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By Arthur T. Benjamin
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Additional resources for The Secrets of Mental Math
If the divisor ends in 6, we add 4 times the previous quotient, and if it ends in 5, we add 5 times the previous quotient. If the divisor ends in 1, 2, 3, or 4, we go down to reach a round number and subtract the previous quotient multiplied by that digit. In other words, the multiplier for these divisors would be 1, 2, 3, or 4. This subtraction step sometimes yields negative numbers; if this happens, we reduce the previous quotient by 1 and increase the remainder by the 1-digit divisor. 53 To get comfortable with Vedic division, you’ll need to practice, but you’ll eventually ¿nd that it’s usually faster than short or long division for most 2-digit division problems.
The ¿rst part of the calculation is now 10 × 16. To that result, we add the square of the number that went up and down (3): 10 × 16 = 160 and 160 + 32 = 169. Numbers that end in 5 are especially easy to square using this method, as are If you’re quick with 2-by-1 numbers near 100. multiplications, you can practice the “math of Finally, our ¿fth mental multiplication strategy is the close-together method, least resistance”—look which we saw in the last lecture. For a at the problem both ways problem like 26 × 23, we ¿rst ¿nd a round and take the easier path.
Going. For 1475 ÷ 29, we go up 1 to 30, so 3 is our divisor; 3 goes into 14, 4 times with a remainder of 2. The 4 goes above the line and the 2 goes next to the 7. Next, we do 3 into 27 + 4, which is 31; 3 goes into 31, 10 times with a remainder of 1. We write the 10 above the line, as before, making sure that the 1 goes in the previous column. When we reach the remainder step, we have to make sure to add 15 + 10, rather than 15 + 0. The result here is 50 with a remainder of 25. If the divisor ends in 8, 7, 6, or 5, the procedure is almost the same.
The Secrets of Mental Math by Arthur T. Benjamin