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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.
Quotition is the concept of division most used in measurement. For example, measuring the length of a table using a measuring tape involves comparing the table to the markings on the tape. This is conceptually equivalent to dividing the length of the table by a unit of length, the distance between markings.
In modular arithmetic, unit fractions can be converted into equivalent whole numbers, allowing modular division to be transformed into multiplication. Every rational number can be represented as a sum of distinct unit fractions; these representations are called Egyptian fractions based on their use in ancient Egyptian mathematics. Many infinite ...
Decimal numbers are not divided directly, the dividend and divisor are multiplied by a power of ten so that the division involves two whole numbers. Therefore, if one were dividing 12,7 by 0,4 (commas being used instead of decimal points), the dividend and divisor would first be changed to 127 and 4, and then the division would proceed as above.
Integer arithmetic is not closed under division. This means that when dividing one integer by another integer, the result is not always an integer. For instance, 7 divided by 2 is not a whole number but 3.5. [73] One way to ensure that the result is an integer is to round the result to a whole number.
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
Police say a TikTok video post has led to the capture of a Florida man who was on the run for more than three years after he allegedly lured his estranged girlfriend to a cemetery where he killed her.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
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