Multiply mixed numbers

  2. Basic Math Decoded
  3. Multiply mixed numbers
 
   6      1
2 —— × 3 ——
  35     16
 
Convert mixed numbers to fractions. Multiply the integer portion by the denominator and add the numerator, the result will be the numerator of the fraction, keeping the same denominator.
 
  2 × 35 + 6   3 × 16 + 1
= —————————— × ——————————
      35           16    
 
  76   49
= —— × ——
  35   16
 
It is often simplest to 'cancel' before doing the multiplication. Cancelling is dividing one factor of the numerator and one factor of the denominator by the same number.
 
Simplify the 76 of the first numerator, and the 16 of the second denominator. Use the number 4 for the simplification.
 
  19   49
= —— × ——
  35    4
 
Simplify the 49 of the second numerator, and the 35 of the first denominator. Use the number 7 for the simplification.
 
  19   7
= —— × —
   5   4
 
Multiply the numerators of the fractions and multiply the denominators of the fractions. Place the product of the numerators over the product of the denominators.
 
  19 × 7
= ——————
   5 × 4
 
Partial multiplications
 
  19
×  7
 133
 
5 × 4 = 20
 
  133
= ———
   20
 
 
This fraction is improper (numerator larger than or equal to the denominator). Convert it to a mixed number. The integer portion is the quotient when dividing the numerator by the denominator, the numerator of the fraction portion is the rest of that division, and keeps the same denominator.
 
     6 R 13
20)133
   120
    13
 
Final answer
 
  13
6 ——
  20
 
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