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.
Other Related Questions
At the Crest Coffee Shop, the cost of a plain bagel was $0.75 last year. This year the cost of a plain bagel is $0.90. By what percent did the cost of a plain bagel increase from last year to this year?
- A. 10%
- B. 15%
- C. 17%
- D. 20%
Correct Answer & Rationale
Correct Answer: D
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
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.
Multiplying a certain nonzero number by 0.01 gives the same result as dividing the number by
- A. 100
- B. 10
- C. 1/10
- D. 1/100
Correct Answer & Rationale
Correct Answer: A
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
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.