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Fractions and Square Root Practice Questions

1. Which of the following is listed in order from least to greatest?

  1. -3/4,-7 4/5,-8,18%,0.25,2.5
  2. -8,-7 4/5,-3/4,0.25,2.5,18%
  3. 18%,0.25,-3/4,2.5,-7 4/5,-8
  4. -8,-7 4/5,-3/4,18%,0.25,2.5

2. Which of the following fractions is larger than 2 1/4 but smaller than 2 2/5?

  1. 2 1/2
  2. 2 3/8
  3. 2 6/11
  4. 2 5/9

3. Jason chooses a number that is the square root of four less than two times Amy's number. If Amy's number is 20, what is Jason's number?

  1. 6
  2. 7
  3. 8
  4. 9

4. In a square built with unit squares, which of the following would represent the square root of the square?

  1. The number of unit squares comprising a side
  2. The total number of unit squares within the square
  3. Half of the total number of unit squares within the square
  4. The number of unit squares comprising the perimeter of the square

5. Brianna used five 3/4 cups of sugar while baking. How many cups of sugar did she use in all?

  1. 3 2/3
  2. 3 3/4
  3. 3 1/4
  4. 3 1/2

6. A publishing company has been given 29 manuscripts to review. If the company divides the work equally amongst 8 editors, which of the following represents the number of manuscript each editor will review?

  1. 3 3/5
  2. 3 5/8
  3. 3 7/9
  4. 3 2/3

7. A lake near Armando's home is reported to be 80% full of water. Which fraction is equivalent to 80% and in simplest form?

  1. 1/80
  2. 8/10
  3. 4/5
  4. 80/1

8. Alma collected coins. In the bag where she kept only dimes, she had dimes from four different years. She had 20 dimes minted in 1942, 30 minted in 1943, 40 minted in 1944, and 10 minted in 1945. If Alma reached into the bag without looking and took a dime, what is the probability that she took a dime minted in 1945?

  1. 2/5
  2. 3/10
  3. 1/5
  4. 1/10

9. A recipe calls for 3 3/4 cups of flour. Which fraction below is equivalent to this amount?

  1. 5/2
  2. 15/4
  3. 3/2
  4. 9/4

10. If , then x could be equal to

  1. 9
  2. 5
  3. 3
  4. -4
  5. -7

Answers & Explanations

1. D: The smallest negative integers are those that have the largest absolute value. Therefore, the negative integers, written in order from least to greatest, are -8,-7 4/5,-3/4. The percent, 18%, can be written as the decimal, 0.18; 0.18 is less than 0.25. The decimal, 2.5, is the greatest rational number given. Thus, the values, -8,-7 4/5,-3/4,18%,0.25,2.5, are written in order from least to greatest.

2. B: The fraction, 2 1/4, can be written as the decimal,2.25. The fraction, 2 2/5, can be written as the decimal, 2.40. The fraction, 2 3/8, can be written as the decimal, 2.375; 2.375 is larger than 2.25 but smaller than 2.40.

3. A: Jason's number can be determined by writing the following expression: ?(2x-4), where x represents Amy's number. Substitution of 20 for x gives ?(2(20)-4), which simplifies to ?36, or 6. Thus, Jason's number is 6. Jason's number can also be determined by working backwards. If Jason's number is the square root of 4 less than 2 times Amy's number, Amy's number should first be multiplied by 2 with 4 subtracted from that product and the square root taken of the resulting difference.

4. A: The square root of a square is equal to the length of one of the sides, or the number of unit squares comprising a side. For example, a square representing 7 squared will have 7 unit squares on each side; 7^2=49, and 7 is the square root of 49. The square will contain 49 unit squares, with 7 unit squares comprising each side.

5. B: In order to determine the total number of cups of sugar used while baking, the product of 5 and 3/4 should be calculated: 5?3/4=15/4, which can be simplified to 3 3/4. Thus, she used 3 3/4 cups in all.

6. B: In order to determine the number of manuscripts each editor will review, the total number of manuscripts should be divided by the number of editors; 29 / 8 can be written as 29/8, which simplifies to the mixed fraction 3 5/8. Notice that the quotient is 3 with a remainder of 5.

7. C: The 80% means 80 out of 100, which can be written as 80/100 . This fraction can be written in lowest terms by dividing both the numerator and denominator by the greatest common factor of 20, to get the fraction, 4/5.

8. D: By adding all of the dimes, we find that there are a total of 100 dimes in the bag. 10 of them were minted in 1945. The probability, then, of choosing a dime minted in 1945 is 10 out of 100, which is equivalent to the fraction 1/10.

9. B: 15/4 . The value of 3 is equivalent to 12/4. Therefore, 3 3/4=12/4+3/4=15/4. Another way of of finding this is sometimes called the "C" method. 3 3/4 equals (4x3+3)/4=15/4 .

10. E: . When you take the square root of a number, the answer is the positive and negative values of the root. Therefore, and x=-7. Only -7 is an answer choice.

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