7th Grade Graded Quiz #6

 $\frac{5}{-\frac{2}{8}}=$  

Answer explanation

First, you set up the problem like a division problem.
 $\frac{5}{-\frac{2}{8}}=\ \ \ \ 5\div-\frac{2}{8}\ \ \ \ =\ \ \ \ \frac{5}{1}\div-\frac{2}{8}$ 
Next, you do keep change flip and then multiply across.
 $\frac{5}{1}\times-\frac{8}{2}=\ \ \ \ -\frac{40}{2}$  
Finally, you simplify.
 $-\frac{40\div2}{2\div2}=\ \ \ \ -\frac{20}{1}=\ \ \ \ -20$  

 $5\frac{1}{3}\div\left(-1\frac{1}{2}\right)=$  

Answer explanation

First, Convert the mixed numbers to improper fractions.
 $5\frac{1}{3}\div\left(-1\frac{1}{2}\right)=\ \ \ \frac{16}{3}\div-\frac{3}{2}$ 
Next, you do keep change flip and then multiply across.
 $\frac{16}{3}\times-\frac{2}{3}=\ \ \ \ -\frac{32}{9}$  
This fraction can't be simplified so it's the answer.
 $-\frac{32}{9}$ 

 $\frac{-120}{-6}=$  

Answer explanation

Remember, two negatives cancel each other out when dividing.
 $\frac{-120}{-6}=20$  

 $\frac{-\frac{4}{5}}{-\frac{2}{3}}=$  

Answer explanation

First, you set up the problem like a division problem.
 $\frac{-\frac{4}{5}}{-\frac{2}{3}}=-\frac{4}{5}\div-\frac{2}{3}$ 
Next, you do keep change flip and then multiply across.
 $-\frac{4}{5}\div-\frac{2}{3}=\ \ \ -\frac{4}{5}\times-\frac{3}{2}=\ \ \ \ \frac{12}{10}$  
Finally, you simplify.
 $\frac{12\div2}{10\div2}=\ \ \frac{6}{5}\ \ OR\ \ 1.2$  

 $1.03\div\left(-10.3\right)=$  

Answer explanation

 $1.03\div\left(-10.3\right)=-0.1$  

 $\frac{-0.4}{80}=$  

Answer explanation

 $\frac{-0.4}{80}=-0.005$  

 $1\div\frac{9}{5}=$  

Answer explanation

First, you place your whole number over 1 to turn it into a fraction.
 $1\div\frac{9}{5}=\ \ \frac{1}{1}\div\frac{9}{5}$ 
Next, you do Keep Change Flip and multiply across.
 $\frac{1}{1}\div\frac{9}{5}=\ \ \ \frac{1}{1}\times\frac{5}{9}=\ \ \ \frac{5}{9}$ 

Since you can't simplify any further  $\frac{5}{9}$ is your answer.

 $\frac{\frac{-1}{4}}{\frac{23}{24}}=$  

Answer explanation

First, you set up the problem like a division problem.
 $\frac{\frac{-1}{4}}{\frac{23}{24}}=\ \ \frac{-1}{4}\div\frac{23}{24}$ 
Next, you do keep change flip and then multiply across.
 $\frac{-1}{4}\div\frac{23}{24}=\ \ \ \ \frac{-1}{4}\times\frac{24}{23}=\ \ \ \ \frac{-24}{92}$  
Finally, you simplify.
 $\frac{-24\div4}{92\div4}=\frac{-6}{23}$  

 $\frac{-10.35}{-2.3}=$  

Answer explanation

 $\frac{-10.35}{-2.3}=4.5$  

Alex usually runs for 21 hours a week, training for a marathon. If he is unable to run for 3 days, describe how to find out how many hours of training time he loses, and write the appropriate integer to describe how it affects his time.

Answer explanation

Alex usually runs for 21 hours a week, training for a marathon. If he is unable to run for 3 days, describe how to find out how many hours of training time he loses, and write the appropriate integer to describe how it affects his time.

If Alex usually runs $21$ hours per week, then you would need to divide by $7$ to find out how much time he usually spends per day, which is three hours. Since he is unable to run for three days, his time is decreased by $9$ hours or, $-9$ .