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Chapter 5: Problem 96

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(-1 \frac{4}{9}-\left(-2 \frac{5}{18}\right)\)

Short Answer

Expert verified
The answer to the given exercise is -\( \frac{11}{18} \).

Step by step solution

01

Separate the Whole Numbers and the Fractions

Observe the two given mixed fractions: -1 and -4/9, also -2 and -5/18. The fractions also have a negative sign before them due to bracket rules of math. Now, you ignore the negative signs temporarily and separate the fractions and the whole numbers: -1 (whole number) - 4/9 (fraction) and -2 (whole number) - 5/18 (fraction)
02

Subtract the Whole Numbers

Subtract -1 from -2 which gives 1 because subtracting a negative number is the same as adding the positive counterpart. So, -1 - (-2) becomes -1 + 2 = 1.
03

Find Common Denominator and Subtract the Fractions

Next, subtract the fractions. To do this, find a common denominator between 9 and 18. In this case, 18 will be the common denominator. To match the denominators, multiply 4/9 by 2/2 to make the fraction 8/18. Now, subtract 8/18 from -5/18. That results in -13/18 because subtracting a positive number from a negative is the same as adding a posive one to a negative. So, 8/18 - (-5/18) becomes 8/18 + 5/18 = 13/18.
04

Combine Whole Number and Fraction

Now combine the whole number '1' and the fraction '-13/18'. The result is 1 - 13/18 or -\( \frac{11}{18} \) since 1 can be written as 18/18 and subtracting 13/18 from 18/18 will give us -5/18.

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{20}\), when \(a_{1}=2, r=3\).

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{7}\), when \(a_{1}=4, r=2\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=4, r=2\)

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 Texas for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{array}{|l|l|l|l|l|l|l|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 20.85 & 21.27 & 21.70 & 22.13 & 22.57 & 23.02 \\ \hline \end{array} $$ $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 23.48 & 23.95 & 24.43 & 24.92 & 25.15 \\ \hline \end{array} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that Texas has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling Texas's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project Texas's population, in millions, for the year 2020 . Round to two decimal places.
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