How do you evaluate #(- \frac { 3} { 5} ) ( - \frac { 8} { 15} ) \div ( - 1\frac { 1} { 5} )#?

Question

Levi Adams · Accepted Answer

#-4/15#

#(-3/5)(-8/15)-:(-1 1/5)#

Let's take that right fraction and convert it into an improper form:

#(-3/5)(-8/15)-:(-6/5)#

When dividing by a fraction, we can multiply by its reciprocal:

#(-3/5)(-8/15)(-5/6)#

We have some opportunities to cancel:

#(cancel(-)cancel3/cancel5)(cancel(-)cancel8^4/15)(-cancel5/cancel6^cancel2)=-4/15#

Benjamin Altschul · Answer

undefined To evaluate the expression (- \frac { 3} { 5} ) ( - \frac { 8} { 15} ) \div ( - 1\frac { 1} { 5} ), follow these steps:

Step 1: Multiply the numerators together and the denominators together.
Step 2: Divide the result of the multiplication by the given divisor.

(- \frac { 3} { 5} ) ( - \frac { 8} { 15} ) = \frac {3 	imes 8} {5 	imes 15} = \frac {24} {75}

Now, divide \frac {24} {75} by - 1\frac { 1} { 5}.

- 1\frac { 1} { 5} = - \frac {6} {5}

So, \frac {24} {75} \div (- \frac {6} {5}) = \frac {24} {75} 	imes (- \frac {5} {6}) = - \frac {24 	imes 5} {75 	imes 6} = - \frac {4} {5}

Therefore, the value of the expression is - \frac {4} {5}.