Question

Help me please!! I've tried it but it was wrong.

Answer 1

We start by solving the following expression:

`(-(3)/(4))((7)/(8))`

To multiply fractions we follow this rule:

`((a)/(b))((c)/(d))=(a* c)/(b* d)`

So we do this with the expression:

`(-(3)/(4))((7)/(8))=-(3*7)/(4*8)`

Solving the operations:

`(-(3)/(4))((7)/(8))=-(21)/(32)`

Now we solve another of the expressions:

`((2)/(3))(-4)(9)`

In this case, we can solve the multiplication between 4 and 9 first:

`((2)/(3))(-4)(9)=((2)/(3))(-36)`

And we consider that the rule to multiply a fraction by an integer is:

`((a)/(b))(c)=(a* c)/(b)`

So in this case:

`((2)/(3))(-4)(9)=(2(-36))/(3)`

And we solve the operations:

`\begin{gathered} ((2)/(3))(-4)(9)=(-72)/(3) \\ ((2)/(3))(-4)(9)=-24 \end{gathered}`

Next, we will solve the expression:

`((5)/(16))(-2)(-4)(-(4)/(5))`

In this case, we can also multiply the integers first, note that (-2)(-4) will be a positive number because we multiply two minus signs, so we get:

`((5)/(16))(-2)(-4)(-(4)/(5))=((5)/(16))(8)(-(4)/(5))`

Now we multiply the first fraction by the integer following the same rule as in the last expression:

`\begin{gathered} ((5)/(16))(-2)(-4)(-(4)/(5))=((5*8)/(16))(-(4)/(5)) \\ ((5)/(16))(-2)(-4)(-(4)/(5))=((40)/(16))(-(4)/(5)) \end{gathered}`

Now we multiply the fractions:

`\begin{gathered} ((5)/(16))(-2)(-4)(-(4)/(5))=((40)/(16))(-(4)/(5)) \\ ((5)/(16))(-2)(-4)(-(4)/(5))=-(40*4)/(16*5) \\ ((5)/(16))(-2)(-4)(-(4)/(5))=-(160)/(80) \end{gathered}`

And the final result for this expression is:

`((5)/(16))(-2)(-4)(-(4)/(5))=-2`

Now we solve the last expression:

`(2(3)/(5))((7)/(9))`

in this expression, we have a mixed number which we need to convert to a fraction, the procedure to convert it is as follows:

`2(3)/(5)=(2*5+3)/(5)=(13)/(5)`

We substitute this in our expression:

`(2(3)/(5))((7)/(9))=((13)/(5))((7)/(9))`

And multiply the fractions to get the final result:

`\begin{gathered} (2(3)/(5))((7)/(9))=(13*7)/(5*9) \\ (2(3)/(5))((7)/(9))=(91)/(45) \end{gathered}`