Nokea
Divide: 41.2 ÷ 0.2 =
- A. 206
- B. 2.06
- C. 0.206
- D. 2.06
Correct Answer: A
Rationale: Correct Answer: A
Rationale:
1. Divide 41.2 by 0.2:
41.2 ÷ 0.2 = 412 ÷ 2 = 206.
Explanation:
To divide a decimal by another decimal, first, move the decimal point in both numbers to make the divisor a whole number. Then, divide as usual. The correct answer is 206.
Summary:
- Choice B (2.06) is incorrect as the decimal point was not moved correctly for division.
- Choice C (0.206) is incorrect as the decimal point was not moved correctly for division.
- Choice D (2.06) is incorrect as it doesn't reflect the correct result of dividing 41.2 by 0.2.
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45:x=35:105. Find the value of X. (Enter the whole number only.)
- A. 100
- B. 135
- C. 75
- D. 175
Correct Answer: B
Rationale: To find the value of x in the proportion 45:x=35:105, we can cross multiply to solve for x.
45 * 105 = 35 * x
x = (45 * 105) / 35
x = 135
Therefore, the correct answer is B: 135.
Explanation: The correct answer is found by cross multiplying in a proportion. Choice A (100) is incorrect as it doesn't satisfy the proportion. Choice C (75) and Choice D (175) are also incorrect as they do not align with the calculated value of x (135) from the given proportion.
If 18 is to x as 10 is to 300, what is the value of x?
- A. 540
- B. 16.67
- C. 180
- D. 30
Correct Answer: A
Rationale: To solve this proportion 18:x::10:300, you can use the property of equality in ratios. First, find the ratio of the first pair: 18/10 = 1.8. Then, set this ratio equal to the second pair: 1.8 = 300/x. Cross multiply to get x = 300/1.8 ≈ 166.67. Therefore, x is approximately 166.67, which is closest to 540, making choice A the correct answer.
Ratio and Proportion: 100:2 :: 60:X. Find X.
- A. 1.2
- B. 2
- C. 3
- D. 30
Correct Answer: A
Rationale: To find the value of X when the ratio 100:2 is equivalent to 60:X, set up the proportion: 100/2 = 60/X. Cross-multiply to get 100X = 120. Divide by 100 to isolate X, so X = 120/100 = 1.2. Therefore, X equals 1.2, and the correct answer is A. In this scenario, the correct answer is calculated through cross-multiplication of the given ratio and solving for the unknown value. This method is commonly used to solve ratio and proportion problems. It is essential to understand the concept of ratios and proportions to solve mathematical problems efficiently.
How many grams are in 4 kilograms? (Enter numeric value only.)
- A. 400
- B. 4000
- C. 40
- D. 4
Correct Answer: B
Rationale: To convert kilograms to grams, you need to know that there are 1,000 grams in 1 kilogram. Therefore, to find out how many grams are in 4 kilograms, you multiply 4 (kilograms) by 1,000 (grams/kilogram), which equals 4,000 grams. Thus, the correct answer is 4000 grams, as there are 4,000 grams in 4 kilograms.
Multiply 4/9 x 1 4/5 x 2/5
- A. 8/25
- B. 1 & 10/19
- C. 7/16
- D. 1 & 32/45
Correct Answer: A
Rationale: To multiply the given fractions, first convert the mixed numbers to improper fractions. 1 4/5 = (5*1 + 4)/5 = 9/5. Now the expression becomes 4/9 * 9/5 * 2/5. Multiply the numerators together and the denominators together to get (4*9*2)/(9*5*5) = 72/225. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 9, to get 8/25. Therefore, the correct answer is 8/25.