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Chapter 5: Problem 93

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(-5 \frac{2}{3}+3 \frac{1}{6}\)

Short Answer

Expert verified
-1 \frac{1}{6}

Step by step solution

01

Convert mixed numbers to improper fractions

The first step is to convert the mixed numbers into improper fractions. Here's how: Multiply the whole number by the denominator and then add the numerator to get the new numerator. The denominator remains the same. A mixed number can be converted to an improper fraction by using the formula: \(a \frac{b}{c} = \frac{a*c+b}{c}\). So, \(-5 \frac{2}{3} = \frac{-5*3+2}{3} = \frac{-13}{3}\) and \(3 \frac{1}{6} = \frac{3*6+1}{6} = \frac{19}{6}\)
02

Addition of improper fractions

The next step is to add the two improper fractions. The common denominator of 3 and 6 is 6. So, convert \(-\frac{13}{3}\) to a fraction with 6 as denominator by multiplying the numerator and the denominator by 2. We have \(-\frac{13}{3} = -\frac{26}{6}\). Now both fractions have the same denominator and can be added together. The addition \(-\frac{26}{6} + \frac{19}{6} = -\frac{7}{6}\)
03

Convert the improper fraction back to a mixed number

The last step is to convert the result back into a mixed number. The number -7 divided by 6 gives -1 as quotient and 1 as the remainder. So, the mixed number is -1 \frac{1}{6}. This fraction cannot be reduced further and is in the 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. \(7,-7,7,-7, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{5}, r=\frac{1}{2}\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=-3\)

What is an arithmetic sequence? Give an example with your description.
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