Question
Alexia ran three laps around her neighborhood. Each lap is 1 3/8 miles. Which is the best estimate of the number of miles that Alexia ran?
A. 2 miles
B. 3 1/2 miles
C. 4 1/2 miles
A. 2 miles
B. 3 1/2 miles
C. 4 1/2 miles
Answers
Answer
A diver dives 17 2/3 yards and then comes back to the surface. Then, she dives 9 3/8 yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?
A. -27 7/24
B. -27 1/24
C. -8 1/24
A. -27 7/24
B. -27 1/24
C. -8 1/24
Answer
A science experiment calls for mixing 3 2/3 cups of distilled water with 1 3/4 cups of vinegar and 2/3 cups of liquid detergent. How much liquid in all, in cups, is needed?
A. 2 1/12
B. 5 1/12
C. 6 1/12
A. 2 1/12
B. 5 1/12
C. 6 1/12
Answer
Eliza's backpack weighs 18 7/8 pounds with her math book in it. Without her math book, her backpack weighs 14 7/9 * 1 pounds. How
nuch does Eliza's math book weigh?
A. 3 11/72 pounds
B. 4 7/72 pounds
C. 4 11/70 pounds
nuch does Eliza's math book weigh?
A. 3 11/72 pounds
B. 4 7/72 pounds
C. 4 11/70 pounds
Answered by
GPT 3.5
To find the total distance Alexia ran, we can multiply the number of laps (3) by the distance per lap (1 3/8 miles).
3 × 1 3/8 = (3 × 1) + (3 × 3/8) = 3 + 9/8 = 3 9/8 miles.
Since 9/8 is greater than 1/2, it is closer to 1 than 0. So the best estimate of the distance is 3 1/2 miles.
Therefore, the answer is B. 3 1/2 miles.
3 × 1 3/8 = (3 × 1) + (3 × 3/8) = 3 + 9/8 = 3 9/8 miles.
Since 9/8 is greater than 1/2, it is closer to 1 than 0. So the best estimate of the distance is 3 1/2 miles.
Therefore, the answer is B. 3 1/2 miles.
Answered by
GPT 3.5
To find the diver's depth, we need to find the total distance she has traveled below the surface.
The first dive is 17 2/3 yards.
The second dive is 9 3/8 yards deeper than the first dive. To find the total depth of the second dive, we add 9 3/8 to 17 2/3.
To add these fractions, we need a common denominator, which is 24.
Converting 17 2/3 to an improper fraction, we have (3 * 17 + 2) / 3 = 53/3.
Converting 9 3/8 to an improper fraction, we have (8 * 9 + 3) / 8 = 75/8.
Adding 53/3 and 75/8, we have (53/3)(8/8) + (75/8)(3/3) = 424/24 + 225/24 = 649/24.
Therefore, the diver's depth is 649/24 yards below the surface.
The answer is not given in fractions, but it can be rewritten as a mixed number: 27 1/24.
Therefore, the correct answer is B. -27 1/24.
The first dive is 17 2/3 yards.
The second dive is 9 3/8 yards deeper than the first dive. To find the total depth of the second dive, we add 9 3/8 to 17 2/3.
To add these fractions, we need a common denominator, which is 24.
Converting 17 2/3 to an improper fraction, we have (3 * 17 + 2) / 3 = 53/3.
Converting 9 3/8 to an improper fraction, we have (8 * 9 + 3) / 8 = 75/8.
Adding 53/3 and 75/8, we have (53/3)(8/8) + (75/8)(3/3) = 424/24 + 225/24 = 649/24.
Therefore, the diver's depth is 649/24 yards below the surface.
The answer is not given in fractions, but it can be rewritten as a mixed number: 27 1/24.
Therefore, the correct answer is B. -27 1/24.
Answered by
GPT 3.5
To find the total amount of liquid needed, we need to add together the amounts of water, vinegar, and detergent.
The amount of water is 3 2/3 cups.
The amount of vinegar is 1 3/4 cups.
The amount of detergent is 2/3 cups.
To add these fractions, we need a common denominator, which is 12.
Converting 3 2/3 to an improper fraction, we have (3 * 3 + 2) / 3 = 11/3.
Converting 1 3/4 to an improper fraction, we have (4 * 1 + 3) / 4 = 7/4.
Adding 11/3, 7/4, and 2/3, we have (11/3)(4/4) + (7/4)(3/3) + 2/3 = 44/12 + 21/12 + 8/12 = 73/12.
Therefore, the total amount of liquid needed is 73/12 cups.
The answer is not given in fractions, but it can be rewritten as a mixed number: 6 1/12.
Therefore, the correct answer is C. 6 1/12 cups.
The amount of water is 3 2/3 cups.
The amount of vinegar is 1 3/4 cups.
The amount of detergent is 2/3 cups.
To add these fractions, we need a common denominator, which is 12.
Converting 3 2/3 to an improper fraction, we have (3 * 3 + 2) / 3 = 11/3.
Converting 1 3/4 to an improper fraction, we have (4 * 1 + 3) / 4 = 7/4.
Adding 11/3, 7/4, and 2/3, we have (11/3)(4/4) + (7/4)(3/3) + 2/3 = 44/12 + 21/12 + 8/12 = 73/12.
Therefore, the total amount of liquid needed is 73/12 cups.
The answer is not given in fractions, but it can be rewritten as a mixed number: 6 1/12.
Therefore, the correct answer is C. 6 1/12 cups.
Answered by
GPT 3.5
To find the weight of Eliza's math book, we need to subtract the weight of the backpack without the math book from the weight of the backpack with the math book.
The weight of the backpack with the math book is 18 7/8 pounds.
The weight of the backpack without the math book is 14 7/9 * 1 pounds.
To multiply a whole number by a fraction, we multiply the whole number by the numerator of the fraction and keep the denominator the same.
14 * 9/7 = 126/7 pounds.
Subtracting 126/7 from 150/8, we have (150/8)(7/7) - 126/7 = 1050/56 - 126/7 = (1050 - 144)/56 = 906/56.
Simplify 906/56 by dividing numerator and denominator by their greatest common divisor, which is 2.
906/56 = (2 * 453)/(2 * 28) = 453/28.
Therefore, Eliza's math book weighs 453/28 pounds.
The answer is not given in fractions, but it can be rewritten as a mixed number: 16 5/28 pounds.
Therefore, the correct answer is not listed.
The weight of the backpack with the math book is 18 7/8 pounds.
The weight of the backpack without the math book is 14 7/9 * 1 pounds.
To multiply a whole number by a fraction, we multiply the whole number by the numerator of the fraction and keep the denominator the same.
14 * 9/7 = 126/7 pounds.
Subtracting 126/7 from 150/8, we have (150/8)(7/7) - 126/7 = 1050/56 - 126/7 = (1050 - 144)/56 = 906/56.
Simplify 906/56 by dividing numerator and denominator by their greatest common divisor, which is 2.
906/56 = (2 * 453)/(2 * 28) = 453/28.
Therefore, Eliza's math book weighs 453/28 pounds.
The answer is not given in fractions, but it can be rewritten as a mixed number: 16 5/28 pounds.
Therefore, the correct answer is not listed.
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