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For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. [2] As another example, if a × b = a × c , then the multiplicative term a can be canceled out if a ≠0, resulting in the equivalent expression b = c ; this is equivalent to dividing through by a .
Because of the identity property of multiplication, multiplying any quantity (physical or not) by the dimensionless 1 does not change that quantity. [5] Once this and the conversion factor for seconds per hour have been multiplied by the original fraction to cancel out the units mile and hour, 10 miles per hour converts to 4.4704 metres per second.
A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of, [22] [23] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see § Multiplication).
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Several algorithms in number theory and cryptography use differences of squares to find factors of integers and detect composite numbers. A simple example is the Fermat factorization method , which considers the sequence of numbers x i := a i 2 − N {\displaystyle x_{i}:=a_{i}^{2}-N} , for a i := ⌈ N ⌉ + i {\displaystyle a_{i}:=\left\lceil ...
The subtracting of two nearly equal numbers is called subtractive cancellation. [3] When the leading digits are cancelled, the result may be too small to be represented exactly and it will just be represented as 0 {\displaystyle 0} .
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