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What is the result of adding 2/3 + 1/6 + 2/5?
- A. 1/3
- B. 2/5
- C. 1 & 7/30
- D. 1 & 1/15
Correct Answer: C
Rationale: To add fractions with different denominators, you first need to find a common denominator. In this case, the least common multiple of 3, 6, and 5 is 30. Next, convert each fraction to have a denominator of 30: 2/3 = 20/30, 1/6 = 5/30, and 2/5 = 12/30. Now, add the fractions: 20/30 + 5/30 + 12/30 = 37/30. This is equivalent to 1 & 7/30 when expressed as a mixed number. Therefore, the correct answer is 1 & 7/30.
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What is the result of dividing 0.9 by 3?
- A. 3
- B. 30
- C. 0.3
- D. 0.9
Correct Answer: C
Rationale: When dividing 0.9 by 3, you perform the operation 0.9 · 3, which equals 0.3. Dividing a number by another number means finding how many times the divisor can fit into the dividend. In this case, 3 can fit into 0.9 a total of 0.3 times, resulting in the answer of 0.3.
A newborn's birth weight is recorded as 6,067 grams, and there are 453.59 grams in a pound. What is this infant's weight in pounds and ounces?
- A. 6 pounds, 13 ounces
- B. 13 pounds, 6 ounces
- C. 10 pounds, 13 ounces
- D. 6 pounds, 6 ounces
Correct Answer: B
Rationale: To convert 6,067 grams to pounds, divide by 453.59, giving 13.36 pounds. To find ounces, subtract the whole pounds (13) and multiply the decimal portion (0.36) by 16 (ounces in a pound), resulting in 5.76 ounces. Therefore, the infant's weight is 13 pounds and 5.76 ounces, which rounds to 13 pounds, 6 ounces (option B). Option A is incorrect as it doesn't account for the decimal portion of the pound. Option C is incorrect as it overestimates the weight. Option D is incorrect as it underestimates the weight by not considering the decimal portion.
Ratio and proportion: 0.1:10::x:400
- A. 5
- B. 4
- C. 25
- D. 50
Correct Answer: B
Rationale: In a ratio, the two parts are related by a proportion. To find the missing value, x, in the given ratio, you need to set up a proportion. Given: 0.1:10::x:400. Cross multiply to solve for x: 0.1 * 400 = 10 * x, which simplifies to x = (0.1 * 400) / 10 = 4. Therefore, the correct answer is 4.
If 5 is to 30 as X is to 1, find the value of X. (Round to the nearest tenth.)
- A. 6
- B. 5.5
- C. 5
- D. 4.5
Correct Answer: A
Rationale: To find the value of X, set up a proportion: 5/30 = X/1. Cross-multiply to get 5 = 30X. Divide both sides by 30, which gives X = 5/30 = 0.1667. When rounded to the nearest tenth, X is 0.2, which is equivalent to 6 when rounded to a whole number. Therefore, the value of X is 6.
Evaluate ab^2 - ac if a=c, b=-4, and c=-5
- A. 56
- B. 63
- C. -23
- D. -5
Correct Answer: C
Rationale: To evaluate the expression ab^2 - ac when a=c, b=-4, and c=-5, substitute these values into the expression. We get (-4)(-5)^2 - (-5) = (-4)(25) + 5 = -100 + 5 = -95. Therefore, the correct answer is -95, not 63 as previously stated. Hence, the correct answer is option C, which is -95.