Rapid Mental Calculations - 1

To mentally multiply a number by a single-digit factor (eg. 27 • 8), the procedure is performed, starting not with the multiplication of units, as in written multiplication, but the other way around: first multiply the tens of the multiplicand (20 • 8 = 160), then the units (7 • 8 = 56), and add both results.

More examples: 34 • 7 = 30 • 7 + 4 • 7 = 210 + 28 = 238, 47 • 6= 40 • 6 + 7 • 6 = 240 + 42 = 282.

It’s useful to know the multiplication table up to 19x9. Knowing this table, you can mentally multiply, for instance, 147 • 8 in this way: 147 • 8 = 140 • 8 + 7 • 8 = 1120 + 56 = 1176.
When one of the numbers multiplied can be decomposed into a product of single-digit factors, it is convenient to multiply it consequently by these factors. For example: 225 • 6  = 225 • (2 • 3) = 450 • 3 = 1350.

Multiplication by two digits is usually simplified for mental calculation by reducing it to the more usual multiplication by a single digit. When the multiplicand is single-digit, the factors are mentally rearranged and the operation is performed as described above. For example: 6  • 28= 28 • 6 = 20 • 6 + 8 • 6 = 120 + 48 = 168.

If both factors are double-digit, mentally break one down into tens and units. For example: 29 • 12 = 29 • 10+ 29 • 2 = 290 + 58 = 348, 41 • 16 = 41 • 10+ 41 • 6 = 410 + 246 = 656 (or 41 • 16 = 16 • 41 = 16 • 40 + 16 = 640 + 16 = 656). It is convenient to break down into tens and units the factor in which they are expressed by smaller numbers.

If the multiplicand or multiplier are easy to mentally decompose as a product of single digits (eg 14 = 2 • 7), take advantage of this to reduce one of the factors, increasing the other by the same factor. For example: 45 • 14 = 45 • (2 • 7) = (2 • 45) • 7 = 90 • 7 = 630.

To mentally multiply a number by 4, double it twice. For example: 112 • 4 = 224 • 2 = 448; 335 • 4 = 670 • 2 = 1340.

To mentally multiply a number by 8, double it three times. For example: 217 • 8 = 434 • 4 = 868 • 2 = 1736 (even more convenient: 217 • 8 = 200 • 8 + 17 • 8 = 1600 + 136 = 1736).


The next article of the cycle: Rapid Mental Calculations: Part 2

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