Member-only story
Multiplying 2 Mixed Numbers
Multiplying a fraction or a whole number times a mixed number is easy: You break the mixed number apart and multiply the fraction or whole number times each part. (I’ve talked about this in articles here and here) Multiplying 2 mixed numbers, however, has been problematical.
Recently, I was working with a student who needed some advanced training in fractions. We were working a problem that had us multiplying 20 3/4 times 3 1/2. One way I showed the student is to split it apart and use the FOIL method. FOIL stands for First two numbers, Outer two numbers, Inner two numbers and Last two numbers.
(20 + 3/4)(3 + 1/2)
20 X 3 = 60
20 X 1/2 = 10
3/4 X 3 = 9/4 = 2 1/4
3/4 X 1/2 = 3/8
60 + 10 + 2 1/4 + 3/8 = 72 5/8
A second way was to write 20 3/4 as 21–1/4, so we had (21–1/4)(3 1/2).
21 X 3 1/2 = 63 + 10 1/2 = 73 1/2
1/4(3 1/2) = 3/4 + 1/8 = 7/8
Since 1/2 = 4/8,
73 1/2–7/8 = 73–3/8 = 72 5/8.
