Those Dreaded Fractions - Pretest

1) Calculate 3/5 + 2/3

5/8

2/5

19/30

1

19/15

To add fractions, we need to find a common denominator. In this case, the common denominator is 15. To convert 3/5 to have a denominator of 15, we multiply the numerator and denominator by 3, resulting in 9/15. Similarly, to convert 2/3 to have a denominator of 15, we multiply the numerator and denominator by 5, resulting in 10/15. Adding these fractions together gives us 9/15 + 10/15 = 19/15. Therefore, the correct answer is 19/15.

Explanation

To add fractions, we need to find a common denominator. In this case, the common denominator is 15. To convert 3/5 to have a denominator of 15, we multiply the numerator and denominator by 3, resulting in 9/15. Similarly, to convert 2/3 to have a denominator of 15, we multiply the numerator and denominator by 5, resulting in 10/15. Adding these fractions together gives us 9/15 + 10/15 = 19/15. Therefore, the correct answer is 19/15.

2) Find the sum of 4/9 and 3/4

43/36

4/7

1/3

7/13

3

To find the sum of fractions, we need to have a common denominator. In this case, we can use 36 as the common denominator. We then convert 4/9 and 3/4 into fractions with the denominator 36. Multiplying the numerator and denominator of 4/9 by 4, we get 16/36. Multiplying the numerator and denominator of 3/4 by 9, we get 27/36. Adding these two fractions together, we get 43/36. Therefore, the correct answer is 43/36.

Explanation

To find the sum of fractions, we need to have a common denominator. In this case, we can use 36 as the common denominator. We then convert 4/9 and 3/4 into fractions with the denominator 36. Multiplying the numerator and denominator of 4/9 by 4, we get 16/36. Multiplying the numerator and denominator of 3/4 by 9, we get 27/36. Adding these two fractions together, we get 43/36. Therefore, the correct answer is 43/36.

3) Which of the following is NOT equivalent to the other fractions?

3/5

60/100

4/6

21/35

6/10

The fractions 3/5, 60/100, and 6/10 are all equivalent because they represent the same value, which is 0.6 or 60%. However, the fraction 4/6 is not equivalent to the others because it can be simplified to 2/3, which is a different value.

Explanation

The fractions 3/5, 60/100, and 6/10 are all equivalent because they represent the same value, which is 0.6 or 60%. However, the fraction 4/6 is not equivalent to the others because it can be simplified to 2/3, which is a different value.

4) Without calculating anything, what whole number is 7/8 + 15/16 closest to?

1

2

4

22

24

Without calculating anything, we can determine that 7/8 is slightly less than 1 and 15/16 is slightly less than 1 as well. When adding these fractions together, we can estimate that the sum will be slightly less than 2. Therefore, the whole number that 7/8 + 15/16 is closest to without calculating is 2.

Explanation

Without calculating anything, we can determine that 7/8 is slightly less than 1 and 15/16 is slightly less than 1 as well. When adding these fractions together, we can estimate that the sum will be slightly less than 2. Therefore, the whole number that 7/8 + 15/16 is closest to without calculating is 2.

5) Which of the following problems would be solved by finding the product 18 1/2 times 12 1/4?

The correct answer is that Sue wants to carpet her living room. Her room measures 18 1/2 feet long and 12 1/4 feet wide. To determine how many square feet of carpeting she should order, we need to find the product of the length and width of the room.

Explanation

The correct answer is that Sue wants to carpet her living room. Her room measures 18 1/2 feet long and 12 1/4 feet wide. To determine how many square feet of carpeting she should order, we need to find the product of the length and width of the room.

6) Which of the following problems would be solved by finding the difference of 18 1/2 and 12 1/4?

The correct answer is "Amanda weighed 12 1/4 pounds at age three months. By six months her weight was up to 18 1/2 pounds. How much did she gain in that time?" This question involves finding the difference between Amanda's weight at three months and her weight at six months to determine how much weight she gained in that time period.

Explanation

The correct answer is "Amanda weighed 12 1/4 pounds at age three months. By six months her weight was up to 18 1/2 pounds. How much did she gain in that time?" This question involves finding the difference between Amanda's weight at three months and her weight at six months to determine how much weight she gained in that time period.

7) Calculate 9/8 divided by 3/4

27/32

2/3

24/36

36/24

3/2

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, 9/8 divided by 3/4 is equal to (9/8) * (4/3). Multiplying the numerators gives us 36, and multiplying the denominators gives us 24. Therefore, the answer is 36/24, which simplifies to 3/2.

Explanation

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, 9/8 divided by 3/4 is equal to (9/8) * (4/3). Multiplying the numerators gives us 36, and multiplying the denominators gives us 24. Therefore, the answer is 36/24, which simplifies to 3/2.

8) Which of the following problems would be solved by finding the quotient of 48 1/2 and 12 1/4?

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Explanation

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9) Find the least common multiple (lcm) of 35 and 42.

1

7

210

1470

There is none

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers. In this case, we need to find the LCM of 35 and 42. The prime factors of 35 are 5 and 7, while the prime factors of 42 are 2, 3, and 7. To find the LCM, we need to take the highest power of each prime factor that appears in either number. Therefore, the LCM of 35 and 42 is 2 * 3 * 5 * 7 = 210.

Explanation

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers. In this case, we need to find the LCM of 35 and 42. The prime factors of 35 are 5 and 7, while the prime factors of 42 are 2, 3, and 7. To find the LCM, we need to take the highest power of each prime factor that appears in either number. Therefore, the LCM of 35 and 42 is 2 * 3 * 5 * 7 = 210.

10) Find the product of 7/8 and 4/5

28/40

7/10

35/32

32/35

72/40

To find the product of fractions, we multiply the numerators together and the denominators together. In this case, multiplying 7/8 and 4/5 gives us (7*4)/(8*5) = 28/40. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. Simplifying 28/40 gives us 7/10. Therefore, the correct answer is 7/10.

Explanation

To find the product of fractions, we multiply the numerators together and the denominators together. In this case, multiplying 7/8 and 4/5 gives us (7*4)/(8*5) = 28/40. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. Simplifying 28/40 gives us 7/10. Therefore, the correct answer is 7/10.