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Change the following fraction into a ratio: 19/40
- A. 19:40
- B. 40:19
- C. 19:4
- D. 40:4
Correct Answer: A
Rationale: To change a fraction into a ratio, you replace the fraction bar (/) with a colon (:). Therefore, 19/40 as a ratio is written as 19:40. Choice B (40:19) is incorrect as it reverses the order of the numbers. Choice C (19:4) is incorrect as it uses the denominator as the second number, which is not the correct way to represent a ratio. Choice D (40:4) is incorrect as it does not reflect the original fraction accurately.
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If a student earns $120 for a 10-hour tutoring session and works 6 hours, how much did the student earn?
- A. $72
- B. $90
- C. $80
- D. $50
Correct Answer: A
Rationale: To find the amount earned for 6 hours of work, calculate the hourly rate by dividing the total earnings ($120) by the total hours worked (10 hours): $120 · 10 = $12 per hour. Then, multiply the hourly rate by the number of hours worked (6): $12 6 = $72. Therefore, the student earned $72 for working 6 hours. Choice B ($90) is incorrect because it miscalculates the hourly rate. Choice C ($80) is incorrect as it does not consider the correct hourly rate. Choice D ($50) is incorrect as it calculates the earnings based on the wrong hourly rate.
Bill has 2.5 vacation days left for the rest of the year and 1.25 sick days left. If Bill uses all of his sick days and his vacation days, how many days will he have off work?
- A. 1 day
- B. 3 days
- C. 2 days
- D. 4 days
Correct Answer: D
Rationale: To find the total number of days Bill will have off, add his vacation days and sick days together. Bill has 2.5 vacation days and 1.25 sick days:
2.5 + 1.25 = 3.75 days
When rounding to the nearest whole number, 3.75 rounds up to 4. Therefore, Bill will have 4 days off work.
25 1/7 - 12 5/7 = ?
- A. 12 3/7
- B. 14 1/7
- C. 13 5/6
- D. 13
Correct Answer: A
Rationale: To subtract mixed numbers, subtract the whole numbers and fractions separately. If necessary, borrow from the whole number when the fraction in the minuend is smaller than the fraction in the subtrahend.
The whole numbers are:
25 - 12 = 13. The fractions: 1/7 - 5/7. Since 1/7 is smaller, borrow 1 from 13, making it 12. Then convert 1 whole into 7/7, so the fraction becomes: (7/7 + 1/7) - 5/7 = 8/7 - 5/7 = 3/7. Thus, 25 1/7 - 12 5/7 = 12 3/7.
Ratio and proportion: 6:10=24:x
- A. 40
- B. 25
- C. 240
- D. 4
Correct Answer: A
Rationale: To solve for x, use cross-multiplication:
6x = 10 x 24
6x = 240
Now, divide both sides by 6 to find x:
x = 240 / 6 = 40
Therefore, the correct answer is A. 40.
Choice B, 25, is incorrect because it does not satisfy the proportion.
Choice C, 240, is incorrect because it represents the value that is given in the proportion and not the value of x.
Choice D, 4, is incorrect as it does not align with the correct calculation for x.
Sally eats 3/5 of her lunch. John eats 75%. Who ate more?
- A. John
- B. Sally
- C. Both the same
- D. Neither
Correct Answer: A
Rationale: To compare, convert both to decimals or percentages:
Sally ate 3/5, which is 0.6 or 60%. John ate 75%. Since 75% is greater than 60%, John ate more than Sally. Thus, the correct answer is A. John. Choice B is incorrect because Sally ate a smaller percentage of her lunch compared to John. Choice C is incorrect as the percentages consumed are different. Choice D is incorrect as one of them ate more.