Question

Match each division expression to its quotient

Answer 1

$\frac{122}{10}*(-\frac{10}{61} )$Let's start by calculating their values one by one, and then we can match them.

Starting with $-2\frac{2}{5} \div\frac{4}{5}$, we can simplify this more by adding $2*5$ to the nominator. That gives us $-\frac{12}{5} \div\frac{4}{5}$. Now we can apply the Keep-Change-Flip rule. Keep the first fraction as it is, change the division sign into multiplication, flip the second fraction. $-\frac{12}{5} *\frac{5}{4}$. We apply fraction multiplication which is simply multiplying the first nominator by the first nominator and the same for the dominator.  and the result is $-\frac{60}{20}$ or simply -3.

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

Now, we calculate the second one, $-12.2\div(-6.1)$. This can be re-written as $-\frac{122}{10}\div(-\frac{61}{10} )$. As we did in the previous part we apply the  Keep-Change-Flip, this will give us $-\frac{122}{10}*(-\frac{10}{61} )$. Do the multiplication and the result will be $\frac{1220}{610}$, we can divide both the nominator and dominator by 10 which will result $\frac{122}{61}$ and finally we know that $61*2=122$ and we can divide both of them again by 61 which will result $\frac{2}{1} =2$

$-12.2\div(-6.1)=2$

You can try solving the rest by yourself but here's is the final answer for them both:

$16\div(-8)=-2\\3\frac{3}{7} \div1\frac{1}{7} =3$