By Hukum Singh
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Extra resources for A Handbook for Designing Mathematics Laboratory in Schools
DIVIDING INTO LONGER NUMBERS Now let’s try another division problem: 1,743/7. You might find it helpful to have a multiplication table for the divisor, in this case 7, at the side. This table enables you to subtract the number in the quotient all in one “bite,” rather than one piece at a time as a calculator does. The remainder each time is less than the divisor, so “bring down” the next digit or figure and continue for the next place in the quotient. Figure 4-3 shows what you really do, and then how it is usually written.
Suppose 8 ounces don’t tip the scale. If 4 ounces are added to make 12 ounces, it still doesn’t tip. But when we add a 2-ounce weight, which brings the weight up to 2 pounds 14 ounces, it tips. If the 1-ounce weight is used instead of the 2-ounce weight, the scale doesn’t tip. Now we know that the parcel weighs more than 2 pounds 13 ounces, and less than 2 pounds 14 ounces. If we want to be more accurate, we can follow this method until it balances with 2 pounds, 13 ounces, and 3 drams. QUESTIONS AND PROBLEMS This is an open-book quiz.
The whole thing is written down in one “piece” or algorithm, as the professional mathematicians call it. This is how people performed multiplication before they had computers. At one time, the “new math” consisted in multiplying from the other direction. In Fig. 3-6, the same multiplication is performed in the reverse order: first the 20 and then the 7. The answer is the same either way, provided no mistakes are made. If the multiplier (that is, the second number or the lower number) has three or more digits, we must work consistently, either from left to right or from right to left.
A Handbook for Designing Mathematics Laboratory in Schools by Hukum Singh