Operations on Fractions
"Master adding, subtracting, and multiplying fractions with unlike denominators."
A Today you'll learn
- Add and subtract fractions with unlike denominators using LCM.
- Multiply fractions and simplify products to lowest terms.
- Solve multi-step word problems involving fraction operations.
B Let's understand
LCM of 2 and 3 = 6; Common denominator allows clean addition
Fractions represent equal parts of a whole or set. When adding or subtracting fractions with unlike denominators, we cannot simply combine numerators because the parts are different sizes. First, find the Least Common Multiple (LCM) of the denominators to create equivalent fractions with a common denominator. Then add or subtract the numerators while keeping the common denominator unchanged. When multiplying fractions, multiply numerator by numerator and denominator by denominator, and simplify the resulting fraction by dividing by common factors.
C See it step by step
- Step 1: The denominators are 4 and 5. Their LCM is 20.
- Step 2: Convert both fractions: 3/4 = (3 × 5) / (4 × 5) = 15/20; 2/5 = (2 × 4) / (5 × 4) = 8/20.
- Step 3: Add numerators: 15/20 + 8/20 = 23/20.
- Step 4: Convert to mixed fraction: 23/20 = 1 3/20.
- Step 1: Multiply numerators: 2 × 9 = 18.
- Step 2: Multiply denominators: 3 × 10 = 30. Result = 18/30.
- Step 3: Simplify by dividing both by GCD (6): 18 ÷ 6 = 3, 30 ÷ 6 = 5.
- Step 4: Final simplified answer = 3/5.
D Your turn
E Ready to practise?
Key idea 1
Unlike denominators must be made common using LCM before addition or subtraction.
Key idea 2
Never add or subtract denominators; only add or subtract numerators.
To multiply fractions
To multiply fractions, multiply top by top and bottom by bottom.
Key idea 4
Always simplify fractions to simplest form by dividing by the greatest common divisor.
Key idea 5
An improper fraction has a numerator greater than or equal to its denominator and can be written as a mixed number.