Title: Unit 9 Quiz
Course: Technical Math for Industry

Q: Evaluate when and when . Which gives you the larger value and what is that value?
- will give you the larger value of 34. (Incorrect. You may have forgotten the order of operations and subtracted 20 minus 3 before multiplying by 2. Multiplication comes before addition.)
- will give you the larger value of 11. (Incorrect. This is the correct value of the expression when . However, will give you a larger value.)
- will give you the larger value of 14. (Correct. When , . When , .)
- will give you the larger value of 51. (Incorrect. You may have forgotten the order of operations and subtracted 20 minus 3 before multiplying by 3. Multiplication comes before addition.)
A: will give you the larger value of 14.

Q: Evaluate when and .
- 69 (Incorrect. You may have used the incorrect order of operations and subtracted before multiplying. You need to do the multiplication first, and then subtract.)
- 21 (Incorrect. You may have subtracted . When a number is next to a variable, like or like , it means that you have to multiply. So you should multiply 7 and 4, multiply 5 and 3, and then subtract.)
- 13 (Correct. Substituting 4 for a and 3 for b gives . First multiply to get , then subtract to get 13.)
- 1 (Incorrect. You may have substituted incorrectly and computed . You need to compute .)
A: 13

Q: Which list shows the set of integers?
- ..., , , , (Incorrect. This set includes only 0 and negative integers. The set of integers also includes positive integers, or the numbers 1, 2, 3, ...)
- 0, 1, 2, 3, ... (Incorrect. This set includes only 0 and positive integers. The set of integers also includes negative integers, or the numbers , ...)
- 1, 2, 3, ... (Incorrect. This set includes only positive integers. The set of integers also includes 0 and the negative integers, or the numbers , ...)
- ..., , , , , , , , ... (Correct. The set of integers includes negative numbers, 0, and positive numbers.)
A: ..., , , , , , , , ...

Q: What is the value of x in ?
- 6 (Correct. , because is 6 units from 0 on the number line.)
- 6 and (Incorrect. The number x is equal to the absolute value of a number. Absolute value cannot be negative. It is the distance that a number is from 0 on the number line.)
- 0 (Incorrect. The number x is equal to the absolute value of a number. It is the distance that the number is from 0 on the number line. The distance from to 0 is not 0.)
A: 6
If wrong: Incorrect. The number x is equal to the absolute value of a number. Absolute value cannot be negative. It is the distance that a number is from 0 on the number line.

Q: Which pair of numbers are not opposites?
- and (Incorrect. A number and its opposite have the same absolute value and different signs. The first number is equal to 7, and the second is . So these are opposites.)
- 72 and (Incorrect. A number and its opposite have the same absolute value and different signs. These are both true for this pair, so they are opposites.)
- 27 and (Correct. A number and its opposite have the same absolute value and different signs. , so these are the same two numbers, not opposites.)
- 27 and (Incorrect. A number and its opposite have the same absolute value and different signs. These are both true for this pair, so they are opposites.)
A: 27 and

Q: Which subset(s) of numbers does belong to?
- whole and rational numbers (Incorrect. The number . Because it can be written as a ratio of two integers, it is a rational number. However, is between 8 and 9 on the number line, so it cannot be a whole number.)
- rational and natural numbers (Incorrect. The number . Because it can be written as a ratio of two integers, it is a rational number. However, is between 8 and 9 on the number line, so it cannot be a natural number.)
- real and rational numbers (Correct. The number . Since it can be written as a ratio of two integers, it is a rational number. All rational numbers are real numbers.)
- integers and real numbers (Incorrect. Because is between 8 and 9 on the number line, it cannot be an integer. It is a real number, though.)
A: real and rational numbers

Q: Which point represents on the number line?
- Point D (Incorrect. Negative numbers are to the left of 0. Point D is less than 1 unit to the right of 0. Therefore it represents a number between 0 and 1, not between and .)
- Point A (Incorrect. Point A is more than 3 units to the left of 0 and less than 4 units to the left of 0. Therefore it represents a number between and , not between and .)
- Point E (Incorrect. Negative numbers are to the left of 0. Point E is more than 2 units to the right of 0 and less than 3 units to the right of 0. Therefore it represents a number between 2 and 3, not between and .)
- Point C (Incorrect. Point C is more than 1 unit to the left of 0 and less than 2 units to the left of 0. Therefore it represents a number between and , not between and .)
- Point B (Correct. Point B is more than 2 units to the left of 0 and less than 3 units to the left of 0. Therefore it represents a number between and . It is the only point in this interval.)
A: Point B

Q: Which of the following are true?

A.

B.

C.

D.
- A and C (Incorrect. Both A and C are false. 6.8 is to the right of 5.9 on a number line, so . Negative numbers are always to the left of positive numbers on a number line, so .)
- B and D (Correct. is to the left of on a number line, so . Positive numbers are always to the right of negative numbers on a number line, so .)
- C and D (Incorrect. Positive numbers are always to the right of negative numbers on a number line, so . However, negative numbers are always to the left of positive numbers on a number line, so .)
- A and B (Incorrect. is to the left of on a number line, so . However, 6.8 is to the right of 5.9 on a number line, so .)
A: B and D

Q: Which statements are true for irrational numbers written in decimal form?

A. Irrational numbers are nonterminating.

B. Irrational numbers are repeating.

C. Irrational numbers are nonrepeating.

D. Irrational numbers are terminating.
- A and C (Correct. An irrational number is nonterminating and nonrepeating when written as a decimal.)
- C and D (Incorrect. An irrational number is nonrepeating when written as a decimal. However, a number that has a terminating decimal is rational.)
- B and D (Incorrect. These are both false statements. A number that has a repeating or terminating decimal is rational.)
- A and B (Incorrect. An irrational number is nonterminating when written as a decimal. However, a number that has a repeating decimal is rational.)
A: A and C

Q: Find .
- 282 (Incorrect. You added the absolute values, but you omitted a negative sign in the answer. The sum must have the same sign as the numbers you are adding.)
A: (a choice with no text)
If wrong: Incorrect. You forgot to add a regrouped ten when adding the absolute values.
If right: Correct. All the addends are negative, so the sum is negative.
If wrong: Incorrect. You subtracted 63 and 11 from 208 and gave the result the same sign as the numbers in the problem. You need to add 63, 208, and 11, and then give the sum the same sign as the addends.

Q: Find .
- 55 (Incorrect. You may have incorrectly added to get , and then correctly added . To add two negative numbers, you must add their absolute values (), and place a negative sign on the result.)
- 25 (Correct. Add the first two numbers. Because they are both negative, you need to add their absolute values () and place a negative sign on the result: . Now add . Because the two numbers have different signs, you need to find the difference of their absolute values (). Since , the result is positive.)
A: 25
If wrong: Incorrect. You may have correctly added to get , but then incorrectly added . When you are adding numbers with different signs, and the positive addend has a greater absolute value, the sum is positive. If the negative addend has a greater absolute value, the sum is negative.
If wrong: Incorrect. You may have incorrectly added to get , and then incorrectly added . To add two negative numbers, you must add their absolute values (), and place a negative sign on the result (). To add and 70, find the difference of their absolute values. Since , the result will be positive.

Q: Find .
- 61.5 (Incorrect. You added the absolute values of the decimals but forgot to give the sum the right sign. Since all the addends in the problem are negative, their sum is negative.)
A: (a choice with no text)
If right: Correct. All addends in the problem are negative, so their sum is negative.
If wrong: Incorrect. You did not line up the decimals before adding the absolute values. The first step is to add .
If wrong: Incorrect. You added 3.9 and 20 to . Instead, you should first add the absolute values of the decimals. Then, because all the addends in the problem are negative, their sum is negative.

Q: Find
A: (a choice with no text)
If wrong: Incorrect. You did not find a common denominator for the fractions, and incorrectly attempted to subtract the numerators and denominators. First subtract , using a common denominator of 8. Then compare and to see if the answer is positive or negative.
If wrong: Incorrect. You may have added , and then supplied the answer with a negative sign. However, you need to find the difference of . The answer will be negative, because .
If wrong: Incorrect. You correctly found the difference of the absolute values. However, you have to compare and . If the negative number has a greater absolute value, the answer is negative. If the positive number has a greater absolute value, the answer is positive.
If right: Correct. The number with the greater absolute value is negative, so the sum is negative.

Q: What is , when ?
- 7 (Correct. Substituting 12 for y gives , which is equal to , or 7.)
- 0 (Incorrect. You may have thought that adding 0 to other numbers changes the total value to 0. The identity property states that adding 0 to other numbers does not change their value.)
A: 7
If wrong: Incorrect. You may have mistakenly added and when evaluating the expression for .
If wrong: Incorrect. The identity property states that adding 0 to other numbers does not change their value. You also need to remember that when you add numbers with different signs the result has the same sign as the number with the greater absolute value.

Q: The freezing point of nitrogen is about . The freezing point of mercury is about higher. What is the approximate freezing point of mercury?
A: (a choice with no text)
If right: Correct. The freezing point is . First, find the difference of the absolute values: . Since the negative addend has the greater absolute value, the sum will be negative.
If wrong: Incorrect. The freezing point is . You added the absolute values of the addends, and applied a negative sign. However, the addends have different signs, so you must find the difference of the absolute values and give the sum the same sign as the addend with the greater absolute value.
If wrong: Incorrect. The freezing point is . You correctly found the difference of the absolute values of the addends. You need to apply the sign of the addend with the greater absolute value.
If wrong: Incorrect. The freezing point is . You added the absolute values of the addends. However, the addends have different signs, so you must find the difference of the absolute values and give the sum the same sign as the addend with the greater absolute value.

Q: Find .
- 400 (Incorrect. You added 276 instead of adding the opposite of 276, which would be . Find the difference of the absolute values. Then, because the addend with the greater absolute value is negative, the answer is negative.)
- 152 (Incorrect. You used the wrong sign. Rewrite the problem as adding the opposite: . Find the difference of the absolute values. Then, because the addend with the greater absolute value is negative, the answer is negative.)
A: (a choice with no text)
If right: Correct. . Now find the difference of the absolute values: . Because the addend with the greater absolute value is negative, the answer is negative.
If wrong: Incorrect. You added the opposites of both numbers instead of just adding the opposite of 276, which would be . Find the difference of the absolute values. Then, because the addend with the greater absolute value is negative, the answer is negative.

Q: Find .
- 39.9 (Correct. Start with . Since , and , . Then add 8 to get 1.4. Finally, rewrite as to get 39.9.)
- 37.1 (Incorrect. You may have done the first subtraction correctly to get , but then got the sign of incorrect. Since , this should result in a positive 1.4.)
A: 39.9
If wrong: Incorrect. You may have subtracted 38.5 as your last step. You should be subtracting , which is the same as adding 38.5.
If wrong: Incorrect. You probably did the first subtraction correctly to get , but then got the wrong sign for . Since , this should result in a positive 1.4. Then you probably subtracted 38.5 as your last step. You should be subtracting , which is the same as adding 38.5.

Q: The lowest temperature ever recorded in Minneapolis was . The lowest temperature ever recorded in Chicago was . Was the Chicago temperature warmer or colder, and by how many degrees?
- colder (Incorrect. You probably started with the correct calculation: Since the number with the greater absolute value is positive, the result will be positive, which means warmer.)
- warmer (Correct. To see the difference, take the Chicago temperature and subtract the Minneapolis temperature:)
- warmer (Incorrect. You added the absolute values of the temperatures instead of subtracting to find the difference in temperatures.)
- colder (Incorrect. You added the absolute values of the temperatures instead of subtracting to find the difference in temperatures. Also, though is warmer than , is warmer than .)
A: warmer

Q: Find .
- 24 (Incorrect. This number has the correct sign, because there are four negative factors. However, you may have multiplied only those negative factors, forgetting to include the factor 5.)
- 120 (Correct. Multiply the absolute values of the numbers. . The number of negative factors is even, so the product is positive.)
A: 120
If wrong: Incorrect. You correctly multiplied the absolute values of the factors, but you gave the product the wrong sign. The number of negative factors is even.
If wrong: Incorrect. You may have forgotten to multiply by the last factor in the product, which is .

Q: What is , when ?
A: (a choice with no text)
If wrong: Incorrect. Remember that a positive number times a negative number is negative.
If wrong: Incorrect. You may have been thinking about the reciprocal of , but remember that the identity property of 1 states that .
If right: Correct. The question is asking for the value of . The identity property of 1 states that , so
If wrong: Incorrect. You subtracted instead of multiplied.

Q: Find . Write the answer in lowest terms.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. The result has the correct sign, but you multiplied the fractions instead of performing division. To divide, you need to multiply the first fraction by the reciprocal of the second fraction.
If wrong: Incorrect. The result has the correct sign, but you multiplied the reciprocal of the first fraction by the second fraction. To divide, you need to multiply the first fraction by the reciprocal of the second fraction.
If wrong: Incorrect. It appears that you correctly turned division by into multiplication by , but forgot that a negative number multiplied or divided by a negative number is positive.

Q: Across a horizontal distance of 25 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is feet, compared to its height at the top of the drop. What is the average amount that the roller coaster's height changes over each horizontal foot?
- 5 ft (Incorrect. You correctly divided the absolute values, but since you are dividing a negative height by a positive number of horizontal feet, the answer is negative.)
- ft (Incorrect. You divided the horizontal distance by the change in height. The question asked for the change in height over the horizontal distance.)
- ft (Correct.)
- ft (Incorrect. To find the average amount that the height changes for each horizontal foot, divide -125 by 25 or . You divided the horizontal distance by the change in height and used the wrong sign.)
A: ft

Q: Which of the following equations uses the commutative property of addition to rewrite ?
A: (a choice with no text)
If wrong: Incorrect. This is a correct statement, but it is not an illustration of the commutative property. The terms of the sum have not been switched, just their numerators.
If wrong: Incorrect. This is a correct statement, but it is not an illustration of the commutative property.
If wrong: Incorrect. This is a correct statement that shows how to find the sum of the fractions, but it is not an illustration of the commutative property.
If right: Correct. The commutative property of addition states that . Therefore, you may switch the order of and .

Q: Which of the following properties could be used to rewrite the expression as ?
- The commutative property followed by the associative property (Incorrect. This is what you get when you apply these two properties in this order: or)
- The associative property followed by the commutative property (Correct. You get by using the associative property to regroup. Then you get by applying the commutative property.)
- The associative property used once (Incorrect. This is what you would get by using the associative property to regroup:)
- The commutative property used twice (Incorrect. If you did this, you would be switching the order inside and outside the parentheses. You would not regroup. This would be the result:)
A: The associative property followed by the commutative property

Q: Use the distributive property to evaluate when .
- 16 (Incorrect. You may have incorrectly distributed the 4 and gotten , instead of , and then incorrectly computed by subtracting first, instead of multiplying.)
- 20 (Correct. . Substitute 3 for :)
- 4 (Incorrect. You may have forgotten to substitute 3 for , and incorrectly treated as if it were just 2. You can either distribute the 4 and then substitute the 3 for , or substitute first and then distribute.)
- 23 (Incorrect. You may have correctly substituted 3 for and gotten , but then interpreted this incorrectly as . Using the distributive property, it is correctly rewritten as .)
A: 20

Q: Simplify:
- 0 (Correct. First simplify inside the brackets. To do so, you must multiply and then add. .)
- 12 (Incorrect. You may have simplified by subtracting 3 from 9 and adding that to the product of 2 and 3. You must first completely simplify inside the brackets before doing other operations.)
- 24 (Incorrect. You may have done all the operations from left to right. You must first completely simplify inside the brackets before doing the subtraction. To simplify inside the brackets, you must multiply and then add.)
A: 0
If wrong: Incorrect. You may have simplified the expression in the brackets incorrectly by adding before multiplying. The first step should be: .

Q: Simplify:
A: (a choice with no text)
If wrong: Incorrect. You may have incorrectly calculated by multiplying first to get . The correct order of operations is exponents before multiplication, and so .
If wrong: Incorrect. You may have ignored the absolute value symbols and thought that was equal to . Remember that the absolute value of a negative number is positive, and therefore .
If right: Correct. Simplify the numerator: Simplify the denominator: Divide:
If wrong: Incorrect. You may have thought that was equal to . Remember that the absolute value of a negative number is positive, and therefore . You may have also incorrectly calculated by multiplying first to get . The correct order of operations is exponents before multiplication, and so .