Section 1
Symbols and Sets of Numbers
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10. 410
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10.85
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10. 73
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10. 915
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10.$6.26 \quad 6.26$
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10.$1.13 \quad 1.13$
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10. $0 \quad 7$
Objectives A C Mixed Practice Insert $<,>$, or $=$ in the space between the paired numbers to make each statement true. See Examples 1 through 6 and 10.200
The freezing point of water is $32^{\circ}$ Fahrenheit. The boiling point of water is $212^{\circ}$ Fahrenheit. Write an inequality statement using $<$ or $>$ comparing the numbers 32 and 212.
The freezing point of water is $0^{\circ}$ Celsius. The boiling point of water is $100^{\circ}$ Celsius. Write an inequality statement using $<$ or $>$ comparing the numbers 0 and 100.
An angle measuring $30^{\circ}$ and an angle measuring $45^{\circ}$ are shown. Write an inequality statement using $\leq$ or $\gtrsim$ comparing the numbers 30 and 45 .
The sum of the measures of the angles of a parallelogram is $360^{\circ}$. The sum of the measures of the angles of a triangle is $180^{\circ}$. Write an inequality statement using $\leq$ or $\geqq$ comparing the numbers 360 and 180 .
Determine whether each statement is true or false. See Examples 1 through 6 and 10. $11 \leq 11$
Determine whether each statement is true or false. See Examples 1 through 6 and 10.$8 \geq 9$
Determine whether each statement is true or false. See Examples 1 through 6 and 10. $-11>-10$
Determine whether each statement is true or false. See Examples 1 through 6 and 10. $-16>-17$
Determine whether each statement is true or false. See Examples 1 through 6 and 10.$5.092<5.902$
Determine whether each statement is true or false. See Examples 1 through 6 and 10. $1.02>1.021$
Determine whether each statement is true or false. See Examples 1 through 6 and 10.$\frac{9}{10} \leq \frac{8}{9}$
Determine whether each statement is true or false. See Examples 1 through 6 and 10.$\frac{4}{5} \leq \frac{9}{11}$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10. $25 \geq 20$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10. $-13 \leq 13$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10. $0<6$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10. $5>3$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10.$-10>-12$
Rewrite each inequality so that the inequality symbol points in the opposite direction and the resulting statement has the same meaning as the given one. See Examples 1 through 6 and 10. $-4<-2$
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7. Seven is less than eleven.
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7. Twenty is greater than two.
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7. Five is greater than or equal to four.
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7.Negative ten is less than or equal to thirty-seven.
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7. Fifteen is not equal to negative two.
Objectives B C Mixed Practice-Translating Write each sentence as a mathematical statement. See Example 7. Negative seven is not equal to seven.
Use integers to represent the value(s) in each statement. See Example 8. The highest elevation in California is Mt. Whitney, with an altitude of 14,494 feet. The lowest elevation in California is Death Valley, with an altitude of 282 feet below sea level. (Source: U.S. Geological Survey)
Use integers to represent the value(s) in each statement. See Example 8.Driskill Mountain, in Louisiana, has an altitude of 535 feet. New Orleans, Louisiana, lies 8 feet below sea level. (Source: U.S. Geological Survey)
Use integers to represent the value(s) in each statement. See Example 8.The number of graduate students at the University of Texas at Austin was 28,288 fewer than the number of undergraduate students. (Source: University of Texas at Austin, 2016)
Use integers to represent the value(s) in each statement. See Example 8.The number of students admitted to the class of 2020 at UCLA was 79,647 fewer students than the number that had applied. (Source: UCLA, 2016)
Use integers to represent the value(s) in each statement. See Example 8. A community college student deposited $$\$ 475$$ in her savings account. She later withdrew $$\$ 195$$.
Use integers to represent the value(s) in each statement. See Example 8.A deep-sea diver ascended 17 feet and later descended 15 feet.
Graph each set of numbers on the number line. See Example 9.$-4,0,2,-2$
Graph each set of numbers on the number line. See Example 9. $-3,0,1,-5$
Graph each set of numbers on the number line. See Example 9.$-2,4, \frac{1}{3},-\frac{1}{4}$
Graph each set of numbers on the number line. See Example 9.$-5,3,-\frac{1}{3}, \frac{7}{8}$
Graph each set of numbers on the number line. See Example 9. $-4.5, \frac{7}{4}, 3.25,-\frac{3}{2}$
Graph each set of numbers on the number line. See Example 9.$4.5,-\frac{9}{4}, 1.75,-\frac{7}{2}$
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11. 0
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11.$\frac{1}{4}$
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11. -7
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11.$-\frac{1}{7}$
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11.265
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11. 7941
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11. $\frac{2}{3}$
Tell which set or sets each number belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. See Example 11. $\sqrt{3}$
Determine whether each statement is true or false.Every rational number is also an integer.
Determine whether each statement is true or false. Every natural number is positive.
Determine whether each statement is true or false. 0 is a real number.
Determine whether each statement is true or false.$\frac{1}{2}$ is an integer.
Determine whether each statement is true or false.Every negative number is also a rational number.
Determine whether each statement is true or false.Every rational number is also a real number.
Determine whether each statement is true or false.Every real number is also a rational number.
Determine whether each statement is true or false.Every whole number is an integer.
Objective D Find each absolute value. See Example 12.$|8.9|$
Objective D Find each absolute value. See Example 12. $|11.2|$
Objective D Find each absolute value. See Example 12. $|-20|$
Objective D Find each absolute value. See Example 12. $|-17|$
Objective D Find each absolute value. See Example 12.$\left|\frac{9}{2}\right|$
Objective D Find each absolute value. See Example 12. $\left|\frac{10}{7}\right|$
Objective D Find each absolute value. See Example 12. $\left|-\frac{12}{13}\right|$
Objective D Find each absolute value. See Example 12.$\left|-\frac{1}{15}\right|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13.$|-5| \quad-4$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13. $|-12|$ $|0|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13. $\left|-\frac{5}{8}\right| \quad\left|\frac{5}{8}\right|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13.$\left|\frac{2}{5}\right| \quad\left|-\frac{2}{5}\right|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13.$|-2| \quad|-2.7|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13.$|-5.01| \quad|-5|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13. $|0| \quad|-8|$
Insert $<,>$, or $=$ in the appropriate space to make each statement true. See Examples 12 and 13. $|-12| \frac{-24}{2}$
Perform each indicated operation. See Section 1.9. $90+12^2-5^3$
Perform each indicated operation. See Section 1.9.$3 \cdot(7-4)+2 \cdot 5^2$
Perform each indicated operation. See Section 1.9.$12 \div 4-2+7$
Perform each indicated operation. See Section 1.9.$12 \div(4-2)+7$
The bar graph shows corn production from the top six corn-producing states. (Source: National Agricultural Statistics Service) Write an inequality comparing the corn production in Illinois with the corn production in Iowa.
The bar graph shows corn production from the top six corn-producing states. (Source: National Agricultural Statistics Service)Write an inequality comparing the corn production in Minnesota with the corn production in South Dakota.
The bar graph shows corn production from the top six corn-producing states. (Source: National Agricultural Statistics Service)Determine the difference between the corn production in Nebraska and the corn production in Illinois.
The bar graph shows corn production from the top six corn-producing states. (Source: National Agricultural Statistics Service)Determine the difference between the corn production in Indiana and the corn production in Minnesota.
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90. The apparent magnitude of the sun is -26.7 . The apparent magnitude of the star Arcturus is -0.04 . Write an inequality statement comparing the numbers -0.04 and -26.7 .
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90. The apparent magnitude of Antares is 0.96 . The apparent magnitude of Spica is 0.98 . Write an inequality statement comparing the numbers 0.96 and 0.98 .
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90. Which is brighter, the sun or Arcturus?
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90.Which is dimmer, Antares or Spica?
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90. Which star listed is the brightest?
The apparent magnitude of a star is the measure of its brightness as seen by someone on Earth. The smaller the apparent magnitude, the brighter the star. Below, the apparent magnitudes of some stars are listed. Use this table to answer Exercises 85 through 90.Which star listed is the dimmest?
In your own words, explain how to find the absolute value of a number.
Give an example of a real-life situation that can be described with integers but not with whole numbers.