/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 Perform the indicated operations... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 77

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

Short Answer

Expert verified
\(\frac{7}{10}\)

Step by step solution

01

Find Common Denominator

To add or subtract fractions, a common denominator (the bottom number in a fraction) is needed. So, in order to add \(\frac{1}{2}\) and \(\frac{1}{5}\), their lowest common denominator must be found. The lowest common multiple of 2 and 5 is 10. Thus, 10 is their lowest common denominator.
02

Convert Fractions to Like Fractions

Next, the fractions \(\frac{1}{2}\) and \(\frac{1}{5}\) will be converted to like fractions (fractions with the common denominator). To do this, multiply the numerator and denominator of both fractions by the necessary number to make the denominator equal to 10. For \(\frac{1}{2}\), it is multiplied by 5 (top and bottom). So, \(\frac{1}{2} * \frac{5}{5} = \frac{5}{10}\). For \(\frac{1}{5}\), it is multiplied by 2 (top and bottom). So, \(\frac{1}{5} * \frac{2}{2} = \frac{2}{10}\). So, \(\frac{1}{2}\) becomes \(\frac{5}{10}\) and \(\frac{1}{5}\) becomes \(\frac{2}{10}\).
03

Add the Like Fractions

Now that we have like fractions, they can be added together. Add the numerators and write the sum over the common denominator: \(\frac{5}{10} + \frac{2}{10} = \frac{7}{10}\).
04

Simplify the Result

The result of the sum of the fractions, \(\frac{7}{10}\), cannot be simplified any further as 7 and 10 do not have any common factors other than 1. Therefore, \(\frac{7}{10}\) is in its simplest form.

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Most popular questions from this chapter

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

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

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of California for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 33.87 & 34.21 & 34.55 & 34.90 & 35.25 & 35.60 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 36.00 & 36.36 & 36.72 & 37.09 & 37.25 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that California has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling California's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project California's population, in millions, for the year 2020 . Round to two decimal places.

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.

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