ✅ Answer:
🔹 Inner bracket: 6 + 3 = 9
🔹 Curly bracket: 18 − 9 = 9
🔹 Division: 9 ÷ 3 = 3

🔒 ❓ Question 20
Write two examples showing the use of brackets in expressions.

📌 ✅ Answer:
🔹 (12 + 8) ÷ 5
🔹 (9 − 3) × 4

🔒 ❓ Question 21
Explain what happens if BODMAS rule is not followed.

📌 ✅ Answer:
🔹 The answer may become incorrect
🔹 Different students may get different results
🔹 Calculations become confusing

🔒 ❓ Question 22
Evaluate 40 ÷ (5 × 2) + 3.

📌 ✅ Answer:
🔹 Brackets first: 5 × 2 = 10
🔹 Division next: 40 ÷ 10 = 4
🔹 Addition last: 4 + 3 = 7

🔴 Section D – Long Answer (4 × 8 = 32 marks)

🔒 ❓ Question 23
Evaluate 8 + 16 ÷ 4 × 3 using BODMAS rule.

📌 ✅ Answer:
🔹 Division first: 16 ÷ 4 = 4
🔹 Multiplication next: 4 × 3 = 12
🔹 Addition last: 8 + 12 = 20

🔒 ❓ Question 24
Evaluate (8 + 16) ÷ 4 × 3.

📌 ✅ Answer:
🔹 Brackets first: 8 + 16 = 24
🔹 Division next: 24 ÷ 4 = 6
🔹 Multiplication last: 6 × 3 = 18

🔒 ❓ Question 25
Explain the difference between an arithmetic expression and an equation with examples.

📌 ✅ Answer:
🔹 An arithmetic expression has numbers and operations only
🔹 It does not contain an equal sign
🔹 Example: 5 + 3 × 2
🔹 An equation has an equal sign
🔹 Example: 5 + 3 = 8

🔒 ❓ Question 26
Evaluate 25 − {10 − (4 + 1)} × 2.

📌 ✅ Answer:
🔹 Inner bracket: 4 + 1 = 5
🔹 Curly bracket: 10 − 5 = 5
🔹 Multiplication: 5 × 2 = 10
🔹 Subtraction: 25 − 10 = 15

🔒 ❓ Question 27
Write four common mistakes students make while simplifying arithmetic expressions.

📌 ✅ Answer:
🔹 Ignoring brackets
🔹 Not following BODMAS
🔹 Doing addition before division
🔹 Skipping calculation steps

🔒 ❓ Question 28
Evaluate 36 ÷ 6 + 2 × 5.

📌 ✅ Answer:
🔹 Division first: 36 ÷ 6 = 6
🔹 Multiplication next: 2 × 5 = 10
🔹 Addition last: 6 + 10 = 16

🔒 ❓ Question 29
Write an arithmetic expression for the following situation and find its value.
A pen costs 10 rupees. Find the cost of 5 pens and add 15 rupees.

📌 ✅ Answer:
🔹 Cost of 5 pens = 5 × 10
🔹 Arithmetic expression = 5 × 10 + 15
🔹 Value = 50 + 15 = 65

🔒 ❓ Question 30
Explain the importance of arithmetic expressions in daily life.

📌 ✅ Answer:
🔹 They help in calculations during shopping
🔹 They are used in time and distance problems
🔹 They help solve word problems easily
🔹 They form the base for higher mathematics

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