When two 2-digit numbers are multiplied together, such as 31 x 32, it is easy to know the first and last numbers of the answer:
Multiply the tens digits together for the first numbers of the answer, and the ones digits together for the last number of the answer. In this case, 3 x 3x=x9 and 1 x 2 = 2, so we have 9 _ 2.
To get the middle number:
Multiply together the outer digits, and multiply together the inner digits, and these two figures added together give the middle digit of the answer. There may be a carry figure. In this case, we have (3 x 2) + (3 x 1) = 9
The answer of our example is 991.
One may recognize this as the FOIL method of multiplying variables in algebra, with the letters representing multiplication steps: First, Outer, Inner, Last. When learning algebra, many wonder how it can be usefully applied, and this is one valuable way. FOIL makes multiplying many 2-digit numbers quite easy and quick, with practice.
Another example:
24 x 62 =
Quickly, F: 2 x 6 gives 12 _ _.
Then, L: 4 x 2 gives 12 _ 8.
Lastly, (O+I): (2 x 2) + (6 x 4) = 4+24 gives 28. This 8 is the middle digit of the answer, with the 2 carried to the first digits of the answer, making the first digits now 12 + 2 = 14.
The answer is 1488.
Practice, practice, practice using low digits at first to get the mind used to the process. This is a useful formula.
