6[4 + 2(1 - 3)] =
- B. 20
- C. 24
- D. 48
Correct Answer & Rationale
Correct Answer: A
To solve the expression 6[4 + 2(1 - 3)], begin by simplifying inside the brackets. The calculation within the parentheses, 1 - 3, equals -2. Next, multiply by 2 to get -4. Now, the expression inside the brackets is 4 - 4, which simplifies to 0. Finally, multiplying 6 by 0 results in 0. Option B (20), C (24), and D (48) arise from miscalculations, such as incorrectly handling the order of operations or not simplifying the expression fully. None of these options account for the zero outcome from the calculations.
To solve the expression 6[4 + 2(1 - 3)], begin by simplifying inside the brackets. The calculation within the parentheses, 1 - 3, equals -2. Next, multiply by 2 to get -4. Now, the expression inside the brackets is 4 - 4, which simplifies to 0. Finally, multiplying 6 by 0 results in 0. Option B (20), C (24), and D (48) arise from miscalculations, such as incorrectly handling the order of operations or not simplifying the expression fully. None of these options account for the zero outcome from the calculations.
Other Related Questions
2,3/8 + 5,5/6 =
- A. 7,5/24
- B. 7,4/7
- C. 8,5/24
- D. 8,4/7
Correct Answer & Rationale
Correct Answer: C
To solve 2,3/8 + 5,5/6, first convert the mixed numbers into improper fractions. For 2,3/8, this becomes (2 * 8 + 3)/8 = 19/8. For 5,5/6, it is (5 * 6 + 5)/6 = 35/6. Next, find a common denominator, which is 24. Convert the fractions: 19/8 becomes 57/24, and 35/6 becomes 140/24. Adding these gives 197/24, which converts back to a mixed number as 8,5/24. Options A and B do not match this result. Option D, while close, inaccurately represents the fraction.
To solve 2,3/8 + 5,5/6, first convert the mixed numbers into improper fractions. For 2,3/8, this becomes (2 * 8 + 3)/8 = 19/8. For 5,5/6, it is (5 * 6 + 5)/6 = 35/6. Next, find a common denominator, which is 24. Convert the fractions: 19/8 becomes 57/24, and 35/6 becomes 140/24. Adding these gives 197/24, which converts back to a mixed number as 8,5/24. Options A and B do not match this result. Option D, while close, inaccurately represents the fraction.
3 × (1/2 + 1/3) =
- A. 2,1/2
- B. 2,5/6
- C. 3,1/6
- D. 3,5/6
Correct Answer & Rationale
Correct Answer: A
To solve 3 × (1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. This gives us (3/6 + 2/6) = 5/6. Multiplying by 3 results in 3 × (5/6) = 15/6, which simplifies to 2 1/2 (Option A). Option B (2 5/6) incorrectly adds an extra fraction. Option C (3 1/6) miscalculates the multiplication. Option D (3 5/6) also misinterprets the original problem, leading to an incorrect total. Thus, only Option A accurately represents the solution.
To solve 3 × (1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. This gives us (3/6 + 2/6) = 5/6. Multiplying by 3 results in 3 × (5/6) = 15/6, which simplifies to 2 1/2 (Option A). Option B (2 5/6) incorrectly adds an extra fraction. Option C (3 1/6) miscalculates the multiplication. Option D (3 5/6) also misinterprets the original problem, leading to an incorrect total. Thus, only Option A accurately represents the solution.
Which of the following inequalities is true?
- A. 0.7 < 0.1 < 0.11 < 0.101
- B. 0.1 < 0.7 < 0.101 < 0.11
- C. 0.1 < 0.7 < 0.11 < 0.101
- D. 0.1 < 0.101 < 0.11 < 0.7
Correct Answer & Rationale
Correct Answer: D
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
3/8 expressed as a percent is
- A. 3.75%
- B. 37.50%
- C. 38%
- D. 38,1/3%
Correct Answer & Rationale
Correct Answer: B
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.