Question 3

A)Multiply −1 1/6 by 7. Write the answer as a mixed number.(1 point)
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Question 4
A) Of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.(1 point)
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Question 5
A)Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 as deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)(1 point)
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Question 6
A)Divide −72 by −4. Then divide the quotient by −9. What is the final quotient? (1 point)
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3 answers

Let's solve each question one by one:

Question 3

Multiply −1 1/6 by 7. Write the answer as a mixed number.

First, convert the mixed number \(-1 \frac{1}{6}\) to an improper fraction: \[ -1 \frac{1}{6} = -\left(\frac{6}{6} + \frac{1}{6}\right) = -\frac{7}{6} \]

Now, multiply by \(7\): \[ -\frac{7}{6} \times 7 = -\frac{7 \times 7}{6} = -\frac{49}{6} \]

Now, convert \(-\frac{49}{6}\) to a mixed number: \[ -49 \div 6 = -8 \quad \text{remainder } -1 \] So, the mixed number is \(-8 \frac{1}{6}\).

Answer for Question 3: \(-8 \frac{1}{6}\)


Question 4

Of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered?

First, find the fraction of cars that are gray: \[ \frac{2}{5} \]

Next, find the fraction of the gray cars that are electrically powered: \[ \frac{1}{3} \]

Now, to find the fraction of the total cars that are both gray and electrically powered, multiply the two fractions: \[ \frac{2}{5} \times \frac{1}{3} = \frac{2 \times 1}{5 \times 3} = \frac{2}{15} \]

Answer for Question 4: \(\frac{2}{15}\)


Question 5

Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 as deep. What is the elevation at the bottom of Lake Segundo?

First, calculate the depth of Lake Segundo: \[ \text{Depth of Lake Segundo} = \frac{5}{6} \times 84 = \frac{5 \times 84}{6} = \frac{420}{6} = 70 \text{ feet} \]

Since the elevation is below sea level, we express this as: \(-70\) feet.

Answer for Question 5: \(-70\) ft


Question 6

Divide −72 by −4. Then divide the quotient by −9. What is the final quotient?

First, divide: \[ -72 \div -4 = 18 \]

Now, divide this quotient by \(-9\): \[ 18 \div -9 = -2 \]

Answer for Question 6: \(-2\)


To summarize:

  1. Question 3: \(-8 \frac{1}{6}\)
  2. Question 4: \(\frac{2}{15}\)
  3. Question 5: \(-70\) ft
  4. Question 6: \(-2\)
Write down all the answers.

Here are all the answers summarized:

  1. Question 3: \(-8 \frac{1}{6}\)
  2. Question 4: \(\frac{2}{15}\)
  3. Question 5: \(-70\) ft
  4. Question 6: \(-2\)
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