Choose the best answer. If necessary, use the paper you were given.
Which of the following is equal to 3 * 9?
- A. 6 * 6
- B. 9 * 3
- C. 3 * 3 * 6
- D. 3 * 3 * 3 * 3
Correct Answer & Rationale
Correct Answer: B
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Option B, 9 * 3, is equal to 3 * 9 due to the commutative property of multiplication, which states that changing the order of factors does not change the product. Option A, 6 * 6, equals 36, which does not match 27 (the product of 3 * 9). Option C, 3 * 3 * 6, calculates to 54, also not equal to 27. Option D, 3 * 3 * 3 * 3, equals 81, further confirming it is not equivalent to 27. Thus, only option B accurately represents the value of 3 * 9.
Other Related Questions
Last year Joan's salary was $18,000. If she receives a $900 raise for this year, what percent of last year's salary is her raise?
- A. 2%
- B. 5%
- C. 20%
- D. 50%
Correct Answer & Rationale
Correct Answer: B
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
What is rounded to the nearest hundredth? 48/27
- A. 1.7
- B. 1.77
- C. 1.78
- D. 1.8
Correct Answer & Rationale
Correct Answer: C
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
Of the following, which is closest to (2(12/15) - 1/10) / (16/6)?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.
To evaluate the expression (2(12/15) - 1/10) / (16/6), we first simplify the numerator. Calculating 2(12/15) gives us 16/15. Next, we convert 1/10 to a common denominator of 30, resulting in 3/30. Thus, the numerator becomes (16/15 - 3/30). Converting 16/15 to a denominator of 30 yields 32/30, leading to (32/30 - 3/30) = 29/30. Now, simplifying the denominator, 16/6 reduces to 8/3. Dividing (29/30) by (8/3) is equivalent to multiplying by its reciprocal: (29/30) * (3/8) = 87/240, which approximates to 0.36, closest to 1. Options C (2) and D (3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result.