Basic(Elementary) Mathematics

Back

Multiplication of Fractions

Multiplication of Proper and Improper Fractions

  1. Multiply Numerator to Numerator and Denominator to denominator
  2. Reduce the fraction
Examples:
1. Perform the indicated operation: \( \frac{13}{11} \:x\: \frac{2}{3} \)
  1. \( \frac{13}{11} \:x\: \frac{2}{3} \) = \( \frac{13x2}{11x3}\) = \( \frac{26}{33}\)
  2. Since the numerator and denominator has no common factors, then the fraction is in its simplest form.
2. Perform the indicated operation: \( \frac{16}{11} \:x\: \frac{9}{4} \)
  1. \( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{16x9}{11x4}\) = \( \frac{144}{44}\)
    2. Simplify / Reduce:
  2. \( \frac{144}{44}\) = \( \frac{2x2x2x2x3x3}{2x2x11}\)
  3. \( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{2x2x3x3}{11}\)
  4. \( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{36}{11}\)
3. You can also simplify the fraction before multiplying mexample: \( \frac{16}{11} \:x\: \frac{9}{4} \)
  1. \( \frac{16}{11} \:x\: \frac{9}{4} \) = \( \frac{16x9}{11x4}\)
    2. Factor every number with its prime factors.
  2. \( \frac{16x9}{11x4}\) =\( \frac{2x2x2x2 \:x\:3x3}{11x2x2}\)

    3. Cancel / divide similar factors

  3. \( \frac{16x9}{11x4}\) =\( \frac{2x2 \:x\:3x3}{11}\)

    4. Multiply the remaining numbers.

  4. \( \frac{16x9}{11x4}\) =\( \frac{36}{11}\)

Multiplication of mixed fractions

  1. Transform mixed fraction to its equivalent improper fraction.
  2. Use the procedures for multiplying improper fractions.