60 ÷ 3/3 =
- A. 20
- B. 21
- C. 23
- D. 24
Correct Answer & Rationale
Correct Answer: A
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.
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.
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.
Alexia, Bob, and Comelia recorded the number of pages of books they read last month. Alexia read 135 pages, Bob read 26 pages less than Alexia, and Comelia read 3 and one-half times more pages than Alexia and Bob combined. Which of the following represents the total number of pages that Alexia, Bob, and Comelia read last month?
- A. 3.5(135 + 26)
- B. 3.5[2(135) - 26]
- C. 4.5[2(135) - 26]
- D. 4.5[2(135) + 26]
Correct Answer & Rationale
Correct Answer: C
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
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.