Question

Match each division expression to its quotient

Answer 1

`(122)/(10)*(-(10)/(61) )`Let's start by calculating their values one by one, and then we can match them.

Starting with
`-2(2)/(5) /(4)/(5)`, we can simplify this more by adding
`2*5` to the nominator. That gives us
`-(12)/(5) /(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.
`-(12)/(5) *(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
`-(60)/(20)` or simply -3.

`-2(2)/(5) /(4)/(5) = -3`

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

`-12.2/(-6.1)=2`

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

`16/(-8)=-2\\3(3)/(7) /1(1)/(7) =3`