Question 1

Solve the problem.
-A deep-sea diver dives from the surface to 80 feet below the surface. She then dives down 16 more feet. Find the diver's depth.
A)62 feet below the surface
B)99 feet below the surface
C)96 feet below the surface
D)64 feet below the surface

Accepted Answer

The diver initially dives 80 feet below the surface and then dives an additional 16 feet, totaling 80 + 16 = 96 feet below the surface.

Question 2

Subtract.
-1 - 3
A)-4
B)4
C)2
D)-2

Accepted Answer

Subtracting 3 from 1 gives -2.

Question 3

Subtract.
-13 - (-2)
A)-15
B)-11
C)11
D)15

Accepted Answer

Subtracting a negative number is the same as adding its positive counterpart, so 13 - (-2) = 13 + 2 = 15.

Question 4

Solve the problem.
-Lauren scored 13 points in her basketball game on Monday, 11 on Wednesday, 14 on Friday, and 19 on Saturday. Find her total points scored for the week.
A)57 points
B)56 points
C)58 points
D)38 points

Accepted Answer

To find the total points scored for the week, add the points from each game: 13 + 11 + 14 + 19 = 57 points.

Question 5

Solve the problem.
-In a card game, it is possible to have a negative score. If Ellie's score is 22, what is her new score if she loses 27 points?
A)49 points
B)-49 points
C)5 points
D)-5 points

Accepted Answer

If Ellie loses 27 points from her original score of 22, you subtract 27 from 22, resulting in -5.

Question 6

Subtract.
--13 - (-5)
A)8
B)-18
C)-8
D)18

Accepted Answer

To subtract a negative number, we can change it to adding the opposite. Therefore, -13 - (-5) is the same as -13 + 5, which equals -8. Choice C is the only option that matches this result.

Question 7

Subtract.
--7 - 8
A)-1
B)15
C)1
D)-15

Accepted Answer

When you subtract a positive number from a negative number, you move further into the negative. So, -7 - 8 equals -15.

Question 8

Add.
-$$- \frac { 3 } { 8 } + \frac { 7 } { 9 }$$
A) $\frac { 4 } { 9 }$
B) $\frac { 29 } { 72 }$
C) $\frac { 1 } { 18 }$
D) $\frac { 29 } { 9 }$

Accepted Answer

To add fractions with different denominators, find a common denominator, which in this case is 72. Convert each fraction: $-\frac{3}{8} = -\frac{27}{72}$ and $\frac{7}{9} = \frac{56}{72}$. Adding these gives $\frac{29}{72}$.

Question 9

Solve the problem.
-The temperature on a December morning is -7° F at 3a.m. If the temperature drops 3° by 4 a.m., rises 8° by 5 a.m., and then drops 7° by 6a.m., find the temperature at 6 a.m.
A)-25° F
B)-9° F
C)9° F
D)25° F

Accepted Answer

Starting at -7° F, the temperature changes as follows: drops 3° to -10° F by 4 a.m., rises 8° to -2° F by 5 a.m., and then drops 7° to -9° F by 6 a.m.

Question 10

Add.
-8.29 + 12.48 + (- 7.5)
A)-3.31
B)28.27
C)13.27
D)-11.69

Accepted Answer

When you add 8.29 and 12.48, you get 20.77. Subtracting 7.5 from 20.77 gives you 13.27.

Question 11

Solve the problem.
-On part of a scenic tour of underground caves, Dave and Neil started at an elevation of 41 feet below sea level. They then rose 22 feet. Represent their distance below sea level as a signed integer.
A)63 feet
B)-19 feet
C)-63 feet
D)19 feet

Accepted Answer

Starting at -41 feet and rising 22 feet results in -41 + 22 = -19 feet below sea level.

Question 12

Add.
-$\frac { 6 } { 7 } + \left( - \frac { 1 } { 3 } \right)$
A) $\frac { 11 } { 21 }$
B) $\frac { 11 } { 7 }$
C) $\frac { 5 } { 7 }$
D) $\frac { 5 } { 21 }$

Accepted Answer

To add fractions with different denominators, first find a common denominator. The least common denominator (LCD) of 7 and 3 is 21. Convert each fraction: $\frac{6}{7} = \frac{18}{21}$ and $\left(-\frac{1}{3}\right) = \left(-\frac{7}{21}\right)$. Adding these gives $\frac{18}{21} + \left(-\frac{7}{21}\right) = \frac{11}{21}$.

Question 13

Solve the problem.
-The population of a particular species of insect was 10,000 in 1960. In 1980, there were 600 fewer, and this year, there are 3800 fewer. What is the current population?
A)6800 insects
B)14,400 insects
C)13,200 insects
D)5600 insects

Accepted Answer

The answer of Solve the problem.
-The population of a particular...

Question 14

Add.
--1.2 + 0.2 + (-0.8)+ 0.1
A)0)7
B)-1.7
C)2)5
D)-0.1

Accepted Answer

-1.2 + 0.2 + (-0.8)+ 0.1 = -1.7

Question 15

Add.
-12 + (-22)+ 4 + (-2)
A)-8
B)-12
C)40
D)-16

Accepted Answer

Adding the numbers: 12 + (-22) + 4 + (-2) = -8.

Question 16

Subtract.
--13 - 13
A)0
B)-13
C)26
D)-26

Accepted Answer

Subtracting -13 - 13 gives -26, because you are moving 13 units further in the negative direction from -13.

Question 17

Solve the problem.
-Jared borrowed $223 from his friend Linda. He paid her back $25, but then had to borrow another $78. How much does he still owe her?
A)$170
B)$276
C)$326
D)$120

Accepted Answer

Jared initially borrowed $223, paid back $25, leaving $198. Then he borrowed another $78, making the total $276.

Question 18

Solve the problem.
-The Neighborhood Lemonade Stand, Inc. reported net incomes of -$250, -$427, and -$117 for the past three years. What was its total net income for these three years?
A)-$794
B)-$677
C)-$544
D)$794

Accepted Answer

To find the total net income, add the net incomes for each year: -$250 + (-$427) + (-$117) = -$794.

Question 19

Solve the problem.
-At the start of a chemistry experiment, Sarah measured the temperature of a liquid to be -16° C. At the end of the experiment, it had risen 33° C. What was the liquid's temperature at the end of the experiment?
A)49° C
B)-49° C
C)-17° C
D)17° C

Accepted Answer

The liquid's temperature at the end of the experiment was -16° C + 33° C = 17° C.

Question 20

Solve the problem.
-A deep-sea diver dives from the surface to 197 meters below the surface and then swims up 7 meters, down 17 meters, down another 28 meters, and then up 25 meters. Find the diver's depth after these movements.
A)210 meters below the surface
B)224 meters below the surface
C)120 meters below the surface
D)154 meters below the surface

Accepted Answer

The diver's final depth is calculated by adding the initial depth to the sum of the movements: 197 - 7 + 17 + 28 - 25 = 210 meters below the surface.

Quiz 1: Real Numbers and Variables

Solve the problem. -A deep-sea diver dives from the surface to 80 feet below the surface. She then dives down 16 more feet. Find the diver's depth.

Subtract. -1 - 3

Subtract. -13 - (-2)

Solve the problem. -Lauren scored 13 points in her basketball game on Monday, 11 on Wednesday, 14 on Friday, and 19 on Saturday. Find her total points scored for the week.

Solve the problem. -In a card game, it is possible to have a negative score. If Ellie's score is 22, what is her new score if she loses 27 points?

Subtract. --13 - (-5)

Subtract. --7 - 8

Add. - $- \frac { 3 } { 8 } + \frac { 7 } { 9 }$

Solve the problem. -The temperature on a December morning is -7° F at 3a.m. If the temperature drops 3° by 4 a.m., rises 8° by 5 a.m., and then drops 7° by 6a.m., find the temperature at 6 a.m.

Add. -8.29 + 12.48 + (- 7.5)

Solve the problem. -On part of a scenic tour of underground caves, Dave and Neil started at an elevation of 41 feet below sea level. They then rose 22 feet. Represent their distance below sea level as a signed integer.

Add. - $\frac { 6 } { 7 } + \left( - \frac { 1 } { 3 } \right)$

Solve the problem. -The population of a particular species of insect was 10,000 in 1960. In 1980, there were 600 fewer, and this year, there are 3800 fewer. What is the current population?

Add. --1.2 + 0.2 + (-0.8) + 0.1

Add. -12 + (-22) + 4 + (-2)

Subtract. --13 - 13

Solve the problem. -Jared borrowed $223 from his friend Linda. He paid her back $25, but then had to borrow another $78. How much does he still owe her?

Solve the problem. -The Neighborhood Lemonade Stand, Inc. reported net incomes of -$250, -$427, and -$117 for the past three years. What was its total net income for these three years?

Solve the problem. -At the start of a chemistry experiment, Sarah measured the temperature of a liquid to be -16° C. At the end of the experiment, it had risen 33° C. What was the liquid's temperature at the end of the experiment?

Solve the problem. -A deep-sea diver dives from the surface to 197 meters below the surface and then swims up 7 meters, down 17 meters, down another 28 meters, and then up 25 meters. Find the diver's depth after these movements.