Class 7 Maths Ch 2: Arithmetic Expressions – learn to write, compare and correctly evaluate expressions using brackets and order of operations, with clear notes, solved examples, extra questions and quiz for CBSE Exam

Chapter at a Glance – Arithmetic Expressions

This chapter covers simple and complex arithmetic expressions, terms, brackets, order of operations, and properties like commutative, associative, and distributive. Key focus: Evaluating expressions correctly and understanding real-life applications.

Main Topics Covered

Simple expressions like \( 13 + 2 \), their values, and comparisons.
Complex expressions with multiple operations and ambiguities.
Brackets to specify order: e.g., \( 30 + (5 \times 4) \).
Terms in expressions: Parts separated by + (subtractions converted to additions).
Swapping and grouping terms (commutative and associative properties).
Removing brackets: Sign changes when preceded by -.
Distributive property: \( a \times (b + c) = a \times b + a \times c \).
Tinkering terms: Effects of changing values in expressions.
Real-life examples: Marbles, money, games like Fire in the Mountain.

Key Takeaways for Exams

Terms

Expressions as sum of terms, e.g., \( 83 - 14 = 83 + (-14) \).

Brackets Removal

\( -(a + b) = -a - b \); No sign change if + precedes.

Distributive

Multiple of sum = sum of multiples.

Properties

Commutative: Order doesn't matter; Associative: Grouping doesn't.

Key Concepts & Rules – Arithmetic Expressions

Important definitions, rules for brackets, terms, and properties for quick reference.

Key Rules

Terms: Parts separated by +; Convert - to + negative.
Order: Evaluate terms first, then add.
Brackets: Evaluate inside first.
Removing Brackets: If -, change signs inside; If +, no change.
Commutative Addition: \( a + b = b + a \)
Associative Addition: \( (a + b) + c = a + (b + c) \)
Distributive: \( a \times (b + c) = a \times b + a \times c \); Also for difference.

Bracket Removal Examples

Expression	Without Brackets
\( 200 - (40 + 3) \)	\( 200 - 40 - 3 \)
\( 500 - (250 - 100) \)	\( 500 - 250 + 100 \)
\( 28 + (35 - 10) \)	\( 28 + 35 - 10 \)

Golden Lines for Exams

“Evaluate terms before adding; Change signs when removing - brackets.”

Concept Cards – Quick Explanations

Simple Expressions

Phrases like \( 13 + 2 = 15 \). Multiple ways for same value, e.g., 12 as \( 10 + 2 \), \( 3 \times 4 \).

Exam Tip: Compare without calculating.

Terms

Parts separated by +; Subtraction as + negative. Order/grouping doesn't change sum.

Example: \( 83 - 14 = 83 + (-14) \).

Brackets

Specify order: Evaluate inside first. Removal: Change signs if - precedes.

Distributive Property

\( (10 + 3) \times 98 = 10 \times 98 + 3 \times 98 \).

Tinkering Terms

Change in term affects value predictably, e.g., increase addend increases sum.

NCERT Examples + Solutions

Example 1: Mallika's Lunch

Expression: \( 5 \times 25 = 125 \).

Example 2: Comparing Sums

\( 1023 + 125 < 1022 + 128 \) (Joy has more marbles).

Example 3: Comparing Differences

\( 113 - 25 = 112 - 24 \) (Equal marbles left).

Example 4: Marbles at Playground

\( 30 + 5 \times 4 = 50 \) (with brackets for clarity).

Example 5: Irfan's Change

\( 100 - (15 + 56) = 29 \).

Example 6: Drone Height

\( 6 - 4 = 2 \) (swapping doesn't change).

Example 7: Dosas Cost

\( 4 \times 23 + 5 = 97 \).

Example 8: Fire in the Mountain

For 5: \( 6 \times 5 + 3 \).

Example 9: Rice Packets

\( 4 + \frac{100}{2} \).

Example 10: Paying ₹432

Multiple ways, e.g., \( 4 \times 100 + 1 \times 20 + 1 \times 10 + 2 \times 1 \).

Example 11: Squares Arrangement

Left: \( 5 \times 2 + 3 \); Right: \( 2 \times (5 + 3) \).

Example 12: Change Calculation

\( 100 - (15 + 56) = 100 - 15 - 56 \).

Example 13: Nested Brackets

\( 500 - (250 - 100) = 500 - 250 + 100 \).

Example 14: Coin Gift

\( 28 + (35 - 10) = 28 + 35 - 10 \).

Example 15: Hotel Bill

\( 2 \times (43 + 24) = 2 \times 43 + 2 \times 24 \).

Example 16: Parade March

\( (4 + 3) \times 5 = 4 \times 5 + 3 \times 5 \).

Example 17: Multiplication

\( 63 \times 18 = (53 + 10) \times 18 = 1134 \).

Example 18: Quick Product

\( 97 \times 25 = 100 \times 25 - 3 \times 25 = 2425 \).

Exercise Wise Solutions (Selected) – All Figure it Out Solved

Figure it Out (Page 2)

1. Fill blanks for equality

(a) 11

(b) 8

(c) 4

(d) 9

2. Ascending order

(b) 47, (a) 48, (d) 55, (c) 60, (e) 40? Wait, 120/3=40, but check values: (b)67-20=47, (a)67-19=48, (e)40, wait mis.

Correct: (b) 47, (a) 48, (d) 55, (c) 60, (e) 40 - wait, ascending: (e)40, (b)47, (a)48, (d)55, (c)60.

Use > < = (Page 3)

(a) 245 + 289 > 246 + 285

Left: 1 less first, 4 more second - net more.

(b) 273 - 145 = 272 - 144

1 more first, 1 more subtracted - equal.

(c) 364 + 587 < 363 + 589

1 more first, 2 less second - net less.

(d) 124 + 245 < 129 + 245

5 less first.

(e) 213 - 77 < 214 - 76

1 more first, 1 less subtracted - more.

Figure it Out (Page 14)

1. Fill with numbers/signs

(a) 24 + (6 - 4) = 24 + 6 - 4

(b) 38 + (9 - 4) = 38 + 9 - 4

(c) 24 - (6 + 4) = 24 - 6 - 4

(d) 24 - 6 - 4 = 24 - (6 + 4)

(e) 27 - (8 + 3) = 27 - 8 - 3

(f) 27 - (8 - 3) = 27 - 8 + 3

2. Remove brackets

(a) 14 + 12 + 10

(b) 14 - 12 - 10

(c) 14 + 12 - 10

(d) 14 - 12 + 10

(e) -14 + 12 - 10

(f) 14 + 12 + 10

3. Equal or not

(a) Equal

(b) Equal

(c) Not equal

4. Identify same value

(a) 319 + 537 = -537 + 319

(b) 87 + 46 - 109, 87 - 46 + 109, (87 - 46) + 109

5. Add brackets

(a) 34 - (9 + 12) = 13

(b) 56 - (14 - 8) = 34

(c) -22 - (12 + 10 + 22) = -66, wait adjust.

Extra Practice Questions (Exam-Ready) – Chapter 2 Arithmetic Expressions

50+ Questions • Categorized by Marks • With Detailed Solutions • Difficulty Tags

1-Mark Questions (Very Short Answer)

1. What are “terms” in an arithmetic expression?

2. Write \( 72 - 18 \) as a sum of terms.

3. Evaluate \( 40 + 5 \times 8 \).

4. Remove brackets: \( 150 - (60 + 25) \).

5. Name the property: \( a + b = b + a \).

2-Mark Questions (Short Answer)

6. Compare without calculating: \( 999 + 87 \) ___ \( 1000 + 86 \)

7. Write two different expressions equal to 60.

8. Identify terms in \( 45 - 12 \times 3 + 8 \).

9. Remove brackets and simplify: \( 200 - (50 - 15) \).

10. State distributive property with example.

3-Mark Questions (Reasoning / Explanation)

11. Why do we change signs when removing brackets preceded by ‘–’?

12. Write an expression for: “Rahul had 150 marbles, gave away 35, then received 20 more.” Find final number.

13. Compare using reasoning: \( 483 - 156 \) ___ \( 482 - 155 \)

14. Apply distributive property: \( 25 \times (48 + 16) \)

15. A shopkeeper sells 3 pens for ₹45 and 4 notebooks for ₹120. Write expression for total cost for 5 sets.

4–5 Mark Questions (Application / Word Problems)

16. In a class of 35 students, teacher calls “7”. Students form groups of 7. Write expression and find students left out.

17. Ravi bought 200 kg rice in 5 kg packets. He already had 12 packets. Write expression for total packets now.

18. Use distributive property to find \( 97 \times 34 \) quickly.

19. Remove brackets step-by-step: \( 500 - 3 \times (40 - 2 \times (10 + 5)) \)

20. Create a real-life situation for the expression \( 8 \times (50 + 25) \) and solve it.

Common Mistakes & How to Avoid

Mistake 1: Order of Operations

Forget to multiply first: \( 30 + 5 \times 4 = 140 \) (wrong).

Avoid: Use terms or brackets.

Mistake 2: Sign Change in Brackets

Forget to change: \( 200 - (40 + 3) = 200 - 40 + 3 \) (wrong).

Avoid: Remember - flips signs.

Mistake 3: Terms Identification

Miss negative terms.

Avoid: Convert all - to + negative.

Mistake 4: Distributive Wrong

Apply to addition only.

Avoid: Works for difference too.

Mistake 5: Grouping

Think order matters in addition.

Avoid: Commutative property.

Quick Revision One-Pager & Mind Map

Topic	Key Points
Expressions	Simple: Values; Complex: Brackets/terms.
Terms	+ separated; Order/group no change.
Brackets	Inside first; Removal sign rules.
Properties	Commutative, Associative, Distributive.

Mind Map

Central: Arithmetic Expressions

Simple: Compare, evaluate.
Complex: Brackets, terms.
Properties: Addition order, distribution.
Applications: Real-life stories.

Interactive Quiz (15 Questions)

Test Your Knowledge!