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Like whole numbers, fractions obey the commutative, associative, and distributive laws, and the rule against division by zero. Mixed-number arithmetic can be performed either by converting each mixed number to an improper fraction, or by treating each as a sum of integer and fractional parts.
Logarithm tables can be used to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result. Division can be calculated with a slide rule by aligning the divisor on the C scale with the dividend on the D scale. The quotient can be found on the D scale where it is aligned with the left index on ...
Animated example of multi-digit long division. A divisor of any number of digits can be used. In this example, 1260257 is to be divided by 37. First the problem is set up as follows: 37)1260257 Digits of the number 1260257 are taken until a number greater than or equal to 37 occurs. So 1 and 12 are less than 37, but 126 is greater.
The quotitive concept of division lends itself to calculation by repeated subtraction: dividing entails counting how many times the divisor can be subtracted before the dividend runs out. Because no finite number of subtractions of zero will ever exhaust a non-zero dividend, calculating division by zero in this way never terminates. [3]
The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; [2] [3] this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that ...
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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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.