Title: Unit 1 Quiz
Course: Technical Math for Industry

Q: What does the digit 8 represent in 687,413?
- Eight hundred thousand (Incorrect. Eight hundred thousand would be represented by an 8 in the hundred thousands place.)
- Eight hundred (Incorrect. Eight hundred would be represented by an 8 in the hundreds place.)
- Eighty thousand (Correct. The digit 8 represents 80,000 because it is in the ten thousands place.)
- Eight thousand (Incorrect. Eight thousand would be represented by an 8 in the thousands place.)
A: Eighty thousand

Q: A truck driver traveled four hundred two thousand, three hundred fifty-two miles last year. Write this number in standard form.
- 420,352 (Incorrect. Look at the thousands place value carefully.)
- 402,352 (Correct. Correct. In the word form of this number, no value is written in the ten thousands place.)
- 42,352 (Incorrect. Remember to place 0s in the standard form.)
- 402,352,000 (Incorrect. The number is less than a million.)
A: 402,352

Q: Which is the correct way to write 57,021 in expanded form?
A: (a choice with no text)
If wrong: Incorrect. Even though the digit 0 has no value, its placement affects the values of the 5 and the 7.
If right: Correct. In the standard form of this number there is a 0 in the hundreds place.
If wrong: Incorrect. Be careful not to insert extra zeros.
If wrong: Incorrect. The digit 2 is in the tens place.

Q: Round 713,949 to the nearest hundred.
- 713,000 (Incorrect. Remember, you are rounding to the nearest hundred.)
- 713,900 (Correct. Rounding to the nearest hundred, 713,949 rounds down to 713,900.)
- 713,950 (Incorrect. Remember, you are rounding to the nearest hundred.)
- 714,000 (Incorrect. Try looking at a simpler problem: 949 rounded to the nearest hundred is 900.)
A: 713,900

Q: A factory that dyes clothing has 65,492 pounds of dye stored in a warehouse. Round this number to the nearest thousand.
- 65,000 (Correct. The number 5,492 rounds down to 5,000, so 65,492 rounds down to 65,000.)
- 65,500 (Incorrect. This number is result of rounding to the nearest hundred.)
- 66,400 (Incorrect. Remember that when rounding to the nearest thousand you will need to put a zero in the hundreds place.)
- 66,000 (Incorrect. Since the hundreds place is less than 5, round down to the nearest thousand.)
A: 65,000

Q: Look at the number line.

Which points are less than 13?
- Points P, R, and S (Incorrect. These are the points not equal to 13. However, points R and S are to the right of 13, and therefore they are greater than 13.)
- Points P and Q (Incorrect. Point Q is at 13, not less than 13.)
- Points R and S (Incorrect. Points R and S are to the right of 13, and therefore they are greater than 13.)
- Point P only (Correct. Only point P is to the left of 13.)
A: Point P only

Q: A music playlist has 31 hiphop songs, 42 rock songs, and 16 popular songs. How many songs are in the playlist?
- 86 (Incorrect. Remember to add each place value separately.)
- 87 (Incorrect. Remember to add each place value separately.)
- 88 (Incorrect. Remember to add each place value separately.)
- 89 (Correct. Correct.)
A: 89

Q: A baseball player has 546 plate appearances in his first year, 627 plate appearances in his second year, and 712 plate appearances in his third year. How many plate appearances has the player had in three years?
- 1,885 (Correct. Correct.)
- 1,975 (Incorrect. Remember to regroup the ones and tens places.)
- 1,985 (Incorrect. Remember to be careful when regrouping.)
- 1,875 (Incorrect. Remember to regroup.)
A: 1,885

Q: The diagram is a floor plan for a new building. Find the perimeter.
- 154 (Correct. Correct.)
- 152 (Incorrect. Write out the problem vertically to see it more clearly.)
- 144 (Incorrect. Remember to regroup.)
- 162 (Incorrect. Write out the problem vertically to see it more clearly.)
A: 154

Q: Mia's garden is in the shape of a rectangle that measures about 29 meters long and 15 meters wide. What is the distance around Mia's garden?
- 88 meters (Correct. Correct.)
- 176 meters (Incorrect. Remember that "distance" in this problem means perimeter.)
- 73 meters (Incorrect. Remember that "distance" in this problem means perimeter.)
- 44 meters (Incorrect. Remember that "distance" in this problem means perimeter.)
A: 88 meters

Q: Gina is driving 76 miles to her brother's house. If she stops for gas after driving 34 miles, how many miles does she have to go before she gets to her brother's house?
- 32 (Incorrect. Remember to align each place value before subtracting.)
- 42 (Correct. Correct.)
- 38 (Incorrect. Remember to check which number you're subtracting from.)
- 36 (Incorrect. Remember to check the problem to make sure the solution makes sense.)
A: 42

Q: A workbook contains 1,113 problems. If 827 of the problems have been solved, how many unsolved problems are left in the workbook?
- 276 (Incorrect. Remember when regrouping to cross out the old number and write the new one in the correct place value.)
- 296 (Incorrect. Remember when regrouping to cross out the old number and write the new one in the correct place value.)
- 266 (Incorrect. Remember when regrouping to cross out the old number and write the new one in the correct place value.)
- 286 (Correct. Correct.)
A: 286

Q: Annie is 26 years (312 months) old. Ellen is 74 months younger than Annie. How old is Ellen in months?
- 218 months (Incorrect. Be sure to set the problem up correctly as .)
- 238 months (Correct. Correct. .)
- 248 months (Incorrect. Be sure to set the problem up correctly as .)
- 228 months (Incorrect. Be sure to set the problem up correctly as .)
A: 238 months

Q: Estimate the sum of by rounding each number to the nearest hundred.
- 33,900 (Incorrect. Remember, 24,872 rounds up to 24,900, 651 rounds up to 700, 971 rounds up to 1,000, and 8,499 rounds up to 8,500.)
- 35,100 (Correct. Correct. The number 24,872 rounds up to 24,900, 651 rounds up to 700, 971 rounds up to 1,000, and 8,499 rounds up to 8,500.)
- 34,900 (Incorrect. Remember, 24,872 rounds up to 24,900, 651 rounds up to 700, 971 rounds up to 1,000, and 8,499 rounds up to 8,500.)
- 35,000 (Incorrect. Remember to round to the nearest hundred, not thousand.)
A: 35,100

Q: Use the diagram to estimate the perimeter, rounding each number to the nearest thousand.
- 101,000 centimeters (Incorrect. Remember that 17,167 rounds down to 17,000.)
- 99,000 centimeters (Incorrect. Remember, 17,167 rounds down to 17,000, 39,512 rounds up to 40,000, and 42,812 rounds up to 43,000.)
- 98,000 centimeters (Incorrect. Remember, 39,512 rounds up to 40,000 and 42,812 rounds up to 43,000.)
- 100,000 centimeters (Correct. Correct. The number 17,167 rounds down to 17,000, 39,512 rounds up to 40,000, and 42,812 rounds up to 43,000.)
A: 100,000 centimeters

Q: At Frank's work he can produce 3 widgets every hour. Which of the following expresses how many widgets Frank can make after an 8 hour day?
A: (a choice with no text)
If wrong: Incorrect. For this expression to be correct there needs to be eight 3s.
If wrong: Incorrect. For this expression to be correct there can only be three 8s.
If wrong: Incorrect. Read the question carefully; addition and multiplication are not the same.
If right: Correct. Correct. Multiple parentheses can still be used in a multiplication expression.

Q: A toy factory packs 48 dog toys into each box. Joanna needs to fill an order for 27 boxes of dog toys. How many dog toys will she need to fill her order?
- 1,246 dog toys (Incorrect. Remember to carry the 5 to the tens place.)
- 1,296 dog toys (Correct.)
- 856 dog toys (Incorrect. Remember to multiply each part.)
- 75 dog toys (Incorrect. This is a multiplication problem, not an addition problem.)
A: 1,296 dog toys

Q: There are 40 nickels in a roll. If you have 250 rolls of nickels, how many nickels do you have?
- 10,000 nickels (Correct. Correct.)
- 290 nickels (Incorrect. Remember to multiply, not add.)
- 100,000 nickels (Incorrect. Check to make sure you did not include too many zeros. This product will have extra zeros because .)
- 1,000 nickels (Incorrect. This product will have extra zeros because .)
A: 10,000 nickels

Q: On an average day, 38 customers buy a bag of grapes at Jerry's Market. There are an average of 47 grapes in each bag. Round to the nearest ten and then multiply to estimate the number of grapes Jerry's customers buy every day.
- 2,000 grapes (Correct. You round 47 up to 50 and 38 up to 40 and then multiply.)
- 1,880 grapes (Incorrect. Remember to round both numbers before multiplying.)
- 12,000 grapes (Incorrect. Remember that 47 rounds up to 50 and 38 rounds up to 40. Check the number of zeros you expect in the product.)
- 20,000 grapes (Incorrect. Remember that 47 rounds up to 50 and 38 rounds up to 40. Check the number of zeros you expect in the product.)
A: 2,000 grapes

Q: Aisha bought a rectangular patch of land that is 75 meters long and 47 meters wide. What is the area of the land?
- 2,835 square meters (Incorrect. Remember to multiply all the digits in both numbers.)
- 122 meters (Incorrect. The area is not equal to the sum of the length and the width. Remember also that area is measured in square units.)
- 35,250 square meters (Incorrect. Look at the problem closely to make sure the solution makes sense.)
- 3,525 square meters (Correct. The area is the length times the width.)
A: 3,525 square meters

Q: Michelle is three times as old as Fiona. Fiona is twice as old as Madeline. Madeline is seven years old. How old is Michelle?
- 12 years old (Incorrect. Remember to multiply, not add.)
- 14 years old (Incorrect. Fiona is 14 years old.)
- 42 years old (Correct. Michelle's age is found by multiplying 7 by 2, then multiplying the product by 3.)
- 21 years old (Incorrect. Michelle cannot be 21 years old, because 21 is three times Madeline's age. Michelle is three times Fiona's age, and Fiona is twice as old as Madeline.)
A: 42 years old

Q: Which expression can be used to show a group of twenty seven players divided into three teams?
A: (a choice with no text)
If wrong: Incorrect. The first number, 27, is correct, but the second number should be the number of groups, or 3.
If wrong: Incorrect. The top number should be the original amount, or 27. The bottom number should be the number of groups, or 3.
If wrong: Incorrect. The top number should be the original amount, or 27. The bottom number should be the number of groups, or 3.
If right: Correct. The first number is the original or total amount, and the second number is the number of groups.

Q: How much is 104 divided by 5?
- 20 R1 (Incorrect.)
- 20 R2 (Incorrect.)
- 20 R3 (Incorrect.)
- 20 R4 (Correct.)
A: 20 R4

Q: _____
- 21 R37 (Incorrect. 982 divided by 45 equals 21 R37.)
- 21 R27 (Incorrect. 972 divided by 45 equals 21 R27.)
- 21 R7 (Incorrect. 952 divided by 45 equals 21 R7.)
- 21 R17 (Correct. 21 times 45 plus 17 equals 962.)
A: 21 R17

Q: _____
- 3,500 (Incorrect. Remember to drop a zero at the end.)
- 350 (Correct. Multiplying 350 by 900 gives the product 315,000.)
- 314,100 (Incorrect. This is a division problem.)
- 35,000 (Incorrect. Remember to drop the two zeros at the end.)
A: 350

Q: Which of the following problems would NOT have a solution?
- Pablo is cutting a 20-meter-long board into 5 equal pieces and you want to know how long each piece will be. (Incorrect. This has a solution, because you can divide 20 by 5.)
- Pablo is cutting a 5-meter-long board into 2 equal pieces and you want to know how long each piece will be. (Incorrect. This has a solution, because you can divide 5 by 2, though the answer is not a whole number.)
- Pablo is cutting a 0-meter-long board into 5 equal pieces and you want to know how long each piece will be. (Incorrect. This has a solution, because you can divide 0 by 5.)
- Pablo is cutting a 2-meter-long board into 0 equal pieces, and you want to know how long each piece will be. (Correct. This has no solution, because you cannot divide by 0.)
A: Pablo is cutting a 2-meter-long board into 0 equal pieces, and you want to know how long each piece will be.

Q: An auto transport truck holds 12 cars. A car dealer plans to bring in 1,150 new cars in June and July. If an auto transport truck is filled for each delivery, except for the last one, how many truckloads are needed and how many cars will be in the last truckload?
- 96 truckloads with 10 cars on the last truck (Correct. R10; the remainder of 10 cars are on the ninety-sixth^ truck.)
- 95 truckloads with 12 cars on the last truck (Incorrect. If 95 trucks were filled, there would be cars, so there must be more than 95 trucks to ship 1,150 cars. Also, according to the problem, the last truckload will not be full.)
- 960 truckloads with 10 cars on the last truck (Incorrect. A place value error has been made. Use an estimate to check that your answer is reasonable: .)
- 95 truckloads with 10 cars on the last truck (Incorrect. If 95 trucks were filled, there would be cars, so there must be more than 95 trucks to ship 1,150 cars.)
A: 96 truckloads with 10 cars on the last truck

- 1,000 (Incorrect. You do not put 0 in the ones place and move other digits left by one place value. You do this only if you are multiplying a number by 10.)
- 0 (Incorrect. The answer will be 0 if you multiply 100 by 0, but not if you add 100 to 0.)
- 100 (Correct. Adding 0 to a number does not change a number.)
- 10 (Incorrect. This would be the correct result if you divided 100 by 10.)
A: 100

Q: _____
- 210 (Incorrect. You do not put 0 in the ones place and move other digits left by one place value. You do this only if you are multiplying a number by 10.)
- 21 (Correct. Multiplying a number by 1 repeatedly does not change a number.)
- 1,211 (Incorrect. First multiply and then multiply the result by 1.)
- 23 (Incorrect. The dot symbol tells you to multiply, not add.)
A: 21

Q: Which choice shows rewritten correctly using the commutative property and then simplified correctly?
A: (a choice with no text)
If wrong: Incorrect. Although the result is simplified correctly, the associative property is applied, not the commutative property.
If right: Correct. Using the commutative property, the order of the addends is changed. The answer is simplified correctly.
If wrong: Incorrect. The commutative property is not applied correctly. (An addend is replaced by two addends with an equivalent sum.) The result is not simplified correctly.
If wrong: Incorrect. The commutative property is applied correctly, but the result is not simplified correctly.

Q: Which choice shows rewritten correctly using the commutative property and then simplified correctly?
A: (a choice with no text)
If wrong: Incorrect. Although the result is simplified correctly, the associative property is applied, not the commutative property.
If right: Correct. Using the commutative property, the order of the factors is changed. The answer is simplified correctly.
If wrong: Incorrect. The commutative property is not applied and the result is not simplified correctly.
If wrong: Incorrect. The commutative property is applied correctly, but the result is not simplified correctly.

Q: Which choice shows correctly rewritten using the associative property and then correctly simplified?
A: (a choice with no text)
If wrong: Incorrect. Using the associative property, the order of the addends is not changed and addends should be grouped. The expression is correctly simplified.
If wrong: Incorrect. Although the associative property is correctly applied, the expression is not simplified correctly because the operation inside parentheses should be performed first.
If right: Correct. Using the associative property, the order of the addends is not changed, but the grouping is changed. The expression is simplified correctly.
If wrong: Incorrect. Using the associative property, the order of the addends is not changed. The expression is simplified correctly.

Q: Which choice shows correctly rewritten using the associative property and then correctly simplified?
A: (a choice with no text)
If wrong: Incorrect. Although the associative property is correctly applied, the expression is not simplified correctly because the operation inside parentheses should be performed first.
If right: Correct. Using the associative property, the order of the factors is not changed, but the grouping is changed. The expression is simplified correctly.
If wrong: Incorrect. Using the associative property, the order of the factors is not changed. The expression is simplified correctly.
If wrong: Incorrect. Using the associative property, only the grouping of factors is changed. The expression is not simplified correctly because the digits of different numbers should not be combined to create new numbers.

Q: Rewrite the expression using the distributive property of multiplication over addition.
A: (a choice with no text)
If wrong: Incorrect. The 2 is not correctly distributed. The order of numbers should not be changed when applying the distributive property.
If right: Correct. The 2 is correctly distributed so that it is used to multiply the 10 and the 12 separately.
If wrong: Incorrect. This would be doubling the original value. To correctly distribute the 2, multiply the 10 by 2 and the 12 by 2.
If wrong: Incorrect. The distributive property must be applied before adding.

Q: Rewrite the expression using the distributive property of multiplication over subtraction.
A: (a choice with no text)
If wrong: Incorrect. The distributive property must be applied before subtracting.
If wrong: Incorrect. The 30 is not correctly distributed. The order of numbers should not be changed when applying the distributive property.
If right: Correct. The 30 is correctly distributed so that it is used to multiply the 10 and the 5 separately.
If wrong: Incorrect. This result incorrectly applies the commutative property to subtraction.

Q: What is the value of ?
- 512 (Correct.)
- 482 (Incorrect. Check that you multiplied correctly.)
- 64 (Incorrect. This is the result of finding the value of ; the exponent in this problem indicates that 8 should be multiplied by itself 3 times: .)
- 24 (Incorrect. This is the result of finding the value of , not .)
A: 512

Q: Write in exponential notation.
- 16,384 (Incorrect. 16,384 is equivalent to , but it is not written in exponential notation.)
A: (a choice with no text)
If wrong: Incorrect. Make sure to count the number of 4s that are multiplied, not the number of multiplication symbols.
If wrong: Incorrect. Recall that the base is the number that is repeatedly multiplied, so in this problem the base should be 4.
If right: Correct. The base number 4 is multiplied by itself 7 times, so the equivalent expression is .

Q: Is 27 a perfect square?
- No, because the only proper factors of 27 are 3 and 9, and neither of these factors gives 27 when multiplied by itself. (Correct. , which is less than 27, and , which is greater than 27. The square root of 27 must be between 5 and 6, but there are no whole numbers between 5 and 6, so 27 is not a perfect square.)
- Yes, because there is a number, 54, that equals . (Incorrect. A number is a perfect square if its square root is a whole number.)
- Yes, , so 27 is a perfect square because a number can be multiplied by itself to give 27. (Incorrect. , which is not the same as . A perfect square is the result of multiplying a number by itself one time.)
- No, because perfect squares must be even numbers. (Incorrect. Perfect squares can be even or odd. For example, 9 and 16 are both perfect squares.)
A: No, because the only proper factors of 27 are 3 and 9, and neither of these factors gives 27 when multiplied by itself.

Q: Simplify .
- 4 (Incorrect. Multiplication and division are performed before subtraction.)
- 25 (Incorrect. Remember that division is performed before subtraction.)
- 32 (Incorrect. First simplify inside parentheses and then perform multiplication and division from left to right before adding and subtracting.)
- 53 (Correct.)
A: 53

Q: Simplify .
- 9 (Incorrect. Do not multiply the base by the exponent.)
- 12 (Incorrect. Check to make sure you did not miss an exponent.)
- 6 (Correct.)
- 144 (Incorrect. Remember to compute exponents before adding and subtracting.)
A: 6