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What is the result of adding 6 3/4 and 8 1/6?
- A. 14 11/12
- B. 12 3/24
- C. 35/6
- D. 14 2/5
Correct Answer: A
Rationale: To add mixed numbers, convert them to improper fractions. 6 3/4 = 27/4 and 8 1/6 = 49/6. Find a common denominator, which is 12. Add the fractions: 27/4 + 49/6 = 81/12 + 98/12 = 179/12. Convert the improper fraction back to a mixed number: 179/12 = 14 11/12. Therefore, the correct result of adding 6 3/4 and 8 1/6 is 14 11/12. The sum of the two mixed numbers is expressed as 14 11/12.
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Ratio and Proportion: 9 : X :: 5 : 300
- A. 540
- B. 600
- C. 450
- D. 500
Correct Answer: A
Rationale: To find the value of X, set up the proportion: 9/X = 5/300. Cross-multiply to get 9 * 300 = 5 * X. Solve for X by dividing 2700 by 5, which equals 540. Therefore, the correct answer is A, which is 540.
Subtract 28 3/4 - 5 5/6.
- A. 23 & 1/2
- B. 22
- C. 22 & 11/12
- D. 34 & 1/12
Correct Answer: C
Rationale: To subtract mixed numbers, it is helpful to convert them into improper fractions. 28 3/4 is equivalent to 115/4, and 5 5/6 is equivalent to 35/6. Subtracting the fractions gives 115/4 - 35/6 = 345/12 - 70/12 = 275/12. Converting 275/12 back to a mixed number results in 22 & 11/12. Therefore, the correct answer is 22 & 11/12.
Add: 11,702 + 11,509 =
- A. 23,201
- B. 22,201
- C. 23,211
- D. 22,211
Correct Answer: C
Rationale: The correct answer is C (23,211). To arrive at this answer, you add the two numbers together: 11,702 + 11,509 = 23,211. This is correct because when adding numbers, you add the digits in the same place value position, carrying over when the sum exceeds 9.
Explanation:
1. Add the ones place: 2 + 9 = 11 (write down 1, carry over 1).
2. Add the tens place: 0 + 0 (from the carried-over 1) + 0 = 0 (write down 0, no carry over).
3. Add the hundreds place: 7 + 5 (from the carried-over 1) = 12 (write down 2, carry over 1).
4. Add the thousands place: 1 + 1 (from the carried-over 1) + 1 = 3 (write down 3).
Therefore,
Ratio and Proportion: 0.3:2 = 15:X (Enter numeric value only.)
- A. 50
- B. 75
- C. 100
- D. 125
Correct Answer: C
Rationale: To find the value of X, first, we need to set up a proportion using the given equation: 0.3/2 = 15/X. Cross multiply to solve for X: 0.3X = 2 * 15. Simplify to get 0.3X = 30. Divide by 0.3 to solve for X: X = 30 / 0.3 = 100. Therefore, the correct answer is C. Choice A (50), B (75), and D (125) are incorrect as they do not satisfy the proportion equation given. A summary of the incorrect choices: A is too low, B is also too low, and D is too high compared to the correct answer of 100.
A mailman delivers mail to 540 households. Yesterday he delivered a total of 5,400 pieces of mail on his route. What was the average number of pieces he delivered to each household? (Enter numeric value only. Round to whole number.)
- A. 10
- B. 12
- C. 14
- D. 8
Correct Answer: D
Rationale: Correct Answer: D (8)
Rationale:
1. Total pieces delivered = 5,400
2. Number of households = 540
3. Average pieces per household = Total pieces delivered / Number of households
4. Average = 5,400 / 540 = 10
5. Therefore, the average pieces delivered per household is 10, so choice D (8) is the correct answer.
Summary:
A: 10 - Incorrect. This is the calculated average, not the answer.
B: 12 - Incorrect. This is not the correct average based on the given information.
C: 14 - Incorrect. This is not the correct average based on the given information.