Notes Maths Class 7 Chapter 2 Ganita Prakash

Notes For All Chapters – Ganita Prakash Class 7th

Arithmetic Expressions

1. What is an Arithmetic Expression?

A mathematical phrase using numbers and operations (+, –, ×, ÷).

Examples:

• 13 + 2
• 20 – 4
• 12 × 5
• 18 ÷ 3

2. Value of an Expression

Every expression has a value (result after solving).

Example:

• 13 + 2 = 15

3. Using the Equal Sign ‘=’

Used to show that two expressions or an expression and a number are equal.

Example:

• 5 × 2 = 10

4. Comparing Expressions

Use <, >, or = to compare based on value.

Examples:

• 10 + 2 > 7 + 1
• 13 – 2 < 4 × 3

5. Reading Complex Expressions

Without context or brackets, expressions can be misunderstood.

Example:

30 + 5 × 4

• Wrong: (30 + 5) × 4 = 140
• Correct: 30 + (5 × 4) = 30 + 20 = 50

6. Role of Brackets

Brackets help to decide which operation to do first.

Always solve brackets first.

Example:

• 100 – (15 + 56) = 100 – 71 = 29

7. Terms in an Expression

Parts of an expression separated by ‘+’ signs.

Even subtraction can be rewritten using negative numbers:

83 – 14 → terms are 83 and –14

8. Swapping and Grouping Terms

Changing the order or grouping of terms in addition doesn’t change the value.

This follows:

• Commutative Property: a + b = b + a
• Associative Property: (a + b) + c = a + (b + c)

9. Distributive Property

Multiplying a number with a sum or difference:

a × (b + c) = a × b + a × c

a × (b – c) = a × b – a × c

Example:

• 2 × (43 + 24) = 2 × 43 + 2 × 24

10. Removing Brackets

If a bracket is preceded by a minus (–) sign:

Signs inside the bracket change

Example:

200 – (40 + 3) = 200 – 40 – 3 = 157

If bracket is not preceded by minus, signs remain same.

11. Strategies to Simplify

Use known values to calculate quickly:

• 97 × 25 → (100 – 3) × 25 = 2500 – 75 = 2425