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Topics - Contents
Multiplication of Fractions
Multiplication of Proper and Improper Fractions
Multiply Numerator to Numerator and Denominator to denominator
Reduce the fraction
Examples:
1. Perform the indicated operation: \( \frac{13}{11} \:x\: \frac{2}{3} \)
\( \frac{13}{11} \:x\: \frac{2}{3} \) = \( \frac{13x2}{11x3}\) = \( \frac{26}{33}\)
Since the numerator and denominator has no common factors, then the fraction is in its simplest form.
2. Perform the indicated operation: \( \frac{16}{11} \:x\: \frac{9}{4} \)
\( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{16x9}{11x4}\) = \( \frac{144}{44}\)
Simplify / Reduce:
\( \frac{144}{44}\) = \( \frac{2x2x2x2x3x3}{2x2x11}\)
\( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{2x2x3x3}{11}\)
\( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{36}{11}\)
3. You can also simplify the fraction before multiplying mexample: \( \frac{16}{11} \:x\: \frac{9}{4} \)
\( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{16x9}{11x4}\)
Factor every number with its prime factors.
\( \frac{16x9}{11x4}\) =\( \frac{2x2x2x2 \:x\:3x3}{11x2x2}\)
Cancel / divide similar factors
\( \frac{16x9}{11x4}\) =\( \frac{2x2 \:x\:3x3}{11}\)
Multiply the remaining numbers.
\( \frac{16x9}{11x4}\) =\( \frac{36}{11}\)
Multiplication of mixed fractions
Transform mixed fraction
to its equivalent improper fraction.
Use the procedures for multiplying improper fractions.