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What is 1.25 as a fraction?
- A. 1 1/4
- B. 5/4
- C. 4/5
- D. 25/20
Correct Answer: B
Rationale: To convert a decimal to a fraction, we note that 1.25 can be expressed as 1 + 0.25. Since 0.25 is equivalent to 25/100 or 1/4, we add 1 whole to 1/4 to get 1 1/4, which simplifies to 5/4. Therefore, 1.25 as a fraction is 5/4. Choice A (1 1/4) is the mixed number form of 5/4. Choice C (4/5) and Choice D (25/20) are incorrect fractions that do not represent 1.25.
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What number is 6 equal to 30% of?
- A. 18
- B. 20
- C. 24
- D. 26
Correct Answer: A
Rationale: To find the number that is 30% of 6, you can set up the equation 0.3x = 6. Solving for x gives x = 6 / 0.3 = 20. Therefore, 6 is equal to 30% of 20.
Choice B, 20, is incorrect as it is the result of the calculation. Choice C, 24, and Choice D, 26, are incorrect as they are not the numbers that 6 is equal to 30% of.
What is the median of the set of numbers {2, 3, 9, 12, 15}?
- A. 3
- B. 9
- C. 12
- D. 15
Correct Answer: B
Rationale: The median represents the middle value in an ordered set of numbers. To find the median, the numbers need to be arranged in ascending order: {2, 3, 9, 12, 15}. Since the set has an odd number of elements, the median will be the middle value, which is 9 in this case. Choice A (3) and Choice D (15) are incorrect as they do not fall in the middle of the ordered set. Choice C (12) is also incorrect as it is not the middle value in this particular set.
How will the number 847.89632 be written if rounded to the nearest hundredth?
- A. 847.90
- B. 900
- C. 847.89
- D. 847.896
Correct Answer: A
Rationale: When rounding to the nearest hundredth, we look at the digit in the thousandth place, which is 8. Since the next digit, in the ten-thousandth place, is 9 (greater than or equal to 5), we round up the hundredth place digit. Therefore, 847.89632 rounded to the nearest hundredth is 847.90. Choice B (900) is incorrect as it does not round the number to the nearest hundredth. Choice C (847.89) is also incorrect as it drops the digit 6 in the ten-thousandth place. Choice D (847.896) does not round the number to the nearest hundredth as it retains the thousandth place digit 3.
What is the simplified form of the expression (x^2 + 2x)/(x)?
- A. x + 2
- B. x^2 + 2
- C. x(x + 2)
- D. 1 + 2/x
Correct Answer: A
Rationale: To simplify the expression (x^2 + 2x)/(x), we factor out x from the numerator to get x(x + 2) and then cancel the x in the denominator. This simplifies to x + 2, making choice A the correct answer. Choice B (x^2 + 2) is incorrect as it does not account for the division by x. Choice C (x(x + 2)) is also incorrect as it represents the factored form before cancellation. Choice D (1 + 2/x) is incorrect as it does not simplify the expression correctly.
Which number is larger, 0.5 or 1/3?
- A. 0.5
- B. 1/3
- C. They are equal
- D. Cannot be determined
Correct Answer: A
Rationale: To compare 0.5 and 1/3, we can convert 0.5 to a fraction, which is 1/2. When comparing 1/2 and 1/3, we find that 1/2 is greater than 1/3. Therefore, 0.5 is larger than 1/3. Choice B is incorrect as 1/3 is smaller. Choice C is incorrect as the numbers are not equal. Choice D is incorrect as a clear comparison can be made.