Title: Unit 2 Quiz
Course: Technical Math for Industry

Q: What fraction represents the shaded part of the circle?
A: (a choice with no text)
If wrong: Incorrect. There is confusion here between the whole and the parts. There are five equal shaded parts out of twelve equal parts in total.
If wrong: Incorrect. This fraction represents the unshaded part of the figure. There are five equal shaded parts out of twelve equal parts in total.
If wrong: Incorrect. We are looking for how much is shaded out of how much is there all together. There are five equal shaded parts. There are twelve equal parts all together.
If right: Correct. The total number of equal parts in the whole is the denominator. The number of shaded parts is the numerator.

Q: A pie is cut into 9 equal pieces. If all but 2 pieces are eaten, how much of the pie remains?
A: (a choice with no text)
If right: Correct. There are 2 pieces remaining out of 9 pieces, so remain.
If wrong: Incorrect. There are 9 pieces in all, so the denominator should be 9. There are 2 pieces left, so the numerator should be 2.
If wrong: Incorrect. This represents the fraction of pieces that were eaten.
If wrong: Incorrect. There are 9 pieces in all, so the denominator should be 9.

Q: What type of number is ?
- Improper fraction (Correct. In an improper fraction, the numerator is greater than or equal to the denominator.)
- Whole number (Incorrect. The whole numbers are 0, 1, 2, 3, 4, and so on. This number is between 1 and 2, so it is not a whole number.)
- Proper fraction (Incorrect. A proper fraction's numerator is less than the denominator. Here the numerator is greater than the denominator, so it is not a proper fraction.)
- Counting number (Incorrect. The counting numbers are 1, 2, 3, 4, and so on.)
A: Improper fraction

Q: Change from an improper fraction to a mixed number.
- 8 (Incorrect. After dividing, do not forget to write the fractional part using the remainder.)
A: (a choice with no text)
If right: Correct. The mixed number is found by dividing 53 by 6 to find the whole number part and using the remainder 5 as the fractional part.
If wrong: Incorrect. Do not split the numerator into a whole number and numerator. Divide 53 by 6 to find the whole number part and use the remainder 5 as the fractional part.
If wrong: Incorrect. Do not split the numerator into a numerator and a whole number. Divide 53 by 6 to find the whole number part and use the remainder 5 as the fractional part.

Q: Change from a mixed number to an improper fraction.
A: (a choice with no text)
If wrong: Incorrect. You may have correctly multiplied: , but then forgot to add the numerator 6.
If wrong: Incorrect. You should not add the whole number to the numerator. You need to multiply it by 9 first. Check that your answer is reasonable. is equal to 1.
If right: Correct. . Add this to 6 to get 33. This is the numerator of the improper fraction. The denominator is still 9.
If wrong: Incorrect. You should not combine the whole number and the numerator. You need to multiply it by 9 first, and then add the 6.

Q: Determine whether 452 is divisible by 2, 3, 4, or 6.
- 2, 3, and 6 only (Incorrect. 452 is divisible by 2. However, the digits of 452 add up to 11, and 11 is not divisible by 3, so 452 is not divisible by 3. Since it is not divisible by 3, it is also not divisible by 6. Also, the number formed by the last 2 digits, 52, is divisible by 4, so 452 is also divisible by 4.)
- 2 and 4 only (Correct. 452 ends in 2, an even number, so 452 is divisible by 2. The number formed by the last 2 digits, 52, is divisible by 4, so 452 is also divisible by 4. The digits of 452 add up to 11, and 11 is not divisible by 3, so 452 is not divisible by 3. Since it is not divisible by 3, it is also not divisible by 6.)
- 2, 3, 4, and 6 (Incorrect. 452 is divisible by 2 and 4. However, the digits of 452 add up to 11, and 11 is not divisible by 3, so 452 is not divisible by 3. Since it is not divisible by 3, it is also not divisible by 6.)
- 2 only (Incorrect. 452 is divisible by 2. However, the number formed by the last 2 digits, 52, is divisible by 4, so 452 is also divisible by 4.)
A: 2 and 4 only

Q: Find all the factors of 606.
- 1, 2, 3, 6, 101, 202, 303, and 606 (Correct. The divisibility rules can be used to show that 1, 2, 3, and 6 are factors. Use factor pairs to find more factors: 101, 202, 303, and 606. Then use division to check that there are no factors between 6 and 101.)
- 1, 2, 3, 4, 6, 101, 202, 303, 404, and 606 (Incorrect. 606 is not divisible by 4 or 404.)
- 1, 3, 6, 101, 202, and 606 (Incorrect. Since the last digit of 606 is even, 606 is divisible by 2.)
- 1, 2, 6, 101, 303, and 606 (Incorrect. Any number divisible by 6 is also divisible by 3.)
A: 1, 2, 3, 6, 101, 202, 303, and 606

Q: Determine whether 105 is prime, composite, or neither.
- prime (Incorrect. 105 is divisible by 5, so it is not a prime number because it has more factors than 1 and itself.)
- composite (Correct. 105 is divisible by 5, so it is a composite number because it has more factors than 1 and itself.)
- neither (Incorrect. Only 1 is neither prime nor composite.)
A: composite

Q: Which of the following shows the prime factorization of 216 using exponential notation?
A: (a choice with no text)
If wrong: Incorrect. , not the 216 it should multiply out to.
If right: Correct. The prime factorization is , which can be rewritten with exponents for the factors that repeat.
If wrong: Incorrect. , not the 216 it should multiply out to.
If wrong: Incorrect. , not the 216 it should multiply out to. Count up the number of times each prime appears in your factor tree. That number becomes the exponent of the prime.

Q: A jar contains 65 coins. of the coins are pennies. What fraction of the coins are pennies, using 65 as the denominator?
A: (a choice with no text)
If wrong: Incorrect. You may have added the multiplying factor (13) to the numerator. Instead, multiply the numerator by this factor.
If right: Correct. You have to multiply the denominator 5 by 13 to get 65, so the numerator is .
If wrong: Incorrect. To find equivalent fractions, multiply or divide the numerator and the denominator by the same number. In this case multiply by 13.
If wrong: Incorrect. You do not add the same number to the numerator and the denominator. To find equivalent fractions, multiply or divide the numerator and the denominator by the same number. In this case multiply by 13.

Q: Simplify .
A: (a choice with no text)
If wrong: Incorrect. You may have incorrectly crossed out the 4s. This is not the same as dividing by a common factor. The fraction is not in lowest terms and it is not equivalent to .
If right: Correct. is in lowest terms, as 1 is the only common factor of 3 and 8.
If wrong: Incorrect. Although is an equivalent fraction to , the numerator and denominator have a common factor, 2, so this fraction cannot be in lowest terms.
If wrong: Incorrect. You may have incorrectly crossed out the 4s and then simplified . This is not the same as dividing by a common factor. Although is in lowest terms, it is not equivalent to .

Q: Which of the following pairs consists of equivalent fractions?
- and (Incorrect. Although the same numbers, 4 and 10, are used in each fraction, the numerators and denominators are not equal, so the fractions cannot be equivalent.)
- and (Incorrect. When you rewrite both fractions with a common denominator, 20, the numerators are different, so the two fractions are not equivalent.)
- and (Correct. You can write both fractions with a common denominator, 8. Both fractions simplify to , so they are equivalent.)
- and (Incorrect. You can write both fractions with a common denominator, 12. Rewrite as . Now both fractions have the same denominator but different numerators, so the two fractions are not equivalent.)
A: and

Q: Which of the following is a true statement?
A: (a choice with no text)
If right: Correct. Rewrite both fractions so they have a common denominator, 16. You find that , so as well.
If wrong: Incorrect. Finding a common denominator, you can compare to and see that , which means .
If wrong: Incorrect. Although , you must find a common denominator to compare fractions. Finding a common denominator, you can compare to and see that , which means .
If wrong: Incorrect. Although , you must find a common denominator to compare fractions. Finding a common denominator, you can compare to and see that , which means .

Q: Multiply . Simplify the answer, if possible.
A: (a choice with no text)
If wrong: Incorrect. This is the correct product, but it is not in lowest terms.
If wrong: Incorrect. You may have added the numerators and added the denominators instead of multiplying.
If right: Correct.
If wrong: Incorrect. You may have added the fractions instead of multiplying them.

Q: Multiply . Simplify the answer and express it as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. This mixed number is equivalent to the correct answer, but it is not simplified.
If wrong: Incorrect. You may have added the fraction to the whole number instead of multiplying.
If right: Correct.
If wrong: Incorrect. You may have added the numerators and added the denominators instead of multiplying.

Q: Multiply . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. This is the product, but the answer must be simplified.
If wrong: Incorrect. Do not multiply the whole number parts and the fractional parts separately. You must first change each number to an improper fraction, then multiply numerators and multiply denominators.
If right: Correct.
If wrong: Incorrect. This is the product, but the answer must be simplified and expressed as a mixed number.

Q: A company has budgeted hours to complete a project, with of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.
- hours (Incorrect. You may have multiplied just the fractional parts. To solve this problem, change the mixed number to an improper fraction, and then multiply:)
- hours (Incorrect. You may have multiplied the whole number by the numerators. To solve this problem, change the mixed number to an improper fraction, and then multiply:)
- hours (Correct.)
- hours (Incorrect. This is the correct amount, but the answer needs to be expressed as a mixed number.)
A: hours

Q: What is the reciprocal of ?
A: (a choice with no text)
If wrong: Incorrect. You found the correct improper fraction that represents , but did not find the reciprocal. Find the reciprocal by flipping the numerator and denominator.
If wrong: Incorrect. This is the reciprocal for the fractional part of the number. First you must rewrite the mixed number as an improper fraction: . Then find the reciprocal by flipping the numerator and denominator.
If wrong: Incorrect. This is the whole number added to the reciprocal of the fractional part of the number. You must first write the mixed number as an improper fraction. Then find the reciprocal by flipping the numerator and denominator.
If right: Correct. , so the reciprocal is .

Q: Find . Simplify the answer and write as a mixed number, if possible.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. You may have multiplied the reciprocal of the first number by the second number: . To solve the problem, multiply the first number by the reciprocal of the second number:
If wrong: Incorrect. This is the correct improper fraction, but the answer needs to be a mixed number.
If wrong: Incorrect. You may have multiplied by instead of its reciprocal.

Q: Find . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. This is the correct improper fraction, but the final answer needs to be a mixed number.
If wrong: Incorrect. You may have written as the improper fraction .
If wrong: Incorrect. You may have forgotten to use the reciprocal of , which is .
If right: Correct.

Q: Find . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. This is the correct improper fraction, but the result needs to be a mixed number.
If wrong: Incorrect. You may have used instead of , which is the correct improper fraction to use for .
If right: Correct.
If wrong: Incorrect. You may have multiplied by the reciprocal of , which is . You want to multiply by the reciprocal of , which is .

Q: A lottery has a grand prize of million dollars. There are 5 people who have winning tickets and they share this prize equally. How many millions of dollars does each person get? Express the answer as a mixed number.
- million dollars (Correct.)
- million dollars (Incorrect. This is the result of . This would show the individual share if 5 million dollars were divided into equal amounts. You need to find the size of each share when is divided into 5 equal amounts:)
- million dollars (Incorrect. This is an equivalent fraction to the correct answer, but it has not been written as a mixed number.)
- million dollars (Incorrect. You may have used the multiplication expression . You need to use division to solve the problem:)
A: million dollars

Q: Add . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. This is the correct sum, but the answer is not simplified, and it is not written as a mixed number.
If wrong: Incorrect. When you add fractions with like denominators, only add the numerators, not the denominators. Keep the denominator the same.
If wrong: Incorrect. This is the correct sum, but the answer is not simplified.

Q: What is the least common multiple of 40 and 52?
- 2080 (Incorrect. This is the product of 40 and 52, not the least common multiple.)
- 1040 (Incorrect. This is a common multiple of 40 and 52, but it is not the least common multiple.)
- 520 (Correct. and . The least common multiple is .)
- 260 (Incorrect. This is a multiple of 52, but not of 40.)
A: 520

Q: Rewrite the fractions and as fractions with a least common denominator.
- and (Correct. The least common multiple of 4 and 14 is 28, so rewrite both fractions with a denominator of 28. ;)
- and (Incorrect. 84 is a common denominator, but not the least common denominator. The least common multiple of 4 and 14 is 28, so rewrite both fractions with a denominator of 28.)
- and (Incorrect. 28 is the least common denominator, but these fractions are not equivalent to the original fractions. Remember to multiply both the the numerator and denominator of a fraction by the same number to find an equivalent fraction.)
- and (Incorrect. 56 is a common denominator, but not the least common denominator. The least common multiple of 4 and 14 is 28, so rewrite both fractions with a denominator of 28.)
A: and

Q: Add . Simplify the answer and write it as a mixed number.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. Do not add the denominators. Find a common denominator, rewrite each fraction, and add the numerators.
If wrong: Incorrect. This is the correct sum, but it has not been written as a mixed number.
If wrong: Incorrect. This is the correct sum, but it can be simplified.

Q: Add . Simplify the answer and write it as a mixed number.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. Make sure that you replace each fraction by an equivalent fraction with a common denominator. Do not just change the denominators. This answer is also not simplified.
If wrong: Incorrect. Make sure that you replace each fraction by an equivalent fraction with a common denominator. Do not just change the denominators.
If wrong: Incorrect. To add fractions with unlike denominators, you must rewrite them with a common denominator. You do not add the numerators and denominators.

Q: Felipe planted some seeds for a science project. One of his plants grew inches in the first week, and then it grew inches during the second week. How much did the plant grow during these two weeks?

The answer should be written as a proper mixed number and should be simplified, if possible.
- inches (Incorrect. When you rewrite the fractions with a common denominator, they must be equivalent to the original fractions. The numerators will not all remain unchanged.)
- inches (Incorrect. This is a correct sum, but it is not a proper mixed number.)
- inches (Incorrect. When you change the improper fraction to a mixed number, make sure that you add the whole number amount to the given whole numbers.)
- inches (Correct.)
A: inches

Q: Subtract . Simplify the answer.
A: (a choice with no text)
If wrong: Incorrect. Rewrite each fraction with a common denominator and subtract numerators. Do not subtract the numerators and denominators.
If wrong: Incorrect. When you rewrite fractions with a common denominator, you must create equivalent fractions. Do not change only the denominator.
If wrong: Incorrect. This is the correct difference, but it is not simplified.
If right: Correct.

Q: Subtract . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. Subtract the whole numbers as well as the fractions.
If right: Correct. Find a common denominator and rewrite the mixed numbers before subtracting.
If wrong: Incorrect. Subtract, don't add, the mixed numbers.
If wrong: Incorrect. Change the numerators, too, when rewriting the fractions with a common denominator.

Q: Subtract . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. Be sure to subtract the fraction as well as the whole number. To do this you will have to regroup 8 as .
If wrong: Incorrect. Do not forget to subtract 1 from the first number when you regroup. You need to subtract , not .
If right: Correct. Regroup and subtract: .
If wrong: Incorrect. Subtract, don't add, the quantities.

Q: Cameron used ounces of hydrochloric acid in one experiment. She used ounces of the acid in a second experiment. How much more acid did Cameron use in the second experiment?
- ounce (Correct.)
- ounces (Incorrect. Subtract, don't add, the quantities.)
- ounces (Incorrect. Do not forget to subtract 1 from the first number when you regroup. You need to subtract , not .)
- ounces (Incorrect. You may have subtracted . You need to regroup or rewrite it as an improper fraction, find a common denominator, and then subtract .)
A: ounce