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To calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away "chunks" of the large number, where each "chunk" is an easy multiple (for example 100×, 10×, 5× 2×, etc.) of the small number, until the large number has been reduced to zero – or the remainder is less than the small ...
In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
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.
An example of long division performed without a calculator. A more detailed breakdown of the steps goes as follows: Find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once. In this case, this is simply the first digit, 5.
The quotient and remainder can then be determined as follows: Divide the first term of the dividend by the highest term of the divisor (meaning the one with the highest power of x, which in this case is x). Place the result above the bar (x 3 ÷ x = x 2).
In mathematics, a rate is the quotient of two quantities, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses the corresponding rate of change ...
For example, the divisor 3 may be subtracted up to 6 times from the dividend 20, before the remainder becomes negative: 20 − 3 − 3 − 3 − 3 − 3 − 3 ≥ 0, while 20 − 3 − 3 − 3 − 3 − 3 − 3 − 3 < 0. In this sense, a quotient is the integer part of the ratio of two numbers. [9]
For example, through the standard addition algorithm, the sum can be obtained by following three rules: a) line up the digits of each addend by place value, longer digit addends should go on top, b) each addend can be decomposed -- ones are added with ones, tens are added with tens, and so on, and c) if the sum of the digits of the current place value is ten or greater, then the number must be ...