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 what the numerator and the denominator represent. There are seven equal shaded parts out of twelve equal parts in the whole circle.
If wrong: Incorrect. We are looking for how much is shaded out of how much is there all together. There are seven equal shaded parts. There are twelve equal parts all together.
If wrong: Incorrect. This fraction would represent the unshaded part. There are seven equal shaded parts out of twelve equal parts in the whole circle.
If right: Correct. The total number of equal parts in the whole is the denominator. The number of shaded parts is the numerator.

Q: Write a fraction for the portion of the grid that is NOT shaded.
A: (a choice with no text)
If wrong: Incorrect. There are 15 equal sections in the whole grid, so the denominator should be 15. There are 7 sections that are not shaded, so the numerator should be 7.
If right: Correct. There are 7 sections not shaded and 15 equal sections in the whole, so are not shaded.
If wrong: Incorrect. This represents the fraction of the grid that is shaded. The question asked for the fraction of the gird that is NOT shaded.
If wrong: Incorrect. There are 15 equal sections in the whole grid, so the denominator should be 15. There are 7 sections that are not shaded, so the numerator should be 7.

Q: Which fraction is an improper fraction?
A: (a choice with no text)
If right: Correct. The numerator of an improper fraction is greater than or equal to the denominator.
If wrong: Incorrect. The numerator of an improper fraction is greater than or equal to the denominator. Here the numerator is less than the denominator, so it is not an improper fraction.
If wrong: Incorrect. The numerator of an improper fraction is greater than or equal to the denominator. Here the numerator is less than the denominator, so it is not an improper fraction.
If wrong: Incorrect. The numerator of an improper fraction is greater than or equal to the denominator. Here the numerator is less than the denominator, so it is not an improper fraction.

Q: Change from an improper fraction to a mixed number.
- 9 (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 39 by 9 to find the whole number part and using the remainder 3 as the fractional part.
If wrong: Incorrect. Do not split the numerator into a numerator and a whole number. Divide 39 by 9 to find the whole number part and use the remainder 3 as the fractional part.
If wrong: Incorrect. Do not split the numerator into a whole number and numerator. Divide 39 by 9 to find the whole number part and use the remainder 3 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 1.
If wrong: Incorrect. You should not combine the whole number and the numerator. You need to multiply it by 8 first, and then add the 1.
If wrong: Incorrect. You should not add the whole number to the numerator. You need to multiply it by 8 first. Check that your answer is reasonable. is equal to 1.
If right: Correct. . Add this to 1 to get 57. This is the numerator of the improper fraction. The denominator is still 8.

Q: Determine whether 606 is divisible by 2, 3, 4, or 6.
- 2, 3, and 6 only (Correct. 606 is divisible by 3 because the digits add to 12 and 12 is divisible by 3. 606 is divisible by 2 because the ones digit (6) is an even number. Because 606 is divisible by 2 and 3, it is also divisible by 6. However, the number formed by the last two digits, 6, is not divisible by 4, so 606 is not divisible by 4.)
- 2, 3, 4, and 6 (Incorrect. 606 is divisible by 2, 3, and 6. However, the number formed by the last two digits, 6, is not divisible by 4, so 606 is not divisible by 4.)
- 2 and 3 only (Incorrect. 606 is divisible by 2 and 3. However, if a number is divisible by 2 and 3, then it is also divisible by 6.)
- 3 and 6 only (Incorrect. 606 is divisible by 3 and 6. However, 606 is also divisible by 2 because the last digit of 606 is an even number.)
A: 2, 3, and 6 only

Q: Find all the factors of 99.
- 3, 9, 11, and 33 (Incorrect. 1 and 99 are also factors of 99.)
- 1, 9, 11, and 99 (Incorrect. If a number is divisible by 9, then it is also divisible by 3.)
- 1, 3, 9, 11, 33, and 99 (Correct. The divisibility rules can be used to show that 1, 3, and 9 are factors (and that 2, 4, 5, 6, and 10 are not). Use factor pairs to find the rest of the factors: 11, 33, and 99. Use division to check 7 and 8. Since is less than 10, stop.)
- 1, 3, and 9 (Incorrect. Remember that when you find a factor, you should find the other number in the factor pair.)
A: 1, 3, 9, 11, 33, and 99

Q: Determine whether 97 is prime, composite, or neither.
- composite (Incorrect. 97 is not a composite number because its only factors are 1 and 97.)
- neither (Incorrect. Only the number 1 is neither prime nor composite.)
- prime (Correct. 97 is a prime number because it has no factors other than 1 and 97.)
A: prime

Q: Which of the following shows the prime factorization of 360 using exponential notation?
A: (a choice with no text)
If right: Correct. The prime factorization is , which can be rewritten with exponents for the factors that repeat.
If wrong: Incorrect. , not the 360 it should multiply out to.
If wrong: Incorrect. , not 360. Remember to include the correct exponent for each factor in the prime factorization.
If wrong: Incorrect. , not the 360 it should multiply out to.

Q: A jar contains 75 marbles. of the marbles are black. What fraction of the marbles are black, using 75 as the denominator?
A: (a choice with no text)
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 15.
If wrong: Incorrect. This is an equivalent fraction, but the denominator should be 75, not 125.
If right: Correct. You have to multiply the denominator 5 by 15 to get 75, so the numerator is .
If wrong: Incorrect. To find equivalent fractions, multiply or divide both the numerator and the denominator by the same number. In this case multiply by 15.

Q: Simplify .
A: (a choice with no text)
If wrong: Incorrect. You may have forgotten to divide the denominator by 2 every time you divided the numerator by 2. Although is in lowest terms, it is not equivalent to .
If wrong: Incorrect. Although is an equivalent fraction to , the numerator and denominator have a common factor, 3, so this fraction cannot be in lowest terms.
If right: Correct. is in lowest terms, as 1 is the only common factor of 1 and 4.
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.

Q: Which of the following pairs consists of equivalent fractions?
- and (Incorrect. Divide the numerator and denominator of by 3. You are left with the fraction . Now both fractions have the same denominator but different numerators, so the two fractions are not equivalent.)
- and (Incorrect. You can write both fractions with a common denominator, 5. simplifies to , and simplifies to . Now both fractions have the same denominator but different numerators, so the two fractions are not equivalent.)
- and (Incorrect. Although the same numbers, 5 and 6, are used in each fraction, the numerators and denominators are not equal, so the fractions cannot be equivalent.)
- and (Correct. When you rewrite both fractions with a common denominator, 3, you are left with the fraction . This means that the two fractions are equivalent.)
A: and

Q: Which of the following is a true statement?
A: (a choice with no text)
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 right: Correct. Rewrite both fractions so they have a common denominator, 48. You find that , so as well.
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 your answer, if possible.
A: (a choice with no text)
If wrong: Incorrect. You may have added the numerators and added the denominators instead of multiplying.
If wrong: Incorrect. You may have added the two fractions instead of multiplying them.
If wrong: Incorrect. This is the correct product, but it is not in lowest terms.
If right: Correct. Before multiplying, reorder the numerators and cancel the common factor.

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

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 wrong: Incorrect. This is the product, but the answer must be expressed as a mixed number.
If right: Correct.

Q: Micah is planning a road trip. He estimates that he will drive a total of of hours. He wants to stop for gas after of the total time has passed. How long will he drive before he stops for gas? Express your answer as a mixed number.
- 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 (Incorrect. This is the correct amount of time, but you need to express the 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 (Correct.)
A: hours

Q: What is the reciprocal of ?
A: (a choice with no text)
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 right: Correct. , so the reciprocal is .
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 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.

Q: Find . Simplify the answer and write as a mixed number, if possible.
A: (a choice with no text)
If wrong: Incorrect. You may have multiplied by instead of its reciprocal: . To solve the problem, multiply the first number by the reciprocal of the second number:
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 right: Correct.
If wrong: Incorrect. You may have multiplied the reciprocal of both numbers: . To solve the problem, multiply the first number by the reciprocal of the second number:

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 incorrectly 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 multiplied by the reciprocal of , which is . You want to multiply by the reciprocal of , which is .
If right: Correct.
If wrong: Incorrect. You may have used instead of , which is the correct improper fraction to use for .

Q: An art teacher has pounds of clay and 25 students. Each student will get an equal amount of clay. How much clay does each student get? Write the answer as a mixed number.
A: (a choice with no text)
If right: Correct.
If wrong: Incorrect. This is an equivalent fraction to the correct answer, but it has not been written as a mixed number.
If wrong: Incorrect. You may have used the multiplication expression . You need to use division to solve the problem:
If wrong: Incorrect. This is the result of . This would show the size of each group when 25 is divided into equal groups. You need to find the size of each group when is divided into 25 equal groups.

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

Q: What is the least common multiple of 12 and 44?
- 88 (Incorrect. This is a multiple of 44, but not of 12.)
- 264 (Incorrect. This is a common multiple of 12 and 44, but it is not the least common multiple.)
- 132 (Correct. and . The least common multiple is .)
- 528 (Incorrect. This is the product of 12 and 44, not the least common multiple.)
A: 132

Q: Rewrite the fractions and as fractions with a least common denominator.
- and (Incorrect. 15 is the least common denominator, but these fractions are not equivalent to the original fractions. Remember to multiply both the numerator and denominator of a fraction by the same number to find an equivalent fraction.)
- and (Incorrect. 45 is a common denominator, but not the least common denominator for the fractions. The least common multiple of 3 and 15 is 15, so rewrite the fraction with a denominator of 15.)
- and (Incorrect. Adding denominators does not give you the least common denominator. These fractions are not equivalent to the original fractions. The least common multiple of 3 and 15 is 15, so rewrite the fraction with a denominator of 15.)
- and (Correct. The least common multiple of 3 and 15 is 15, so rewrite the fraction with a denominator of 15.)
A: and

Q: Add . Simplify the answer and write it as a mixed number, if possible.
A: (a choice with no text)
If wrong: Incorrect. This is the correct sum, but it has not been simplified. Divide the numerator and the denominator of the fraction by 2.
If wrong: Incorrect. When you rewrite each fraction with a common denominator, do not use the original numerators. Remember to multiply both the the numerator and denominator of a fraction by the same number to find an equivalent fraction.
If right: Correct.
If wrong: Incorrect. This is the correct sum, but it has not been written as a mixed number.

Q: Add . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If wrong: Incorrect. When the denominators are the same you can add the numerators, but the reverse is not true. You cannot add the denominators if the numerators are the same.
If wrong: Incorrect. Do not forget to include the whole number part of the sum.
If right: Correct.
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: In seventh grade, Emile grew cm, and in eighth grade he grew cm. How much did his height increase during these two years?

The answer should be written as a proper mixed number and should be simplified, if possible.
- cm (Incorrect. This is the correct sum, but it is not a proper mixed number.)
- cm (Correct.)
- cm (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.)
- cm (Incorrect. To add fractions with unlike denominators, you must first rewrite them with a common denominator. You do not add the numerators and denominators.)
A: cm

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. This is the correct difference, but it is not simplified. The correct answer is .
If right: Correct.
If wrong: Incorrect. This is the correct difference, but it is not simplified. The correct answer is .

Q: Subtract . Simplify the answer and write as a mixed number.
- 13 (Incorrect. Subtract, don't add, the mixed numbers.)
A: (a choice with no text)
If wrong: Incorrect. You may have subtracted . You need to rewrite each mixed number as an improper fraction before subtracting:
If right: Correct. Rewrite each mixed number as an improper fraction before subtracting.
If wrong: Incorrect. Don't add the whole numbers to the numerators before subtracting.

Q: Subtract . Simplify the answer and write as a mixed number.
A: (a choice with no text)
If right: Correct. One way to subtract is by regrouping: . Then find a common denominator: .
If wrong: Incorrect. Subtract, don't add, the mixed numbers.
If wrong: Incorrect. Do not forget to subtract 1 from the first mixed number when you regroup. You need to subtract , not .
If wrong: Incorrect. Do not forget to subtract the whole number in the second mixed number.

Q: Cho used cups of flour to bake a cake. She used cups of flour to bake a loaf of bread. How much more flour did Cho use to bake the loaf of bread than to bake the cake?
- cup (Incorrect. You may have subtracted . You need to regroup or rewrite it as an improper fraction, find a common denominator, and then subtract .)
- cups (Incorrect. Do not forget to subtract 1 from the first number when you regroup. You need to subtract , not .)
- cup (Correct.)
- cups (Incorrect. Subtract, don't add, the quantities.)
A: cup