Carry (arithmetic)
In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow.
Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer.
Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder circuits.
A typical example of carry is in the following pencil-and-paper addition:
7 + 9 = 16, and the digit 1 is the carry.
The opposite is a borrow, as in
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:
Traditionally, carry is taught in the addition of multi-digit numbers in the 2nd or late first year of elementary school. However, since the late 20th century, many widely adopted curricula developed in the United States such as TERC omitted instruction of the traditional carry method in favor of invented arithmetic methods, and methods using coloring, manipulatives, and charts. Such omissions were criticized by such groups as Mathematically Correct, and some states and districts have since abandoned this experiment, though it remains widely used.
Kummer's theorem states that the number of carries involved in adding two numbers in base is equal to the exponent of the highest power of dividing a certain binomial coefficient.
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