2 + (2 × 2) + 2 =
- A. 8
- B. 10
- C. 12
- D. 16
Correct Answer & Rationale
Correct Answer: A
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
To solve the expression 2 + (2 × 2) + 2, it’s essential to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). First, calculate the value inside the parentheses: 2 × 2 equals 4. Next, substitute this back into the expression: 2 + 4 + 2. Then, perform the addition from left to right: 2 + 4 equals 6, and then 6 + 2 equals 8. Options B (10), C (12), and D (16) are incorrect because they do not adhere to the proper order of operations or miscalculate the addition steps.
Other Related Questions
If 32% of n is 20.8, what is n?
- A. 64
- B. 65
- C. 66
- D. 154
Correct Answer & Rationale
Correct Answer: B
To find \( n \), we start with the equation \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
To find \( n \), we start with the equation \( 0.32n = 20.8 \). By dividing both sides by 0.32, we calculate \( n = \frac{20.8}{0.32} \), which simplifies to 65. Option A (64) is incorrect; it underestimates \( n \) by miscalculating the percentage. Option C (66) slightly overestimates \( n \), failing to accurately reflect the relationship between the percentage and the total. Option D (154) is far too high, indicating a misunderstanding of the percentage calculation. Thus, 65 is the only value that satisfies the equation.
Which of the following is equivalent to 8,1/4?
- A. 0.0825
- B. 0.825
- C. 8.25
- D. 82.5
Correct Answer & Rationale
Correct Answer: c
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
To convert the mixed number 8 1/4 into an improper fraction, first multiply the whole number (8) by the denominator (4), resulting in 32. Then, add the numerator (1) to get 33, making the improper fraction 33/4. When you divide 33 by 4, you get 8.25. Option A (0.0825) is incorrect as it represents a much smaller value. Option B (0.825) is also incorrect, as it is less than 1. Option D (82.5) is incorrect, being ten times larger than the correct value. Thus, 8.25 accurately reflects the original mixed number.
3,1/2 × 2,1/3 =
- A. 8,1/6
- B. 7,5/6
- C. 6,1/6
- D. 5,5/6
Correct Answer & Rationale
Correct Answer: A
To solve 3 1/2 × 2 1/3, first convert the mixed numbers to improper fractions: 3 1/2 becomes 7/2 and 2 1/3 becomes 7/3. Multiplying these gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
To solve 3 1/2 × 2 1/3, first convert the mixed numbers to improper fractions: 3 1/2 becomes 7/2 and 2 1/3 becomes 7/3. Multiplying these gives (7/2) × (7/3) = 49/6. Converting 49/6 back to a mixed number results in 8 1/6, which matches option A. Option B (7 5/6) is incorrect as it suggests a lower product. Option C (6 1/6) underestimates the multiplication result. Option D (5 5/6) is also too low, indicating a misunderstanding of fraction multiplication. Thus, only option A accurately reflects the product of the two mixed numbers.
Fred worked 39.5 hours last week. Alice worked 6.75 fewer hours than Fred. How many hours did Alice work?
- A. 33.75 HOURS
- B. 33.25 HOURS
- C. 33.35 HOURS
- D. 33.85 HOURS
Correct Answer & Rationale
Correct Answer: A
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.
To determine how many hours Alice worked, subtract the hours she worked less than Fred from Fred's total. Fred worked 39.5 hours, and Alice worked 6.75 hours fewer. Calculating this: 39.5 - 6.75 = 32.75 hours. However, this calculation is incorrect. The correct calculation should be: 39.5 - 6.75 = 32.75 hours. This means option A (33.75 hours) is incorrect. Option B (33.25 hours), C (33.35 hours), and D (33.85 hours) also do not match the correct calculation. Thus, none of the options are correct based on the provided data.