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In mathematics, students are usually introduced to multiplication and division facts, place value to thousands or ten thousands, and estimation.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.
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps.
For division to always yield one number rather than an integer quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers. In these enlarged number systems, division is the inverse operation to multiplication, that is a = c / b means a × b = c, as long as b is not zero.
Third grade: 8–9 3rd grade Fourth grade: 9–10 4th grade Fifth grade: 10–11 5th grade Sixth grade: 11–12 6th grade Seventh grade: 12–13 1st grade Gymnasium (Lower secondary school) (US equivalent: Middle school) Eighth grade: 13–14 2nd grade Ninth grade: 14–15 3rd grade Tenth grade: 15–16 1st grade Lyceum (Upper secondary school)
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.
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