4/9 (3/16 - 1/12) =
- A. 5/108
- B. 5/48
- C. 2/9
- D. 20/48
Correct Answer & Rationale
Correct Answer: A
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.
Other Related Questions
Which of the following integers, when rounded to the nearest thousand, results in 2,000?
- A. 2,567
- B. 1,499
- C. 1,097
- D. 1,601
Correct Answer & Rationale
Correct Answer: d
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
When rounding to the nearest thousand, we look at the hundreds digit. If it is 5 or higher, we round up; if it is 4 or lower, we round down. Option D (1,601) rounds to 2,000 because the hundreds digit (6) is greater than 5, leading to an increase in the thousands place. Option A (2,567) rounds to 3,000, as the hundreds digit (5) prompts rounding up. Option B (1,499) rounds to 1,000 since the hundreds digit (4) indicates rounding down. Option C (1,097) also rounds to 1,000 for the same reason as B. Thus, only D rounds to 2,000.
Which of the four labeled points on the number line above has coordinate-?
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: B
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.
2/3 (6 + 1/2) =
- A. 4,1/3
- B. 4,1/2
- C. 5,1/2
- D. 6,1/3
Correct Answer & Rationale
Correct Answer: A
To solve \( \frac{2}{3}(6 + \frac{1}{2}) \), start by simplifying the expression inside the parentheses. \( 6 + \frac{1}{2} \) equals \( 6.5 \) or \( \frac{13}{2} \). Next, multiply \( \frac{2}{3} \) by \( \frac{13}{2} \): \[ \frac{2}{3} \times \frac{13}{2} = \frac{2 \times 13}{3 \times 2} = \frac{13}{3} = 4 \frac{1}{3} \] Option A is accurate. Option B (4,1/2) incorrectly adds an extra half. Option C (5,1/2) miscalculates the multiplication and addition. Option D (6,1/3) mistakenly assumes a higher total before multiplication.
To solve \( \frac{2}{3}(6 + \frac{1}{2}) \), start by simplifying the expression inside the parentheses. \( 6 + \frac{1}{2} \) equals \( 6.5 \) or \( \frac{13}{2} \). Next, multiply \( \frac{2}{3} \) by \( \frac{13}{2} \): \[ \frac{2}{3} \times \frac{13}{2} = \frac{2 \times 13}{3 \times 2} = \frac{13}{3} = 4 \frac{1}{3} \] Option A is accurate. Option B (4,1/2) incorrectly adds an extra half. Option C (5,1/2) miscalculates the multiplication and addition. Option D (6,1/3) mistakenly assumes a higher total before multiplication.
1,500 ÷ (15 + 5) =
- A. 75
- B. 130
- C. 315
- D. 400
Correct Answer & Rationale
Correct Answer: A
To solve the expression 1,500 ÷ (15 + 5), first calculate the sum inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.
To solve the expression 1,500 ÷ (15 + 5), first calculate the sum inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.