Expanding the FOIL method
Most of us learned the FOIL method as a way to multiply algebraic expressions. FOIL stands for First, Outer, Inner, and Last, which is how we multiply the terms.
(X + 2)(X — 3) = X² -3X + 2X -6 = X² -X -6
However, we can expand the use from algebra to things like multiplying mixed numbers and decimals too. Let’s look at an example.
9 1/2 X 8 1/3 can be written as (9 + 1/2)(8 + 1/3). Using the FOIL method gives us 72 + 3 + 4 + 1/6 = 79 1/6. This is considerably easier than the standard way of multiplying, which entails making improper fractions, multiplying the larger numbers, and then simplifying.
Using the FOIL method, not only is the process shorter, but the numbers are smaller so the math is easier. The toughest thing is multiplying 8X9. In the standard case, we’re multiplying 19 X 25 and then dividing 475 by 6.
Let’s look at a decimal case.
Let’s multiply 45.7 X 6.4.
(45 + .7)(6 + .4) = (45 X 6) + (45 X .4) +(6 X .7) +(.7 X.4)
= 270 +18 + 4.2 + .28 = 292.48
