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[2] In a sense, subtraction is the inverse of addition. That is, c = a − b if and only if c + b = a. In words: the difference of two numbers is the number that gives the first one when added to the second one. Subtraction follows several important patterns. It is anticommutative, meaning that changing the order changes the sign of the answer.
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 ...
Here, 7 − 9 = −2, so try (10 − 9) + 7 = 8, and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which this is commonly taught: The ten is moved from the next digit left, leaving in this example 3 − 1 in the tens column.
The sum of two numbers is unique; there is only one correct answer for a sums. [8] When the sum of a pair of digits results in a two-digit number, the "tens" digit is referred to as the "carry digit". [9] In elementary arithmetic, students typically learn to add whole numbers and may also learn about topics such as negative numbers and fractions.
For example, in the method addition with carries, the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to ...
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in base 10: 9981 – 1899 ...
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