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Chapter 5: Problem 101

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\frac{\frac{7}{9}-3}{\frac{5}{6}} \div \frac{3}{2}+\frac{3}{4}\)

Short Answer

Expert verified
The simplified form of the expression is \(-\frac{19}{60}\).

Step by step solution

01

Subtraction

First, subtract \(3\) from \(\frac{7}{9}\). The number 3 can be written as \(\frac{27}{9}\) for us to be able to subtract it from \(\frac{7}{9}\). So our expression becomes: \(\frac{\frac{7}{9}-\frac{27}{9}}{\frac{5}{6}} \div \frac{3}{2}+\frac{3}{4}\). So, the result of the subtraction is -\(\frac{20}{9}\).
02

Division

Next perform the division operation: \(\frac{-\frac{20}{9}}{\frac{5}{6}} = -\frac{20}{9} 脳 \frac{6}{5} = -\frac{24}{15}\) simplified to be \(-\frac{8}{5}\). Then, divide this result by \(\frac{3}{2}\) to get \(-\frac{8}{5} 脳 \frac{2}{3} = -\frac{16}{15}\).
03

Addition

Lastly, add the result to \(\frac{3}{4}\), which gives us \(-\frac{16}{15}+\frac{3}{4} = -\frac{16}{15}+\frac{45}{60} = -\frac{64}{60}+\frac{45}{60} = -\frac{19}{60}\).

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