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:

$59/105$

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