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