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Chapter 5: Problem 97

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\left(\frac{1}{2}-\frac{1}{3}\right) \div \frac{5}{8}\)

Short Answer

Expert verified
The simplified result of the operation is \(\frac{4}{15}\).

Step by step solution

01

Subtract Fractions

Begin with subtracting the two fractions within the parentheses. They have different denominators so find the least common multiple of 2 and 3, which is 6. Convert these fractions to equivalent fractions with a denominator of 6: \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{1}{3} = \frac{2}{6}\). Subtract these two fractions: \(\frac{3}{6} - \frac{2}{6} = \frac{1}{6}\).
02

Divide Fractions

To divide these fractions, multiply the first fraction by the reciprocal of the second fraction. A reciprocal of a fraction is obtained by swapping numerator and denominator. The reciprocal of \(\frac{5}{8}\) will be \(\frac{8}{5}\). So perform the multiplication: \(\frac{1}{6} * \frac{8}{5} = \frac{8}{30}\).
03

Reduce the Fraction to its Lowest Terms

The last step is to simplify the fraction to its lowest term. The numerator and the denominator of the fraction \(\frac{8}{30}\) have a common factor of 2. We divide both by 2 to get the simplified fraction: \(\frac{8}{30} = \frac{4}{15}\).

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{4}, r=2\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=0.1\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=18, r=-\frac{1}{3}\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{8}, r=-2\)
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