Subtracting Fractions
Overall Steps to Subtract Fractions:
- Find a Common Denominator: Identify the least common multiple (LCM) of the denominators.
- Convert Fractions: Express each fraction with the common denominator found in step 1.
- Subtract Numerators: Subtract the numerators of the fractions.
- Simplify (if necessary): Simplify the resulting fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Addressing Special Cases:
- When the Denominators are Already the Same: Simply subtract the numerators and keep the denominator the same.
- When One Fraction is a Whole Number: Convert the whole number into a fraction with the same denominator as the other fractions before subtracting.
- When Fractions are Mixed Numbers: Convert mixed numbers into improper fractions before subtracting.
Example 1: Subtracting 2 Fractions
Subtract Given Fractions: 3/4 - 1/4
Step 1: Denominators are already the same
Step 2: Subtract numerators: 3/4 - 1/4 = 2/4
Step 3: Simplify if necessary → 2/4 = 1/2
Example 2: Subtracting 3 Fractions
Subtract Given Fractions: 2/3 - 1/6 - 1/4
Step 1: Find LCM of 3, 6, and 4 → LCM(3, 6, 4) = 12
Step 2: Convert fractions: 2/3 becomes 8/12, 1/6 becomes 2/12, 1/4 becomes 3/12
Step 3: Subtract numerators: 8/12 - 2/12 - 3/12 = 3/12
Step 4: Simplify if necessary → 3/12 = 1/4
Example 3: Subtracting a Whole Number and a Fraction
Subtract Given Fractions: 5 - 2/3
Step 1: Convert whole number to fraction with the same denominator as the fraction: 5 = 15/3
Step 2: Subtract numerators: 15/3 - 2/3 = 13/3
Example 4: Subtracting Mixed Numbers
Subtract Given Fractions: 3 1/2 - 1 3/4
Step 1: Convert mixed numbers to improper fractions: 3 1/2 = 7/2, 1 3/4 = 7/4
Step 2: Find a common denominator → LCM(2, 4) = 4
Step 3: Convert fractions: 7/2 becomes 14/4, 7/4 remains 7/4
Step 4: Subtract numerators: 14/4 - 7/4 = 7/4