Chapter 2 - Fractions and Decimals Revision Notes - Class 7 Mathematics

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📌 Key Points

Fractions represent parts of a whole. Written as a/b where a is numerator and b is denominator.
Proper fraction: numerator < denominator (e.g., 3/5). Value < 1.
Improper fraction: numerator ≥ denominator (e.g., 7/5). Value ≥ 1.
Mixed fraction combines whole number and proper fraction (e.g., 2 3/5 = 13/5).
Like fractions: same denominator. Unlike fractions: different denominators.
To add/subtract unlike fractions: find LCM of denominators, convert to like fractions.
Multiplication of fractions: multiply numerators and denominators separately. Simplify by canceling.
Division of fractions: multiply by reciprocal (flip second fraction).
Decimals use base-10 place values: 0.1 (tenths), 0.01 (hundredths), 0.001 (thousandths).
Add/subtract decimals: align decimal points, then operate.
Multiply decimals: multiply without decimal, then place decimal at sum of decimal places.
Divide decimals: move decimal point to make divisor whole, adjust dividend similarly.
Fraction to decimal: divide numerator by denominator.
Decimal to fraction: write over place value denominator, simplify.
Common pairs: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/5=0.2, 2/5=0.4, 3/5=0.6

📘 Important Definitions

Fraction

A number representing a part or division of a whole, expressed as a/b.

Proper Fraction

Fraction where numerator < denominator. Example: 3/5, 2/7. Always less than 1.

Improper Fraction

Fraction where numerator ≥ denominator. Example: 7/5, 9/9. Always ≥ 1.

Mixed Fraction

Combination of whole number and proper fraction. Example: 2 3/5 or 1 1/2.

Like Fractions

Fractions with same denominator. Example: 2/7, 4/7, 6/7.

Unlike Fractions

Fractions with different denominators. Example: 2/3, 5/7, 1/2.

Reciprocal

For fraction a/b, reciprocal is b/a. When multiplied together, result is 1.

Decimal

Number expressed using base-10 with decimal point. Example: 0.5, 3.25, 0.175.

🔢 Formulas & Laws

Mixed to Improper Fraction

a b/c = (a×c + b)/c

Example: 2 3/5 = (2×5 + 3)/5 = 13/5

Addition/Subtraction of Unlike Fractions

a/b ± c/d = (a×d ± c×b)/(b×d)

Find LCM of denominators for simpler calculation

Multiplication of Fractions

a/b × c/d = (a×c)/(b×d)

Simplify by canceling common factors before multiplying

Division of Fractions

a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)

Multiply by reciprocal (flip second fraction)

Fraction to Decimal

a/b = a ÷ b

Example: 3/4 = 3÷4 = 0.75

⚠️ Common Mistakes

✗ Wrong: Adding fractions with different denominators directly: 1/2 + 1/3 = 2/5

✓ Correct: Convert to like fractions first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

✗ Wrong: In division, forgetting to flip the second fraction: 3/4 ÷ 1/2 = 3/2 (wrong method)

✓ Correct: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2 (correct method)

✗ Wrong: Multiplying decimals incorrectly: 0.2 × 0.3 = 0.6

✓ Correct: 0.2 × 0.3 = 0.06 (2 decimal places total)

✗ Wrong: Not simplifying final answer: 6/12 is the final answer

✓ Correct: Always simplify: 6/12 = 1/2

✗ Wrong: Converting decimal incorrectly: 0.35 = 35/10

✓ Correct: 0.35 = 35/100 = 7/20 (place value matters)

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Operations on fractions (addition, subtraction, multiplication, division)

2m★★★

Word problems with fractions (pizza, cloth, time, etc.)

3m★★★

Conversion between fractions and decimals

1m★★

Decimal operations and place values

2m★★

Comparing and arranging fractions in order

2m★★

Simplification and reducing fractions to lowest terms

🎯 Last-Minute Recall