MSC #24 – Vertically and Crosswise: Working with Fractions and Mixed Numbers
Our 24th MATH-Inic Special for Christmas is about multiplication of mixed numbers. We were trained to convert mixed numbers into improper fractions first before performing multiplication and later change the product into mixed numbers. Oftentimes direct application of the distributive law offers a quicker solution.
We purposely chose “easy-to-compute” figures in our example to emphasize the method not the actual computation. But this technique works well for most cases.
Let us consider a “difficult” example 7 4/7 x 9 5/8. We have
7 4/7 x 9 5/9 = 7(9) + 7(5/9) + 9(4/7) + (4/7)(5/9)
= 63 + 35/9 + 36/7 + 20/63
= 63 + 3 8/9 + 5 1/7 + 20/63
= (63 + 3 + 5) + (8/9 + 1/7 + 20/63)
= 71 + (56 + 9 +20)/56
= 71 + 85/63 = 72 22/63
This solution may look long and complicated but it can be actually performed mentally.
The four basic operation of addition, subtraction, multiplication and division of fractions and mixed numbers using Vertically and Crosswise are discussed in Chapter 24 of “30 Master Strategies in Computing”
