Dividing Fractions
Overall Steps to Divide Fractions:
- Multiply by the Reciprocal: Divide by a fraction by multiplying by its reciprocal.
- 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 Dividing by a Whole Number: Convert the whole number into a fraction before dividing.
- When Fractions are Mixed Numbers: Convert mixed numbers into improper fractions before dividing.
Example 1: Dividing 2 Fractions
Divide Given Fractions: 2/3 ÷ 3/4
Step 1: Multiply by the reciprocal of the divisor: 2/3 * 4/3
Step 2: Multiply numerators: 2 * 4 = 8
Step 3: Multiply denominators: 3 * 3 = 9
Result: 2/3 ÷ 3/4 = 8/9
Example 2: Dividing 3 Fractions
Divide Given Fractions: 1/2 ÷ 1/3 ÷ 1/4
Step 1: Multiply by the reciprocal of the divisor: 1/2 * 3/1 * 4/1
Step 2: Multiply numerators: 1 * 3 * 4 = 12
Step 3: Multiply denominators: 2 * 1 * 1 = 2
Result: 1/2 ÷ 1/3 ÷ 1/4 = 12/2
Simplify if necessary → 12/2 = 6
Example 3: Dividing by a Whole Number
Divide Given Fractions: 1/2 ÷ 3
Step 1: Convert whole number to fraction: 3 = 3/1
Step 2: Multiply by the reciprocal of the divisor: 1/2 * 1/3
Step 3: Multiply numerators: 1 * 1 = 1
Step 4: Multiply denominators: 2 * 3 = 6
Result: 1/2 ÷ 3 = 1/6
Example 4: Dividing Mixed Numbers
Divide Given Fractions: 3 1/2 ÷ 2 1/3
Step 1: Convert mixed numbers to improper fractions: 3 1/2 = 7/2, 2 1/3 = 7/3
Step 2: Multiply by the reciprocal of the divisor: 7/2 * 3/7
Step 3: Multiply numerators: 7 * 3 = 21
Step 4: Multiply denominators: 2 * 7 = 14
Result: 3 1/2 ÷ 2 1/3 = 21/14
Simplify if necessary → 21/14 = 3/2
