Multiplying Fractions
Overall Steps to Multiply Fractions:
- Multiply Numerators: Multiply the numerators of the fractions together.
- Multiply Denominators: Multiply the denominators of the fractions together.
- 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 One Fraction is a Whole Number: Convert the whole number into a fraction before multiplying.
- When Fractions are Mixed Numbers: Convert mixed numbers into improper fractions before multiplying.
Example 1: Multiplying 2 Fractions
Multiply Given Fractions: 2/3 * 3/4
Step 1: Multiply numerators: 2 * 3 = 6
Step 2: Multiply denominators: 3 * 4 = 12
Result: 2/3 * 3/4 = 6/12
Simplify if necessary → 6/12 = 1/2
Example 2: Multiplying 3 Fractions
Multiply Given Fractions: 1/2 * 2/3 * 3/4
Step 1: Multiply numerators: 1 * 2 * 3 = 6
Step 2: Multiply denominators: 2 * 3 * 4 = 24
Result: 1/2 * 2/3 * 3/4 = 6/24
Simplify if necessary → 6/24 = 1/4
Example 3: Multiplying a Whole Number and a Fraction
Multiply Given Fractions: 3 * 2/5
Step 1: Convert whole number to fraction: 3 = 3/1
Step 2: Multiply numerators: 3 * 2 = 6
Step 3: Multiply denominators: 1 * 5 = 5
Result: 3 * 2/5 = 6/5
Example 4: Multiplying Mixed Numbers
Multiply Given Fractions: 1 1/2 * 2 1/3
Step 1: Convert mixed numbers to improper fractions: 1 1/2 = 3/2, 2 1/3 = 7/3
Step 2: Multiply numerators: 3/2 * 7/3 = 21/6
Step 3: Simplify if necessary → 21/6 = 7/2
Result: 1 1/2 * 2 1/3 = 7/2