Question

How do you simplify `2 1/2 div 3 1/5`?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number to an improper fraction:

`2 1/2 = 2 + 1/2 = (2/2 xx 2) + 1/2 = 4/2 + 1/2 = (4 + 1)/2 = 5/2`

`3 1/5 = 3 + 1/5 = (5/5 xx 3) + 1/5 = 15/5 + 1/5 = (15 + 1)/5 = 16/5`

We can now rewrite the expression as:

`5/2 -: 16/5 => (5/2)/(16/5)`

We can now use this rule for dividing fractions to evaluate the expression:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(5)/color(blue)(2))/(color(green)(16)/color(purple)(5)) => (color(red)(5) xx color(purple)(5))/(color(blue)(2) xx color(green)(16)) = 25/32`

Answer 2

Flip the dividing fraction and multiply the two together! You'll get `25/32`

Explanation:

The first thing to do is make these mixed fractions into their improper forms:

`2 1/2-:3 1/5 = 5/2 -: 16/5`

Now, we'll invert the divisor:

`(16/5)^(-1)=5/16`

and multiply the first fraction by the inverse of the second:

`5/2*5/16=color(red)(25/32)`

Answer 3

`25/32`

Explanation:

First let's write these as Improper Fractions ("top heavy fractions")

`color(orange)(2) + color(green)(1)/color(blue)(2)` is the same as `(color(orange)(2) xx color(blue)(2)) + color(green)(1)` over the denominator `color(blue)(2)` or `5/2`

`color(orange)(3) + color(green)(1)/color(blue)(5)` is the same as `(color(orange)(3) xx color(blue)(5)) + color(green)(1)` over the denominator `color(blue)(5)` or `16/5`

So now we have `5/2 -: 16/5`

When we divide fractions, we multiply by the recipricol (`1/(t h e color(white)(0) f r a c t i o n)`)

`5/2 xx 5/16`

Now we multiply straight across and get `25/32`