Choose the best answer. If necessary, use the paper you were given.
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 fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
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 fractions yields (7/2) * (7/3) = 49/6. Converting 49/6 back to a mixed number gives 8(1/6). Option B, 7(5/6), results from incorrect multiplication. Option C, 6(1/6), miscalculates the product as well. Option D, 5(5/6), reflects a misunderstanding of fraction multiplication. The proper method confirms that 8(1/6) is indeed the accurate result.
Other Related Questions
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.
2(1/2 + 1/3) =
- A. 1(2/3)
- B. 1(5/6)
- C. 2(1/6)
- D. 2(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
Charlotte is drilling three holes of different sizes in a bird house that she is making. The diameters of the holes are 1(1/2) inches, 1(3/4) inches, and 1(3/8) inches. Which of the following gives the diameters, in inches, in order from least to greatest?
- A. 1(1/2), 1(3/4), 1(3/8)
- B. 1(1/2), 1(3/8), 1(3/4)
- C. 1(3/8), 1(3/4), 1(1/2)
- D. 1(3/8), 1(1/2), 1(3/4)
Correct Answer & Rationale
Correct Answer: D
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
If 40 is 20 percent of a number, then the number is what percent of 40?
- A. 500%
- B. 200%
- C. 80%
- D. 20%
Correct Answer & Rationale
Correct Answer: A
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.
To determine what percent a number (let's call it X) is of 40, we first establish that 40 is 20% of X. This can be represented as the equation: 40 = 0.2X. Solving for X gives us X = 200. Now, to find out what percent 200 is of 40, we use the formula (part/whole) × 100, which results in (200/40) × 100 = 500%. Option B (200%) is incorrect as it mistakenly uses X instead of calculating the percentage of 40. Option C (80%) and Option D (20%) are also incorrect for similar reasons; they do not accurately reflect the relationship between 200 and 40.