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Chapter 5: Problem 59

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(\left(-\frac{1}{10}\right)\left(\frac{7}{12}\right)\)

Short Answer

Expert verified
The answer is \(-\frac{7}{120}\).

Step by step solution

01

Recognizing the Signs

Recognize the signs of the two fractions in the equation. Since there is a negative sign before one fraction and no sign (implicitly positive) before the other, the result of their multiplication will also be a negative number.
02

Multiplying the Numerators

Multiply the numerators of the two fractions together. The numerator of the first fraction is 1 and the numerator of the second fraction is 7. So, their multiplication gives -1*7 = -7.
03

Multiplying the Denominators

Similarly, multiply the denominators of the two fractions together. The denominator of the first fraction is 10 and the denominator of the second fraction is 12. So, their multiplication gives 10*12 = 120.
04

Writing the Product as a Fraction

Write the multiplication result as a fraction. After multiplying the numerators and denominators, the result is -7/120.
05

Simplifying the Fraction

Note that the fraction -7/120 is already in its simplest form since there is no integer that can divide both -7 and 120 exactly. Hence, no need for further simplification.

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sequence \(1,4,8,13,19,26, \ldots\) is an arithmetic sequence.

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.

Simplify the square root. \(\sqrt{20}\)

Express each terminating decimal as a quotient of integers. If possible, reduce to lowest terms. \(0.82\)

Find the least common multiple of the numbers. 220 and 400
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