Section 1
An Introduction to the Integers
Fill in the blanks._____ numbers are greater than 0 and _____ numbers are less than $0 .$
Fill in the blanks.$\{\ldots,-5,-4,-3,-2,-1,0,1,2,3,4,5, \ldots\}$ is called the set of _____.
Fill in the blanks.To ____ an integer means to locate it on the number line and highlight it with a dot.
Fill in the blanks.The symbols $>$ and $<$ are called _______ symbols.
Fill in the blanks.The _____ _____ of a number is the distance between the number and 0 on the number line.
Fill in the blanks.Two numbers that are the same distance from 0 on the number line, but on opposite sides of it, are called _____.
Represent each of these situations using a signed number.a. $\$ 225$ overdrawnb. 10 seconds before liftoffc. 3 degrees below normald. A deficit of $\$ 12,000$e. A 1 -mile retreat by an army
Represent each of these situations using a signed number, and then describe its opposite in words.a. $A$ trade surplus of $\$ 3$ millionb. A bacteria count 70 more than the standardc. A profit of $\$ 67$d. A business $\$ 1$ million in the "black"e. 20 units over their quota
Determine what is wrong with each number line.
a. If a number is less than $0,$ what type of number must it be?b. If a number is greater than $0,$ what type of number must it be?
On the number line, what number isa. 3 units to the right of $-7 ?$b. 4 units to the left of $2 ?$
Name two numbers on the number line that are a distance ofa. 5 away from $-3$b. 4 away from 3
a. Which number is closer to $-3$ on the number line: 2 or $-7 ?$b. Which number is farther from 1 on the number line: $-5$ or $8 ?$
Is there a number that is both greater than 10 and less than 10 at the same time?
a. Express the fact $-12<15$ using an $>$ symbol.b. Express the fact $-4>-5$ using an $<$ symbol.
Fill in the blank: The opposite of the _____ of a number is that number. For any number $a,-(-a)=$.
Complete the table by finding the opposite and the absolute value of the given numbers.(TABLES NOT COPY)
Is the absolute value of a number always positive?
Translate each phrase to mathematical symbols.a. The opposite of negative eightb. The absolute value of negative eightc. Eight minus eightd. The opposite of the absolute value of negative eight
a. Write the set of integers.b. Write the set of positive integers.c. Write the set of negative integers.
Fill in the blanks.a. We read $\geq$ as "is _____ than or to."b. We read $\leq$ as "is _____ than or to."
Which of the following expressions contains a minus sign?$$15-8 \quad-(-15) \quad-15$$
Graph the following numbers on a number line.$$-3,4,3,0,-1$$
Graph the following numbers on a number line.$$2,-4,5,1,-1$$
Graph the following numbers on a number line.The integers that are less than 3 but greater than $-5$
Graph the following numbers on a number line.The integers that are less than 4 but greater than $-3$
Graph the following numbers on a number line.The opposite of $-3,$ the opposite of $5,$ and the absolute value of $-2$
Graph the following numbers on a number line.The absolute value of $3,$ the opposite of $3,$ and the number that is 1 less than $-3$
Graph the following numbers on a number line.2 more than $0,4$ less than $0,2$ more than negative 5 and 5 less than 4
Graph the following numbers on a number line.4 less than $0,1$ more than $0,2$ less than $-2$ and 6 more than $-4$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-5 \quad 5$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$0 \quad-1$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-12 \quad-6$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-7 \quad-6$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-10-17$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-11 \quad-20$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-325 \quad-532$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-401 \quad-104$$
Tell whether each statement is true or false.$$-15 \leq-14$$
Tell whether each statement is true or false.$$-77 \leq-76$$
Tell whether each statement is true or false.$$210 \geq 210$$
Tell whether each statement is true or false.$$37 \geq 37$$
Tell whether each statement is true or false.$$-1,255 \geq-1,254$$
Tell whether each statement is true or false.$$-6,546 \geq-6,465$$
Tell whether each statement is true or false.$$0 \leq-8$$
Tell whether each statement is true or false.$$-6 \leq-6$$
Find each absolute value.$$|9|$$
Find each absolute value.$$|12|$$
Find each absolute value.$$|-8|$$
Find each absolute value.$$|-1|$$
Find each absolute value.$$|-14|$$
Find each absolute value.$$|-85|$$
Find each absolute value.$$|180|$$
Find each absolute value.$$|371|$$
Simplify each expression.$$-(-11)$$
Simplify each expression.$$-(-1)$$
Simplify each expression.$$-(-4)$$
Simplify each expression.$$-(-9)$$
Simplify each expression.$$-(-102)$$
Simplify each expression.$$-(-295)$$
Simplify each expression.$$-(-561)$$
Simplify each expression.$$-(-703)$$
Simplify each expression.$$-|20|$$
Simplify each expression.$$-|143|$$
Simplify each expression.$$-|6|$$
Simplify each expression.$$-|0|$$
Simplify each expression.$$-|-253|$$
Simplify each expression.$$-|-11|$$
Simplify each expression.$$-|-0|$$
Simplify each expression.$$-|97|$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$|-12|-(-7)$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$|-50|-(-40)$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-|-71|-|-65|$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-|-163|-|-150|$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-(-343) \quad-(-161)$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-(-999) \quad-(-998)$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-|-30|-|-(-8)|$$
Place an $<$ or an $>$ symbol in the box to make a true statement.$$-|-100|-|-(-88)|$$
Write the integers in order, from least to greatest.$$82,-52,52,-22,12,-12$$
Write the integers in order, from least to greatest.$$49,-9,19,-39,89,-49$$
Fill in the blanks to continue each pattern.$$5,3,1,-1, \quad ,\quad , \quad ...$$
Fill in the blanks to continue each pattern.$$4,2,0,-2,\quad ,\quad , \quad ...$$
In the 1973 Belmont Stakes, Secretariat won by 31 lengths over second place finisher, Twice a Prince. Some experts call it the greatest performance by a thoroughbred in the history of racing. Express the position of Twice a Prince compared to Secretariat as a signed number. (Source: ezinearticlescom)
NASCAR In the NASCAR driver standings, negative numbers are used to tell how many points behind the leader a given driver is. Jimmie Johnson was the leading driver in 2008 . The other drivers in the top ten were Greg Biffle $(-217),$ Clint Bowyer $(-303),$ Jeff Burton $(-349),$ Kyle Busch $(-498),$ Carl Edwards $(-69),$ Jeff Gordon $(-368),$ Denny Hamlin $(-470),$ Kevin Harvick $(-276),$ and Tony Stewart $(-482) .$ Use this information to rank the drivers in the table below.
A boy launches a water balloon from the top of a building, as shown in the next column. At that instant, his friend starts a stopwatch and keeps track of the time as the balloon sails above the building and then falls to the ground. Use the number line to estimate the position of the balloon at cach time listed in the table below.
At a carnival shooting gallery, players aim at moving ducks. The path of one duck is shown, along with the time it takes the duck to reach certain positions on the gallery wall. Use the number line to estimate the position of the duck at each time listed in the table below.
The readout from a testing device is shown. Use the number line to find the height of each of the peaks and the depth of each of the valleys.
A week of daily reports listing the height of a river in comparison to flood stage is given in the table. Complete the bar graph shown below.
In golf, par is the standard number of strokes considered necessary on a given hole. A score of $-2$ indicates that a golfer used 2 strokes less than par. A score of $+2$ means 2 more strokes than par were used. In the graph in the next column, each golf ball represents the score of a professional golfer on the 16th hole of a certain course.a. What score was shot most often on this hole?b. What was the best score on this hole?c. Explain why this hole appears to be too easy for a professional golfer.
Examine the items listed on the following paycheck stub. Then write two columns on your paper - one headed "positive" and the other "negative." List each item under the proper heading.
The illustration shows the predicted Fahrenheit temperatures for a day in mid-January.a. What is the temperature range for the region including Fargo, North Dakota?b. According to the prediction, what is the warmest it should get in Houston?c. According to this prediction, what is the coldest it should get in Seattle?
The graph on the next page shows the net income of Amazon.com for the years 1998-2007. (Source: Morningstar)a. In what years did Amazon suffer a loss? Estimate cach loss.b. In what year did Amazon first turn a profit? Estimate it.c. In what year did Amazon have the greatest profit? Estimate it.
Number lines can be used to display historical data. Some important world events are shown on the time line below.a. What basic unit is used to scale this time line?b. What can be thought of as positive numbers?c. What can be thought of as negative numbers?d. What important event distinguishes the positive from the negative numbers?
Astronomers use an inverted vertical number line called the apparent magnitude scale to denote the brightness of objects in the sky. The brighter an object appears to an observer on Earth, the more negative is its apparent magnitude. Graph each of the following on the scale to the right.$\cdot$ Visual limit of binoculars $+10$"Visual limit of large telescope $+20$$\cdot$ Visual limit of naked eye $+6$$\cdot$ Full moon $-12$$\cdot$ Pluto $+15$$\cdot$ Sirius (a bright star) $-2$$\cdot$ Sun $-26$$\cdot$ Venus $-4$
LINE GRAPHS Each thermometer in the illustration gives the daily high temperature in degrees Fahrenheit. Use the data to complete the line graph below.
The illustration shows the depths at which the bottoms of various types of flower bulbs should be planted. (The symbol " represents inches.)a. At what depth should a tulip bulb be planted?b. How much deeper are hyacinth bulbs planted than gladiolus bulbs?c. Which bulb must be planted the deepest? How deep?
Explain the concept of the opposite of a number.
What real-life situation do you think gave rise to the concept of a negative number?
Explain why the absolute value of a number is never negative.
Give an example of the use of the number line that you have seen in another course.
DIVING Divers use the terms positive buoyancy, neutral buoyancy, and negative buoyancy as shown. What do you think each of these terms means?
Much of the Netherlands is lowlying, with half of the country below sea level. Explain why it is not under water.
Suppose integer $A$ is greater than integer $B$. Is the opposite of integer $A$ greater than integer $B ?$ Explain why or why not. Use an example.
Explain why $-11$ is less than $-10$.
Round $23,456$ to the nearest hundred.
Evaluate: $19-2 \cdot 3$
Subtract $2,081$ from $2,842$.
Divide 346 by 15.
Give the name of the property shown below:$$(13 \cdot 2) \cdot 5=13 \cdot(2 \cdot 5)$$
Write four times five using three different symbols.