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Use Negatives and Opposites of Integers
In the following exercises, order each of the following pairs of numbers, using<or>.
ⓐ
$9\_\_\_4$
ⓑ
$\mathrm{-3}\_\_\_6$
ⓒ
$\mathrm{-8}\_\_\_\mathrm{-2}$
ⓓ
$1\_\_\_\mathrm{-10}$
ⓐ > ⓑ < ⓒ < ⓓ >
ⓐ
$\mathrm{-7}\_\_\_3$
ⓑ
$\mathrm{-10}\_\_\_\mathrm{-5}$
ⓒ
$2\_\_\_\mathrm{-6}$
ⓓ
$8\_\_\_9$
In the following exercises, find the opposite of each number.
ⓐ 9
ⓑ
$\mathrm{-4}$
In the following exercises, simplify.
$\text{\u2212}\left(\mathrm{-8}\right)$
$\text{\u2212}\left(\mathrm{-11}\right)$
In the following exercises, evaluate.
$\text{\u2212}c$ when
ⓐ
$c=12$
ⓑ
$c=\mathrm{-12}$
ⓐ $\mathrm{-12}$ ⓑ 12
$\text{\u2212}d$ when
ⓐ
$d=21$
ⓑ
$d=\mathrm{-21}$
Simplify Expressions with Absolute Value
In the following exercises, simplify.
ⓐ
$\left|\mathrm{-32}\right|$
ⓑ
$\left|0\right|$
ⓒ
$\left|16\right|$
ⓐ 32 ⓑ 0 ⓒ 16
ⓐ
$\left|0\right|$
ⓑ
$\left|\mathrm{-40}\right|$
ⓒ
$\left|22\right|$
In the following exercises, fill in<,>, or $=$ for each of the following pairs of numbers.
ⓐ
$\mathrm{-6}\_\_\_\left|\mathrm{-6}\right|$
ⓑ
$\text{\u2212}\left|\mathrm{-3}\right|\_\_\_\mathrm{-3}$
ⓐ < ⓑ $=$
ⓐ
$\left|\mathrm{-5}\right|\_\_\_\text{\u2212}\left|\mathrm{-5}\right|$
ⓑ
$9\_\_\_\text{\u2212}\left|\mathrm{-9}\right|$
In the following exercises, simplify.
$\text{\u2212}\left(\mathrm{-5}\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{\u2212}\left|\mathrm{-5}\right|$
$5,\mathrm{-5}$
$\text{\u2212}\left|\mathrm{-9}\right|\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{\u2212}\left(\mathrm{-9}\right)$
$5\left|\mathrm{-5}\right|$
$\left|17-8\right|-\left|13-4\right|$
$18-\left|3\left(8-5\right)\right|$
In the following exercises, evaluate.
ⓐ
$\text{\u2212}\left|p\right|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}p=19$
ⓑ
$\text{\u2212}\left|q\right|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}q=\mathrm{-33}$
ⓐ $\mathrm{-19}$ ⓑ $\mathrm{-33}$
ⓐ
$\text{\u2212}\left|a\right|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}a=60$
ⓑ
$\text{\u2212}\left|b\right|\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}b=\mathrm{-12}$
Add Integers
In the following exercises, simplify each expression.
$\mathrm{-35}+\left(\mathrm{-47}\right)$
$34+\left(\mathrm{-19}\right)$
$\mathrm{-17}+\left(\mathrm{-18}\right)+6$
6 $\mathrm{-38}+27+\left(\mathrm{-8}\right)+126$
$24+3\left(\mathrm{-5}+9\right)$
Subtract Integers
In the following exercises, simplify.
$\mathrm{-6}-\left(\mathrm{-4}\right)$
$\mathrm{-7}-2$
$7-\left(\mathrm{-3}\right)$
ⓐ
$35-16$
ⓑ
$35+\left(\mathrm{-16}\right)$
ⓐ
$46-\left(\mathrm{-37}\right)$
ⓑ
$46+37$
In the following exercises, simplify each expression.
$14-\left(\mathrm{-11}\right)$
$\mathrm{-19}-46$
$\mathrm{-105}-\left(\mathrm{-68}\right)$
$\mathrm{-58}-\left(\mathrm{-67}\right)$
$\mathrm{-3}-8+4$
$64+\left(\mathrm{-17}\right)-9$
$\left(1-8\right)-\left(2-9\right)$
$\text{\u2212}\left(4-5\right)-\left(7-8\right)$
$32-\left[5-\left(15-20\right)\right]$
$5.7-8.2-4.9$
${6}^{2}-{7}^{2}$
Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level.
Use integers to write the elevation of:
ⓐ Mount McKinley.
ⓑ Death Valley.
ⓐ 20,329 ⓑ $\mathrm{-282}$
Extreme temperatures The highest recorded temperature on Earth was $58\text{\xb0}$ Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was $90\text{\xb0}\phantom{\rule{0.2em}{0ex}}\text{below}\phantom{\rule{0.2em}{0ex}}0\text{\xb0}$ Celsius, recorded in Antarctica in 1983.
Use integers to write the:
State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion.
Use integers to write the budget of:
ⓐ Pennsylvania.
ⓑ Texas.
ⓐ $540 million ⓑ $\text{\u2212}\mathrm{\$27}$ billion
College enrollments Across the United States, community college enrollment grew by 1,400,000 students from Fall 2007 to Fall 2010. In California, community college enrollment declined by 110,171 students from Fall 2009 to Fall 2010.
Use integers to write the change in enrollment:
Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:
Monday | $\mathrm{-504}$ |
Tuesday | $+142$ |
Wednesday | $\mathrm{-449}$ |
Thursday | $+410$ |
Friday | $+369$ |
What was the overall change for the week? Was it positive or negative?
$\mathrm{-32}$
Stock Market During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:
Monday | $\mathrm{-201}$ |
Tuesday | $\mathrm{-16}$ |
Wednesday | $\mathrm{-23}$ |
Thursday | $+172$ |
Friday | $\mathrm{-34}$ |
What was the overall change for the week? Was it positive or negative?
Give an example of a negative number from your life experience.
Answers may vary
What are the three uses of the $\text{\u201c}-\text{\u201d}$ sign in algebra? Explain how they differ.
Explain why the sum of $\mathrm{-8}$ and 2 is negative, but the sum of 8 and $\mathrm{-2}$ is positive.
Answers may vary
Give an example from your life experience of adding two negative numbers.
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?
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