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Chapter 5: Problem 88

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{4}{15}-\frac{1}{6}\)

Short Answer

Expert verified
The result of the operation \(\frac{4}{15}-\frac{1}{6}\) is \(\frac{1}{10}\)

Step by step solution

01

Find a Common Denominator

In order to subtract two fractions, they must have the same denominator. Find a common denominator for \(\frac{4}{15}\) and \(\frac{1}{6}\). The easiest way to do this is by multiplying the two denominators together. In this case, \(15*6 = 90\), so the common denominator is 90.
02

Rewrite the Fractions with a Common Denominator

Rewrite the fractions so that each fraction has the common denominator. Multiply the numerator and denominator of each fraction by the number that was multiplied to the original denominator to get the common denominator. \(\frac{4}{15}*6 = \frac{24}{90}\) and \(\frac{1}{6}*15 = \frac{15}{90}\)
03

Perform Subtraction

Now that both fractions have the same denominator, subtract the second fraction from the first by subtracting their numerators. The denominator stays the same. \(\frac{24}{90} - \frac{15}{90} = \frac{9}{90}\)
04

Simplify the Result

When possible, simplify the resulting fraction to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator, and dividing them by it. GCD of 9 and 90 is 9. \(\frac{9}{90} = \frac{1}{10}\) when divided by 9.

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