Important Formulas: Fractions | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Equivalent Fractions

• Two fractions are equivalent if they represent the same value or proportion.

• Example: 1/2 = 2/4 = 3/6

• Rule: Multiply or divide both numerator and denominator by the same number to get an equivalent fraction.

• Example: 3/5 × (2/2) = 6/10

Simplest Form of a Fraction

• A fraction is said to be in its simplest form when the numerator and denominator have no common factors except 1.

• To simplify: Divide both numerator and denominator by their Greatest Common Divisor (GCD).

• Example: 12/18 → divide numerator and denominator by 6 → 2/3

Comparing Fractions

(a) Same Denominator: Compare numerators directly.

• Example: 3/7 and 5/7 → 5/7 is greater.

(b) Same Numerator: Compare denominators. Smaller denominator means larger fraction.

• Example: 2/3 and 2/5 → 2/3 is greater.

(c) Different Denominators: Convert to equivalent fractions with a common denominator.

• Example: Compare 3/4 and 5/6.
  LCM of 4 and 6 is 12.
  3/4 = 9/12, 5/6 = 10/12 → 10/12 is greater, so 5/6 is greater.

Addition of Fractions

(a) Same Denominator: Add numerators, keep the denominator.

• Example: 2/7 + 3/7 = 5/7

• Different Denominators:

  • Step 1: Find LCM of denominators.

  • Step 2: Convert fractions to equivalent fractions with same denominator.

  • Step 3: Add numerators, keep denominator.

  • Example: 2/3 + 5/6

    • LCM of 3 and 6 = 6

    • 2/3 = 4/6

    • 4/6 + 5/6 = 9/6 = 3/2= 1½

Subtraction of Fractions

Same process as addition, but subtract numerators.

Example: 5/6 – 1/4

Solution:

LCM of 6 and 4 = 12

5/6 = 10/12, 1/4 = 3/12

10/12 – 3/12 = 7/12

Multiplication of Fractions

• Multiply numerators with numerators and denominators with denominators.

• Example: 2/3 × 4/5 = (2×4)/(3×5) = 8/15

• Simplify if possible.

Division of Fractions

• Rule: Multiply the first fraction by the reciprocal (inverse) of the second fraction.

• Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

Mixed Numbers and Improper Fractions

(a) Mixed Number → Improper Fraction

• Formula: (Whole number × denominator) + numerator, all over denominator.

• Example: 3 2/5 = (3×5 + 2)/5 = 17/5

(b) Improper Fraction → Mixed Number

• Divide numerator by denominator.

• Example: 22/7 = 3 (whole) and remainder 1 → 3 1/7

Fraction of a Number

• Multiply the number with the fraction.

• Example: 2/5 of 50 = (2/5) × 50 = 20

Rule of Signs in Fractions

• Positive ÷ Positive = Positive

• Negative ÷ Negative = Positive

• Positive ÷ Negative = Negative

• Negative ÷ Positive = Negative

Properties of Fractions

• A fraction always represents a part of a whole.

• If numerator < denominator → Proper fraction (value < 1).

• If numerator > denominator → Improper fraction (value > 1).

• If numerator = denominator → Value = 1.

• Fractions can always be reduced to lowest terms.