The large square above has area 1 and is divided into 25 squares of equal area. Which of the following represents the area of the shaded region?
- A. 0.8
- B. 0.16
- C. 0.24
- D. 0.32
Correct Answer & Rationale
Correct Answer: D
In a large square with an area of 1, each of the 25 smaller squares has an area of \( \frac{1}{25} = 0.04 \). To find the area of the shaded region, count the number of shaded squares. If there are 8 shaded squares, then the area of the shaded region is \( 8 \times 0.04 = 0.32 \). Option A (0.8) is incorrect as it exceeds the total area of the large square. Option B (0.16) represents 4 shaded squares, which is not consistent with the given information. Option C (0.24) suggests 6 shaded squares, which also does not match. Thus, the area of the shaded region is accurately represented by option D, 0.32.
In a large square with an area of 1, each of the 25 smaller squares has an area of \( \frac{1}{25} = 0.04 \). To find the area of the shaded region, count the number of shaded squares. If there are 8 shaded squares, then the area of the shaded region is \( 8 \times 0.04 = 0.32 \). Option A (0.8) is incorrect as it exceeds the total area of the large square. Option B (0.16) represents 4 shaded squares, which is not consistent with the given information. Option C (0.24) suggests 6 shaded squares, which also does not match. Thus, the area of the shaded region is accurately represented by option D, 0.32.
Other Related Questions
6 + 5,1/3 ÷ (6 - 5,1/3) =
- A. 1,1/3
- B. 5,1/3
- C. 16
- D. 17
Correct Answer & Rationale
Correct Answer: C
To solve the equation, first evaluate the expression in the parentheses: \(6 - 5\frac{1}{3}\) equals \(6 - \frac{16}{3} = \frac{18}{3} - \frac{16}{3} = \frac{2}{3}\). Next, compute \(5\frac{1}{3}\) as \(\frac{16}{3}\). The equation now reads \(6 + \frac{16}{3} \div \frac{2}{3}\). Dividing \(\frac{16}{3}\) by \(\frac{2}{3}\) gives \(8\). Adding this to \(6\) results in \(14\), leading to the final answer of \(16\). Option A (1\(\frac{1}{3}\)) is incorrect due to miscalculating the operations. Option B (5\(\frac{1}{3}\)) fails to account for the division correctly. Option D (17) mistakenly adds an extra unit instead of properly evaluating the expression.
To solve the equation, first evaluate the expression in the parentheses: \(6 - 5\frac{1}{3}\) equals \(6 - \frac{16}{3} = \frac{18}{3} - \frac{16}{3} = \frac{2}{3}\). Next, compute \(5\frac{1}{3}\) as \(\frac{16}{3}\). The equation now reads \(6 + \frac{16}{3} \div \frac{2}{3}\). Dividing \(\frac{16}{3}\) by \(\frac{2}{3}\) gives \(8\). Adding this to \(6\) results in \(14\), leading to the final answer of \(16\). Option A (1\(\frac{1}{3}\)) is incorrect due to miscalculating the operations. Option B (5\(\frac{1}{3}\)) fails to account for the division correctly. Option D (17) mistakenly adds an extra unit instead of properly evaluating the expression.
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.
1 is 3 percent of what number?
- A. 1/3
- B. 3
- C. 30
- D. 33,1/3
Correct Answer & Rationale
Correct Answer: D
To find the number of which 1 is 3 percent, we set up the equation: 1 = 0.03 * x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a much smaller value, specifically 0.33. Option B (3) misinterprets the percentage, suggesting that 1 is 33.33% of 3, which is not accurate. Option C (30) also fails, as 3% of 30 is 0.9, not 1. Thus, only option D correctly identifies the number as 33 1/3.
To find the number of which 1 is 3 percent, we set up the equation: 1 = 0.03 * x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a much smaller value, specifically 0.33. Option B (3) misinterprets the percentage, suggesting that 1 is 33.33% of 3, which is not accurate. Option C (30) also fails, as 3% of 30 is 0.9, not 1. Thus, only option D correctly identifies the number as 33 1/3.
165 is what percent of 150?
- A. 95%
- B. 110%
- C. 111%
- D. 115%
Correct Answer & Rationale
Correct Answer: B
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.