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# Multiplying a Fraction by a Fraction

Formula: Note:
The resulting fraction should always be simplified.
Example: Solution: Note:
When multiplicate two fractions, first check if there are common factors
The numerator of the first fraction is 15, and 15 = 3 × 5, 1 × 15
The denominator of the second fraction is 45, and 45 = 5 × 9, 15 × 3, 1 × 45
Both of the numerator and denominator has common factors 1, 3, 5, 15.
Therefore, the greatest common factor (GCF) is 15.
Now divide the numerator of the first fraction by 15, and
divide the denominator of the second fraction by 15,
the result is 1/3, at this time, the only common factor is 1.
The denominator of the first fraction is 24, and 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6
The numerator of the second fraction is 6, and 6 = 1 × 6, 2 × 3
Both of them have the common factors 1, 2, 3, 6
Therefore, the greatest common factor (GCF) is 6.
Now divide the denominator of the first fraction by 6,
divide the numerator of the second fraction by 6,
the result is 1/4, at this time, the only common factor is 1.
The final result is 1/3 × 1/4 = 1/12