# Multiplication of Mixed Numbers

Only 529 out of 1417 or 38% of the contestants in the intermediate level of the 4^{th} Philippine National Vedic Mathematics Olympiad were able to get the correct answer to this question: 8 1/6 x 12 3/4 = ?

This is may be due to the fact that we were only taught one way of multiplying mixed numbers during our elementary years, which is as follows:

- convert the mixed numbers into improper fractions:

8 1/6 x 12 3/4 = 49/6 x 51/4

2. perform the multiplication of fractions:

(49 x 51)/(6 x 4) = 2499/24

Note that 49 x 51 can be easily computed as (50 – 1)(50 + 1) = (2500 – 1)

3. convert back to mixed numbers:

2499/24 = 104 3/24 = 104 1/8

2499/24 is (2400 + 96 + 3)/24 = (100 + 4 + 3/24)

If the contestant knows the arithmetic techniques used above, then he can compute the answer quickly. If not, he will have to resort to the long traditional computations which are prone to errors.

A quicker way to get the product is to treat the mixed numbers as binomials and use the FOIL method.

8 1/6 x 12 3/ 4 = (8 + 1/6)(12 + 3/ 4) = 8(12) + 8(3/4) + 1/6(12) + 1/6(3/4)

= 96 + 6 + 2 + 1/8 = 104 1/8.