7.50 ÷ 0.125 =
- A. 60
- B. 6
- C. 0.6
- D. 1/6
Correct Answer & Rationale
Correct Answer: A
To solve 7.50 ÷ 0.125, it's helpful to convert the division into a more manageable form. Dividing by 0.125 is the same as multiplying by 8 (since 1 ÷ 0.125 = 8). Therefore, 7.50 × 8 equals 60, confirming option A as the right choice. Option B (6) is incorrect; it underestimates the quotient significantly. Option C (0.6) is also wrong, as it suggests a much smaller result than what is obtained. Lastly, option D (1/6) misrepresents the division entirely, implying a fractional outcome that does not align with the calculations.
To solve 7.50 ÷ 0.125, it's helpful to convert the division into a more manageable form. Dividing by 0.125 is the same as multiplying by 8 (since 1 ÷ 0.125 = 8). Therefore, 7.50 × 8 equals 60, confirming option A as the right choice. Option B (6) is incorrect; it underestimates the quotient significantly. Option C (0.6) is also wrong, as it suggests a much smaller result than what is obtained. Lastly, option D (1/6) misrepresents the division entirely, implying a fractional outcome that does not align with the calculations.
Other Related Questions
Sienna has four times as many DVDs as Teri. Robert has half as many DVDs as Teri. If Robert has 32 DVDs, how many DVDs does Sienna have?
- A. 4
- B. 16
- C. 64
- D. 256
Correct Answer & Rationale
Correct Answer: D
To determine how many DVDs Sienna has, start with Robert's count. Since Robert has 32 DVDs and he has half as many as Teri, Teri must have 64 DVDs (32 x 2). Sienna has four times as many DVDs as Teri, so she has 256 DVDs (64 x 4). Option A (4) is incorrect because it underestimates the number of DVDs based on Teri's count. Option B (16) is also incorrect, as it does not align with the calculations derived from Robert's DVDs. Option C (64) mistakenly represents Teri's count rather than Sienna's. Thus, the only valid option reflecting Sienna's total is 256.
To determine how many DVDs Sienna has, start with Robert's count. Since Robert has 32 DVDs and he has half as many as Teri, Teri must have 64 DVDs (32 x 2). Sienna has four times as many DVDs as Teri, so she has 256 DVDs (64 x 4). Option A (4) is incorrect because it underestimates the number of DVDs based on Teri's count. Option B (16) is also incorrect, as it does not align with the calculations derived from Robert's DVDs. Option C (64) mistakenly represents Teri's count rather than Sienna's. Thus, the only valid option reflecting Sienna's total is 256.
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.
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.
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.