Question

How do you evaluate `\frac { 2} { 3} \times ( - \frac { 1} { 3} ) \div ( - \frac { 1} { 2} )`?

Answer 1

Since there are an even number of `-`'s in the multiplication and division, they cancel out two by two.

Explanation:

`=2/3xx1/3div1/2`

You may change the division by multiplication with the inverse (=fraction upside down):

`=2/3xx1/3xx2/1`

`=(2xx1xx2)/(3xx3xx1)=4/9`

Answer 2

`4/9`

Explanation:

When you multiplying or dividing 2 values, if the signs are the same the answer is positive (plus). If they are not the same then answer is negative (minus).

Consider the part that reads: `(-1/3)-:(1/2)`

We are dividing and the signs are the same so the answer for this bit is positive.

So `(-1/3)-:(-1/2)` gives the same answer as `1/3-:1/2`

Using the shortcut method, turn `1/2` upside down and multiply

So `2/3xx(-1/3)-:(-1/2)` becomes:

`" "2/3" "xx" "1/3" "xx" "2/1" " =" "(2xx1xx2)/(3xx3xx1)" " =" " 4/9`