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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
[12] [13] In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. [14] [15] It is said to be an improper fraction, or sometimes top-heavy fraction, [16] if the absolute value of the fraction is greater than or ...
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: + = + =
Systematic methods of computing the value of π exist. If one knows that π is approximately 3.14159, then it trivially follows that π < 22 / 7 , which is approximately 3.142857. But it takes much less work to show that π < 22 / 7 by the method used in this proof than to show that π is approximately 3.14159.
Applying the fundamental recurrence formulas we find that the successive numerators A n are {1, 2, 3, 5, 8, 13, ...} and the successive denominators B n are {1, 1, 2, 3, 5, 8, ...}, the Fibonacci numbers. Since all the partial numerators in this example are equal to one, the determinant formula assures us that the absolute value of the ...
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. By the same principle, 10 is the least common multiple of −5 and −2 as well.
2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ⁄ 5: 0.4 Vulgar Fraction Two Fifths 2156 8534 ⅗ 3 ⁄ 5: 0.6 Vulgar Fraction Three Fifths 2157 8535 ⅘ 4 ⁄ 5: 0.8 Vulgar Fraction Four Fifths 2158 8536 ⅙ 1 ⁄ 6: 0.166... Vulgar Fraction One Sixth 2159 8537 ⅚ 5 ⁄ 6: 0 ...
For instance, the primary pseudoperfect number 1806 is the product of the prime numbers 2, 3, 7, and 43, and gives rise to the Egyptian fraction 1 = 1 / 2 + 1 / 3 + 1 / 7 + 1 / 43 + 1 / 1806 .