Rapid Mental Calculations - 2

To mentally divide a number by 4, divide it by 2 twice. For example: 76 : 4 = 38 : 2 = 19, 236 : 4 = 118 : 2 = 59.

To mentally divide a number by 8, divide it by 2 three times. For example: 464 : 8 = 232 : 4= 116 : 2 = 58, 516 : 8 = 258 : 4 = 129 : 2 = 64.5.

To mentally multiply a number by 5, multiply it by 10/2, that is attach a zero to it, and divide in half. For example: 74 • 5 = 740 : 2 = 370, 243 • 5 = 2430 : 2 = 1215. When the multiplied is even, it is easier to divide by 2 first and attach a zero to the result. For example: 74 • 5 = 74 : 2 • 10 = 370.

To mentally multiply a number by 25, multiply it by 100/4 - that is, if the number is a multiple of 4, divide it by 4 and attach two zeros to the quotient. For example: 72 • 25 = 72 : 4 • 100 = 1800. If the number gives remainder when divided by 4, then, when the remainder equals 1, attach 25 to the quotient, when the remainder equals 2, attach 50 to the quotient, when the remainder equals 3, attach 75. The base for this method is clear from the fact that 100 : 4 = 25; 200 : 4 = 50; 300 : 4 = 75.

To mentally multiply a number by 1.5, add to the multiplicand its half. For example: 34 • 1.5 = 34 + 17 = 51, 23 • 1.5 = 23 + 11.5 = 34.5.

To mentally multiply a number by 1.25, add to the multiplicand its quarter. For example: 48 • 1.25 = 48 + 12 = 60, 58 • 1.25 = 58 + 14.5 = 72.5.

To mentally multiply a number by 2.5, add to twice the number of the multiplicand its half. For example: 18 • 2.5 = 36 + 9 = 45, 39 • 2.5 = 78 + 19.5 = 97.5. Another way is to multiply by 5 and half the product: 18 • 2.5 = 90 : 2 = 45.

To mentally multiply a number by 3/4 (that is, to find three-quarters of this number), multiply the number by 1.5 and divide in half. For example: 30 • 3/4 = (30 + 15):2 = 22.5. A modification of the method is that a quarter of the multiplicand is subtracted from it or to the half of the multiplicand is added a half of that half.

Multiplication by 15 is replaced by multiplying by 10 and then by 1.5 (as 1.5 • 10 = 15). For example: 18 • 15 = 18 • 10 • 1,5 = 270, 45 • 15 = 450 + 225 = 675.

Multiplication by 125 is replaced by multiplying 100 and then by 1.25 (because 100 • 1.25 = 125). For example: 26 • 125 = 26 • 100 • 1.25 = 2600 + 650 = 3250, 47 • 125 = 47 • 100 • 1.25 = 4700 + 4700 : 4 = 4700 + 1175 = 5875.

Multiplication by 75 is replaced by multiplying 100 and then by 3/4 (because 100 • 3/4 = 75). For example: 18 • 75 = 18 • 100 • 3/4 = 1800 • 3/4 = (1800 + 900) : 2 = 1350. Note: some of the examples is conveniently performed through breaking down one of the factors into the product of single-digit factors (or a product of small factors, one of which would be either single-digit or simply convenient for mental calculation), as described above. Thus, you can reduce one of the initial factors, while increasing the second factor by the same number of times.

For instance: 18 • 15 = 18 • (3 • 5) = 90 • 3 = 270, 125 • 26 = 26 • (25 • 5) = 130 • 25 = 3250.

To mentally multiply a number by 9, attach a zero to it and subtract the multiplicand. For example: 62 • 9 = 620-62 = 600-42 = 558, 73 • 9 = 730-73 = 700-43 = 657.

To mentally multiply a number by 11, attach a zero to it and add the multiplicand. For example: 87 • 11 = 870 + 87 = 957.

To mentally divide a number by 5, separate the last digit of the doubled number by a comma (or, equivalently, divide by 10). For example: 68 : 5 = 136 : 10 = 13.6, 237 : 5 = 474 : 10 = 47.4.

To mentally divide a number by 1.5, divide twice the number by 3. For example: 36 : 1.5 = 72 : 3 = 24, 53 : 1.5 = 106 : 3 = 35.333...

To mentally divide a number by 15, divide twice the number by 30. For example: 240 : 15 = 480 : 30 = 48 : 3 = 16, 462 : 15 = 924 : 30 = 900 : 30 + 24 : 30 = 30 + 4 : 5 = 30.8 (or 924: 30 = 308 : 10 = 30.8).


The first article of the series: Rapid Mental Calculations: Part1

The last article of the series: Rapid Mental Calculations: Part3

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