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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