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What is the sum of 2/3 + 4/9?
- A. 8/15
- B. 10/9
- C. 6/12
- D. 9/9
Correct Answer: B
Rationale: To add fractions, find a common denominator, which is 9 in this case. Convert 2/3 to 6/9. Now, add 6/9 + 4/9 to get 10/9, which simplifies to 1 1/9.
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Report all decimal places: 3.7 + 7.289 + 4 =
- A. 14.989
- B. 5.226
- C. 15
- D. 15.07
Correct Answer: A
Rationale: To find the sum of 3.7, 7.289, and 4, add them together: 3.7 + 7.289 + 4 = 14.989. The correct answer is A, 14.989, as it accurately reports all decimal places in the sum. When adding numbers with decimal points, it is crucial to maintain the decimal precision to obtain the correct result. In this case, the sum includes three decimal places, so the answer should also have three decimal places to represent the precise result. Therefore, 14.989 is the accurate sum that includes all the decimal places present in the numbers being added.
Convert 0.07 to a ratio.
- A. 7:10
- B. 7:10,000
- C. 7:1,000
- D. 0.361111
Correct Answer: D
Rationale: To convert 0.07 to a ratio, we first need to express it as a fraction. 0.07 as a fraction is 7/100. To convert this to a ratio, we need to express it in the form of a ratio of two integers. Therefore, 7/100 can be simplified to 7:100. Hence, the correct answer is D: 7:100.
Explanation:
A) 7:10 - Incorrect. This ratio is not equivalent to 0.07.
B) 7:10,000 - Incorrect. This ratio is not equivalent to 0.07.
C) 7:1,000 - Incorrect. This ratio is not equivalent to 0.07.
Summary: The correct ratio for 0.07 is 7:100, which represents the equivalent proportion of the decimal value. Other choices are incorrect as they do not accurately represent the given decimal value.
Solve for the value of x if x=11. x + 44 / 2x =
- A. 33
- B. 2.5
- C. 13
- D. 55/22
Correct Answer: C
Rationale: To solve the equation, substitute x=11 into the expression: 11 + 44 / (2*11) = 11 + 44 / 22 = 11 + 2 = 13. Therefore, the correct answer is C, which is 13.
What is the missing value in the ratio and proportion 15:2000::x:200?
- A. 1.5
- B. 7.777
- C. 0.15
- D. 15
Correct Answer: A
Rationale: To find the missing value x, we set up a proportion: 15/2000 = x/200. Cross multiplying, we get 15 * 200 = 2000x. Solving for x, x = (15 * 200) / 2000 = 1.5. Therefore, the correct answer is A, 1.5, which represents the missing value in the proportion. The ratio 15:2000 can be simplified to 3:400 by dividing both numbers by 5, making the proportion easier to work with. By setting up the proportion correctly and solving for x, we obtain the missing value as 1.5, which completes the proportion 15:2000::1.5:200.
How many cakes are needed to serve a group of 70 students and 3 staff members if each cake provides 24 servings?
- A. 4
- B. 2
- C. 3
- D. 5
Correct Answer: A
Rationale: To determine the number of cakes needed, add the total number of individuals to be served: 70 students + 3 staff members = 73 individuals. Then, divide the total number of individuals by the number of servings per cake: 73 · 24 = 3 with a remainder. Since you cannot serve a fraction of a cake, you will need an additional cake. Therefore, you would need 4 cakes to serve the group of 70 students and 3 staff members, ensuring each person receives a serving.