How do you simplify $\frac{\frac{8}{5}}{4}$ ?

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Answer 1 · 2017-09-25T11:53:49

See below.

There are a few ways to tackle this:

If we look at this as being just like any other fraction, then the same rules will apply:

$(8/5)/4$ we can multiply top and bottom without changing the relationship so, using $8/5 -: 4$

Multiply top and bottom by $5$ :

$((cancel(5)(8))/(cancel(5)))/(5(4))$ = $8/((5)(4)$ = $8/20$ = $color(blue)(2/5)$

Alternatively:

$8/5 -: 4$ is equal to $8/5 xx$ the reciprocal of $4$ . The reciprocal of a number can be found by putting $1$ over the number. So:

Reciprocal of $4$ is $1/4$

So we have:

$8/5 xx 1/4 = (8xx1)/(5 xx 4)= 8/20=color(blue)(2/5)$

There are even more ways to achieve this, but you can just use the one you find easiest.

Answer 2 · 2017-09-25T12:01:34

$(8/5)/4=color(red)(2/5)$

In general $color(blue)a/color(magenta)b=color(blue)axxcolor(magenta)(1/b)$

In this case we have
$color(white)("XXX")color(blue)a=color(blue)(8/5)$ and $color(magenta)b=color(magenta)4$

So
$color(white)("XXX")(color(blue)(8/5))/color(magenta)4=color(blue)(8/5) xx color(magenta)(1/4)$

$color(white)("XXXXX")=(cancel(8)^2)/5xx1/cancel(4)$

$color(white)("XXXXX")=2/5$

How do you simplify \frac{\frac{8}{5}}{4}\frac{\frac{8}{5}}{4}?