Fractions and Square Root Practice Questions

  1. Which of the following sequences is in order from least to greatest?
  1. –\(\tfrac{3}{4}\), -7\(\tfrac{4}{5}\), -8, 18%, 0.25, 2.5
  2. -8, -7\(\tfrac{4}{5}\), –\(\tfrac{3}{4}\), 0.25, 2.5, 18%
  3. 18%, 0.25, –\(\tfrac{3}{4}\), 2.5, -7\(\tfrac{4}{5}\), -8
  4. -8, -7\(\tfrac{4}{5}\), –\(\tfrac{3}{4}\), 18%, 0.25, 2.5
Show Answer
The correct answer is 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 as follows:

-8, -7\(\tfrac{4}{5}\), –\(\tfrac{3}{4}\)

We can write 18% as the decimal 0.18, which is less than 0.25. The decimal 2.5 is the greatest rational number given. Thus, the values in choice D are written in order from least to greatest.

 

  1. Which of the following fractions is larger than 2\(\tfrac{1}{4}\) but smaller than 2\(\tfrac{2}{5}\)?
  1. \(\tfrac{1}{2}\)
  2. \(\tfrac{3}{8}\)
  3. \(\tfrac{6}{11}\)
  4. \(\tfrac{5}{9}\)
Show Answer
The correct answer is B!

The fraction 2\(\tfrac{1}{4}\) can be written as the decimal 2.25. The fraction 2\(\tfrac{2}{5}\) can be written as the decimal 2.40. The fraction 2\(\tfrac{3}{8}\) can be written as the decimal 2.375, which is larger than 2.25 but smaller than 2.40.

 

  1. 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
Show Answer
The correct answer is A!

Jason’s number can be determined by writing the following expression, where \(x\) represents Amy’s number:

\(\sqrt{2x-4}\)

Substitution of 20 for \(x\) gives \(\sqrt{2(20)-4}\), which simplifies to \(\sqrt{36}\), 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 four less than two 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.

 

  1. 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
Show Answer
The correct answer is 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 \(7^2\) will have seven unit squares on each side. Because \(7^2=49\), the square will contain 49 unit squares, with seven unit squares comprising each side.

 

  1. Brianna used five \(\tfrac{3}{4}\) cups of sugar while baking. How many cups of sugar did she use in all?
  1. 3 \(\tfrac{2}{3}\)
  2. 3 \(\tfrac{3}{4}\)
  3. 3 \(\tfrac{1}{4}\)
  4. 3 \(\tfrac{1}{2}\)
Show Answer
The correct answer is B!

In order to determine the total number of cups of sugar used while baking, the product of 5 and \(\tfrac{3}{4}\) should be calculated:

\(5\times \tfrac{3}{4}=\tfrac{15}{4}\)

This can be simplified to 3\(\tfrac{3}{4}\). Thus, she used 3\(\tfrac{3}{4}\) cups in all.

 

  1. A publishing company has been given 29 manuscripts to review. If the company divides the work equally among eight editors, which of the following represents the number of manuscript each editor will review?
  1. 3 \(\tfrac{3}{5}\)
  2. 3 \(\tfrac{5}{8}\)
  3. 3 \(\tfrac{7}{9}\)
  4. 3 \(\tfrac{2}{3}\)
Show Answer
The correct answer is B!

To solve this, we need to split 29 manuscripts equally among eight editors.

\(29 \div 8\)

Since \(8 \times 3 = 24\), each editor can take three whole manuscripts (so 24 total). That means there are \(29-24=5\) manuscripts remaining. These must be shared equally among the eight editors, which is \(\tfrac{5}{8}\) of a manuscript per editor.

Combine the whole number and the fraction to get the final answer:

\(3+\tfrac{5}{8}=3\tfrac{5}{8}\)

 

  1. 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. \(\tfrac{1}{80}\)
  2. \(\tfrac{8}{10}\)
  3. \(\tfrac{4}{5}\)
  4. \(\tfrac{80}{1}\)
Show Answer
The correct answer is C!

We know that 80% means 80 out of 100, which can be written as \(\tfrac{80}{100}\). 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 \(\tfrac{4}{5}\).

 

  1. 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. \(\tfrac{2}{5}\)
  2. \(\tfrac{3}{10}\)
  3. \(\tfrac{1}{5}\)
  4. \(\tfrac{1}{10}\)
Show Answer
The correct answer is D!

By adding all of the dimes, we find that there are a total of 100 dimes in the bag. Ten 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 \(\tfrac{1}{10}\).

 

  1. A recipe calls for 3\(\tfrac{3}{4}\) cups of flour. Which fraction below is equivalent to this amount?
  1. \(\tfrac{5}{2}\)
  2. \(\tfrac{15}{4}\)
  3. \(\tfrac{3}{2}\)
  4. \(\tfrac{9}{4}\)
Show Answer
The correct answer is B!

The value of 3 is equivalent to \(\tfrac{12}{4}\). Therefore:

\(3\tfrac{3}{4}=\tfrac{12}{4}+\tfrac{3}{4}=\tfrac{15}{4}\)