Question

How do you evaluate `\frac { 5} { 8} \times 1\frac { 3} { 9}`?

Answer 1

`5/6`

Explanation:

`• " change mixed numbers to improper fractions"`

`• color(blue)" cancel "" any "color(blue)"common factors"`

`• " repeat, if necessary until simplest form is reached"`

`1 3/9=(9xx1+3)/9=12/9`

`rArr5/8xxcancel(12)^4/cancel(9)^3`

`=5/8xx4/3`

`=5/cancel(8)^2xxcancel(4)^1/3`

`=(5xx1)/(2xx3)=5/6larrcolor(red)"in simplest form"`

`"a fraction is in "color(red)"simplest form"` when no other factor but 1 divides into the numerator/denominator.

Answer 2

`5/6`

Explanation:

`color(blue)("Preamble")`
Note that the value of 1 can be written as `9/9`

So `1 3/9" is the same as " 1+3/9 color(white)("dd")=color(white)("dd") 9/9+3/9color(white)("dd")=color(white)("dd")12/9`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Rewrite `5/8xx1 3/9color(white)("ddd")` as `color(white)("ddd")5/8xx12/9`

But `12/9` is the same as `(12-:3)/(9-:3) = 4/3`

`color(white)("ddddddddddddddddddd")=5/8xx4/3`

`color(white)("ddddddddddddddddddd")= (5xxcancel(4)^1)/(cancel(8)^2xx3)color(white)("d")=color(white)("d")5/6`