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In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets
Download as PDF; Printable version ... hide. 4/9 may refer to: April 9 (month-day ... Commons Attribution-ShareAlike 4.0 License; additional terms may ...
Height functions allow mathematicians to count objects, such as rational points, that are otherwise infinite in quantity.For instance, the set of rational numbers of naive height (the maximum of the numerator and denominator when expressed in lowest terms) below any given constant is finite despite the set of rational numbers being infinite. [2]
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.
So we can write a = 2c, where c is also an integer. Substitution into the original equation yields 2b 2 = (2c) 2 = 4c 2. Dividing both sides by 2 yields b 2 = 2c 2. But then, by the same argument as before, 2 divides b 2, so b must be even. However, if a and b are both even, they have 2 as a common factor.
The big hint here is the use of the verb "reduce": one reduces fractions to a lowest common denominator, whereas one would *find* or *calculate* the lowest common denominator of a set of integers. I would have thought it obvious that in this metaphorical use, people are being compared to fractions and by "reducing us to the lowest common ...
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple. The product of the denominators is always a common denominator, as in: + = + =