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Chapter 1: Problem 33

For the following problems, perform each indicated operation. \(\frac{8}{15}-\frac{3}{10}\)

Short Answer

Expert verified
Answer: The result of the subtraction is \(\frac{7}{30}\).

Step by step solution

01

Find the common denominator

In order to subtract two fractions, they need to have the same denominator. To find the common denominator for \(\frac{8}{15}\) and \(\frac{3}{10}\), we need to find the least common multiple (LCM) of the denominators 15 and 10. The prime factors of 15 are 3 and 5, and the prime factors of 10 are 2 and 5. The LCM(15, 10) is the product of the highest powers of their prime factors, which is \(2\cdot3\cdot5=30\). So, the common denominator is 30.
02

Rewrite the fractions with the common denominator

Now that we have a common denominator of 30, we rewrite both fractions with this denominator: \(\frac{8}{15}\cdot\frac{2}{2}=\frac{8\cdot2}{15\cdot2}=\frac{16}{30}\) \(\frac{3}{10}\cdot\frac{3}{3}=\frac{3\cdot3}{10\cdot3}=\frac{9}{30}\) The subtraction then becomes: \(\frac{16}{30}-\frac{9}{30}\)
03

Subtract the numerators

With the same denominator, we can now subtract the numerators: \(\frac{16}{30}-\frac{9}{30}=\frac{16-9}{30}=\frac{7}{30}\)
04

Simplify if necessary

In this case, the fraction \(\frac{7}{30}\) is already simplified since 7 and 30 have no common factors other than 1. Thus, the result of the subtraction is: \(\frac{8}{15}-\frac{3}{10}=\frac{7}{30}\)

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