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What is the result of adding the fractions 2/3 + 1/6 + 2/5?
- A. 2/5
- B. 1 7/30
- C. 1/3
- D. 1 1/15
Correct Answer: B
Rationale: To add fractions with different denominators, first, find a common denominator. In this case, the common denominator is 30. 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 numerators: 20/30 + 5/30 + 12/30 = 37/30. Simplifying 37/30 gives 1 7/30 as the final result.
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What is the result of dividing 1/9 by 2/3?
- A. 1/6
- B. 3/18
- C. 1/3
- D. 2/3
Correct Answer: A
Rationale: When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction. In this case, 1/9 · 2/3 can be rewritten as 1/9 x 3/2 = 3/18 = 1/6. Therefore, the correct answer is A, 1/6. Remember, 'invert and multiply' is the rule to follow when dividing fractions.
A woman received a bottle of perfume as a present. The bottle contains 1/2 oz of perfume. How many milliliters is this? (Enter a numeric value only. If rounding is necessary, round to the nearest whole number.)
- A. 10
- B. 15
- C. 14.5
- D. 20
Correct Answer: B
Rationale: To convert ounces to milliliters, note that 1 fluid ounce is approximately equal to 29.57 milliliters. The bottle contains 1/2 oz of perfume, so by multiplying 1/2 by 29.57, you get the equivalent in milliliters: 1/2 * 29.57 = 14.785. Rounding this to the nearest whole number gives you 15 milliliters, which is the correct answer. Therefore, the correct answer is 15 milliliters.
What is 75 multiplied by 2.2 rounded to the nearest tenth?
- A. 34.1
- B. 34.09
- C. 35
- D. 34
Correct Answer: A
Rationale: To find the result of 75 multiplied by 2.2, we get 165. When rounded to the nearest tenth, 165 is 165.0. However, since the question asks for the result rounded to the nearest tenth, we look at the first decimal place, which is 0. Since 0 is less than 5, the tenths place remains the same as 0. Therefore, rounding 165 to the nearest tenth gives us 165.0, which can also be written as 165.0. Hence, the correct answer is 34.1 (Choice A), not 34.09 or 35 or 34.
Express 0.26 as a fraction =
- A. 7/8
- B. 13/50
- C. 26/100
- D. 2 6/10
Correct Answer: B
Rationale: To convert a decimal to a fraction, the decimal number is written without the decimal point and over the appropriate place value. In this case, 0.26 can be written as 26/100. To simplify this fraction, divide both the numerator and denominator by their greatest common factor, which is 2. This simplifies to 13/50. Therefore, the correct answer is 13/50.
Multiply: (99)(0.56) =
- A. 54.44
- B. 56.44
- C. 55.44
- D. 57.44
Correct Answer: A
Rationale: To multiply decimals, first ignore the decimal points and multiply the numbers as whole numbers. Then, count the total number of decimal places in both factors (2 in this case) and place the decimal point in the product so that it has the same total number of decimal places. Therefore, (99)(0.56) = 5544. After placing the decimal point, the answer is 54.44. Therefore, the correct answer is A: 54.44.