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Chapter 5: Problem 91

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

Short Answer

Expert verified
The answer is \(1 \frac{1}{6}\)

Step by step solution

01

Converting Mixed Numbers into Improper Fractions

First, convert each mixed number into an improper fraction. For the first mixed number \(3 \frac{2}{3}\), you multiply the whole number 3 by the denominator 3 and then add the numerator. This gives \(3*3+2 = 11\). So, \(3 \frac{2}{3}\) is \(\frac{11}{3}\). Similarly, for the second mixed number \(2 \frac{1}{2}\), you multiply the whole number 2 by the denominator 2 and add the numerator. This gives \(2*2+1 = 5\). So, \(2 \frac{1}{2}\) is \(\frac{5}{2}\).
02

Performing the Subtraction Operation

We now have the equivalent exercise: \(\frac{11}{3} - \frac{5}{2} = x\). To subtract fractions we need a common denominator. For 3 and 2, the least common denominator is 6. Multiply each fraction by a suitable factor so that both fractions have the same denominator, then subtract the two fractions. This gives: \(\frac{22}{6} - \frac{15}{6} = \frac{7}{6}\).
03

Reducing the Answer to Its Lowest Terms

\(\frac{7}{6}\) is already in its lowest terms as an improper fraction but it can also be expressed as a mixed number. To do this, divide the numerator by the denominator. This gives us the whole number \(1\) and the remainder \(1\) is the new numerator. So, in the final answer the mixed number, it is \(1 \frac{1}{6}\)

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?

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

You are offered a job that pays $$\$ 30,000$$ for the first year with an annual increase of \(5 \%\) per year beginning in the second year. That is, beginning in year 2 , your salary will be \(1.05\) times what it was in the previous year. What can you expect to earn in your sixth year on the job? Round to the nearest dollar.

What is the common ratio in a geometric sequence?
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