How do you evaluate #\frac { 8} { 9} \cdot \frac { 6} { 7} - \frac { 1} { 5}#?

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Answer 1 · 2017-05-14T00:35:03

#59/105#

Solve in order of PEMDAS. Multiply first:

#8/9xx6/7#

Break down the numbers into smaller forms so we can see what we can cancel:

#(2xx2xx2)/(3xx3) xx (3xx2)/(7)#

We can see that a #3# on the top and bottom cancel and we're left with:

#(2xx2xx2xx2)/(3xx7)#

This evaluates to:

#16/21#

Now we have to subtract:

#16/21-1/5#

We have to find a common denominator. Multiply #16/21# by #5/5# and multiply #1/5# by #21/21#:

#(16/21)(5/5) - (1/5)(21/21)#

This becomes:

#80/105-21/105#

Now we can just subtract the numerators:

#80-21=59#

So we get:

#59/105#