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Which is the largest expression?
- A. 0.195833
- B. 1:20
- C. 1:22
- D. 1:02
Correct Answer: A
Rationale: Correct Answer: A: 0.195833
Rationale: To compare the expressions, convert them to decimal form. A: 0.195833, B: 1.20, C: 1.22, D: 1.02. A is the largest as it is closest to 1. B is 1.20, C is 1.22, and D is 1.02. A is larger than D by 0.175833, which is the greatest difference among the options, making A the largest expression.
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Ratio and Proportion: 9 : X :: 5 : 300 (Enter numeric value only.)
- A. 450
- B. 540
- C. 600
- D. 480
Correct Answer: B
Rationale: To find the value of X in the proportion 9 : X :: 5 : 300, we can set up the equation (9/X) = (5/300) and cross-multiply. This gives us 9 * 300 = 5 * X. Simplifying further, we get X = (9 * 300) / 5 = 540. Therefore, the correct answer is 540, which is option B.
Subtract: 15.7 - 9.8 =
- A. 6.1
- B. 8.96
- C. 5.9
- D. 4.3
Correct Answer: C
Rationale: To subtract two decimal numbers, align the decimal points and then subtract each place value. In this case, 15.7 - 9.8 = 5.9. Therefore, the correct answer is 5.9. When subtracting decimals, it is crucial to maintain the alignment of the decimal points to ensure accurate calculations. In this subtraction problem, the tenths and ones places are being subtracted individually. Subtracting 8 from 7 in the tenths place results in 1, while subtracting 9 from 15 in the ones place results in 6. Combining these results, we get a final answer of 5.9.
Ratio and Proportion: 240 : X = 80 : 0.8 (Enter a numeric value only.)
- A. 2.4
- B. 3.2
- C. 4
- D. 1.6
Correct Answer: A
Rationale: To solve for X, set up the proportion: 240/X = 80/0.8. Cross-multiply to get 240 — 0.8 = 80 — X, which simplifies to 192 = 80X. Dividing both sides by 80 gives X = 192/80 = 2.4. Therefore, the correct answer is A) 2.4.
What is the result of dividing 5 & 3/4 by 1/2, reduced to the simplest form?
- A. 5 & 1/2
- B. 2 & 3/8
- C. 11 & 1/2
- D. 18
Correct Answer: C
Rationale: To divide a mixed number by a fraction, you first convert the mixed number to an improper fraction. 5 & 3/4 as an improper fraction is 23/4. Dividing 23/4 by 1/2 is equivalent to multiplying 23/4 by 2/1, resulting in 46/4. When simplified back to a mixed number, 46/4 is 11 & 1/2.
Which of the following fractions is the largest?
- A. 3/8
- B. 3/7
- C. 3/9
- D. 3/6
Correct Answer: D
Rationale: To compare fractions, it is essential to look at the denominator. The larger the denominator, the smaller the fraction. In this case, all fractions are multiples of 1/3. By simplifying the fractions, we see that 3/6 is the largest. It simplifies to 1/2, which is greater than 3/7, 3/8, and 3/9. A fraction closer to 1 is larger, hence 3/6 (or 1/2) is the largest fraction among the options provided.