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If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right (or to the left), so that the decimal of the divisor is to the right of the last digit. When doing long division, keep the numbers lined up straight from top to bottom under the tableau.
30,561 10 3,G81 20 ÷ ÷ ÷ 61 10 31 20 = = = 501 10 151 20 30,561 10 ÷ 61 10 = 501 10 3,G81 20 ÷ 31 20 = 151 20 ÷ = (black) The divisor goes into the first two digits of the dividend one time, for a one in the quotient. (red) fits into the next two digits once (if rotated), so the next digit in the quotient is a rotated one (that is, a five). (blue) The last two digits are matched once for ...
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
A subtraction problem such as is solved by borrowing a 10 from the tens place to add to the ones place in order to facilitate the subtraction. Subtracting 9 from 6 involves borrowing a 10 from the tens place, making the problem into +. This is indicated by crossing out the 8, writing a 7 above it, and writing a 1 above the 6.
Depending on the elementary school, third grade students may even begin to work on long division, such as dividings in the double digits, hundreds, and thousands. Decimals (to tenths only) are sometimes introduced. Students begin to work on problem-solving skills working to explain their thinking in mathematical terms.
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