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Chapter 5: Problem 7

Reduce each rational number to its lowest terms. \(\frac{60}{108}\)

Short Answer

Expert verified
The fraction \( \frac{60}{108} \) reduces to \( \frac{5}{9} \) in its lowest terms.

Step by step solution

01

Determining the Greatest Common Divisor (GCD)

The numerator in the fraction is 60, and the denominator is 108. The first step is to find the GCD of 60 and 108. This can be done using a variety of methods, including the Euclidean algorithm, prime factorization, or simple observation. In the case of 60 and 108, the GCD is 12.
02

Dividing by the GCD

After determining the GCD, the next step is to divide both the numerator and the denominator of the fraction by the GCD. So, divide 60 by 12 to get the new numerator, and divide 108 by 12 to get the new denominator. This results in: \( \frac{60}{12} \) / \( \frac{108}{12} \) = \( \frac{5}{9} \)
03

Verification

To verify that the fraction is indeed in lowest terms, attempt to find any common factors shared by the numerator and the denominator. In this case, 5 and 9 share no common factors other than 1. This confirms that \( \frac{5}{9} \) is the fraction \( \frac{60}{108} \) reduced to its lowest terms

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-9,-5,-1,3, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=1000, r=1\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a sequence is geometric, we can write as many terms as we want by repeatedly multiplying by the common ratio.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{5}, 5,5 \sqrt{5}, 25, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)
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