If you divide a number of more than two digits by another number of more than two digits the process is known as long division. Some people can do this in their heads. Others use a traditional algorithm, or methodology, taught in Britain since the 19th century. Since the 1990s, reforms in British mathematics education introduced the chunking method of long division. Its ease is disputed.
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There is a strict mathematical terminology for the numbers involved in long division. The number that is to be divided is the dividend. The divisor is the number that is doing the division. The answer of the division is the quotient. Any number remaining after the quotient is the remainder
The traditional long division method involves multiplication and subtraction. When dividing the number 374 by 12, start with the first digit 3. This does not divide so include the second digit of the dividend to make 37. Divide this number by the divisor. The whole number result is 3 with a remainder of 1. Write 3 above the dividend. Multiply the whole number answer by the divisor to give 36. Write this below the dividend and subtract it from 37 to give the original remainder of 1. Bring down the number 4 from the dividend to make 14 and divide by 12. This gives an answer of 1 with a remainder of 2. Write 1 above the dividend to make a quotient of 31. The answer to the long division is 31 remainder 1.
The chunking method of long division was introduced in Britain in the late 1990s as an easier methodology than traditional long division. It involves a form of repeated subtraction of multiples of the divisor. When dividing 16 into 850, imagine 10 multiples of the divisor that make 160, and 20 multiples that make 320. Subtract two lots of 320, or 40 multiples from 850 in two stages to give a result of 210. Then subtract a further 10 multiples of the divisor, 160, from 210 to give and answer of 50. Subtract two multiples of the divisor from 50 to give 18, and subtract the divisor again from this result to give a final remainder of 2. The final answer to the division is the number of multiples of the divisors used, 53, and the remainder, making 53 remainder 2.
The issue on whether traditional or chunking methods, sometimes called toolbox methods, of long division are a matter of controversy among mathematics educators. According to London Mathematical Society forums, traditionalists claim that chunking is too tortured a technique, inefficient, and impossible to apply to long number or complicated problems. Proponents of chunking claim that traditional methods of long division of large numbers are a 19th century anachronism and unnecessary in the days of smart phone calculators.
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