Fractions and Square Root Flashcards

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

Answer: -8,-7 4/5,-3/4,18%,0.25,2.5

To order numbers from least to greatest, it's helpful to convert them to a common format, such as decimals. Converting the given numbers yields: -8, -7.8 (from -7 4/5), -0.75 (from -3/4), 0.18 (from 18%), 0.25, and 2.5. When arranged in ascending order, this sequence is -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?

Answer: 2 3/8

To determine which fraction fits the criteria, convert all numbers to a common format, such as decimals. 2 1/4 is 2.25, and 2 2/5 is 2.40. Among the options, 2 3/8 converts to 2.375, which is indeed greater than 2.25 and smaller than 2.40. The other options are either too small or too large.

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?

Answer: 6

First, calculate two times Amy's number: 2 * 20 = 40. Next, find four less than that result: 40 - 4 = 36. Finally, Jason's number is the square root of 36, which is 6. Therefore, Jason's number is 6.

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

Answer: The number of unit squares comprising a side

The area of a square is calculated by multiplying its side length by itself (side * side, or side²). Therefore, the square root of the total number of unit squares (which represents the area of the square) will give you the length of one side of that square. This directly corresponds to the number of unit squares comprising a side.

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

Answer: 3 3/4

The phrase 'five 3/4 cups' indicates multiplication. To find the total amount, multiply 5 by 3/4. This calculation results in (5 * 3) / 4 = 15/4. Converting the improper fraction 15/4 to a mixed number yields 3 with a remainder of 3, which is written as 3 3/4 cups.

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?

Answer: 3 5/8

To determine the number of manuscripts each editor will review, divide the total number of manuscripts (29) by the number of editors (8). The division 29 ÷ 8 results in 3 with a remainder of 5. This can be expressed as the mixed number 3 5/8.

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?

Answer: 4/5

To convert a percentage to a fraction, divide the percentage by 100, so 80% becomes 80/100. To simplify this fraction to its simplest form, divide both the numerator and the denominator by their greatest common divisor, which is 20. This simplification results in the fraction 4/5.

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?

Answer: 1/10

First, calculate the total number of dimes Alma has: 20 + 30 + 40 + 10 = 100 dimes. The number of dimes minted in 1945 is 10. The probability of picking a 1945 dime is the number of favorable outcomes (10 dimes) divided by the total number of possible outcomes (100 dimes), which is 10/100. This fraction simplifies to 1/10.

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

Answer: 15/4

To convert a mixed number like 3 3/4 into an improper fraction, multiply the whole number (3) by the denominator (4) and then add the numerator (3). This calculation yields (3 * 4) + 3 = 12 + 3 = 15. The denominator remains the same, so the equivalent improper fraction is 15/4.

10. If , then x could be equal to

Answer: -7

The problem is missing the equation, but based on the options, it likely involves an absolute value equation. Assuming the equation is |x + 5| = 2, there are two possible solutions: x + 5 = 2 or x + 5 = -2. Solving these gives x = -3 or x = -7. Since -7 is one of the provided options, it is a correct possible value for x.