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When dividing 1/9 by 2/3, what is the result?
- A. 1/6
- B. 3/18
- C. 1/3
- D. 2/3
Correct Answer: A
Rationale: To divide fractions, you multiply by the reciprocal of the divisor. In this case, 1/9 divided by 2/3 is the same as 1/9 multiplied by 3/2. Multiplying these fractions results in 3/18. To simplify the result, divide both the numerator and denominator by their greatest common divisor, which is 3 in this case. Dividing 3 by 3 results in 1, and dividing 18 by 3 results in 6. Therefore, 3/18 simplifies to 1/6. Thus, the correct answer is choice A, 1/6.
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Convert 0.75 to a ratio in simplest form.
- A. 5:07
- B. 3:04
- C. 7:05
- D. 0.09375
Correct Answer: B
Rationale: To convert 0.75 to a ratio in simplest form, we first need to express 0.75 as a fraction, which is 75/100 or 3/4. The ratio form of 3/4 is 3:4. Therefore, the correct answer is B. Choice A (5:07) is incorrect as it doesn't represent the correct ratio. Choice C (7:05) is also incorrect because it doesn't match the simplified form of 0.75. Choice D (0.09375) is incorrect as it is not in ratio form and does not represent the given decimal value correctly.
What is the sum of 1/4 + 3/8?
- A. 4/12
- B. 1/3
- C. 5/8
- D. 1/2
Correct Answer: C
Rationale: To add fractions, you need a common denominator. In this case, the common denominator is 8. Converting 1/4 to have a denominator of 8 results in 2/8, while 3/8 remains the same. Adding them gives 2/8 + 3/8 = 5/8. Therefore, the correct sum of 1/4 + 3/8 is 5/8.
Find x. 120:x::40:0.5 =
- A. 16
- B. 0.167
- C. 60
- D. 1.5
Correct Answer: D
Rationale: To solve this proportion, set up the equation: 120/x = 40/0.5. Cross multiply to get 120 * 0.5 = 40 * x. Simplify to 60 = 40x. Divide by 40 to solve for x, which gives x = 1.5. Therefore, the correct answer is 1.5. In this proportion, the first ratio represents 120:x, and the second ratio represents 40:0.5. By solving for x, we find that x is equal to 1.5, making choice D the correct answer.
1.2:x::14:42 =
- A. 0.6
- B. 3.6
- C. 1.2
- D. 2.4
Correct Answer: B
Rationale: To solve this proportion, we use the property that the product of the means is equal to the product of the extremes. In this case, we have 1.2 * 42 = 14 * x. Simplifying, we get 50.4 = 14x. To find the value of x, we divide both sides by 14, giving x = 50.4 / 14 = 3.6. Therefore, the correct answer is 3.6, which corresponds to option B. This means that the relationship between 1.2 and x is the same as the relationship between 14 and 42, following a proportional logic where the ratios are equivalent.
Change 8.08 to a fraction, reduced to the lowest terms.
- A. 8 1\12
- B. 88/1000
- C. 8 2/25
- D. 80/100
Correct Answer: C
Rationale: To change 8.08 to a fraction, we note that 8.08 = 8 + 0.08 = 8 + 8/100 = 8 8/100 = 8 2/25. Therefore, the correct answer is C. Option A is incorrect as it represents a mixed number. Option B is incorrect as it does not represent the decimal 8.08 as a fraction. Option D is incorrect as it does not reduce the fraction to the lowest terms.