Question

Wht is the value of x in the proportion 2 1/4 ÷ x = 1 1/4 ÷ 3 3/5

Answer 1

`x = (162)/(25)`

Explanation:

You need to solve the equation for x.

First change all the mixed numbers to improper fractions. Remember that a improper fraction the numerator (top number) is larger than the denominator (bottom number).

`2(1)/(4) / x = 1(1)/(4) / 3(3)/(5)\\\`

All you need to do is multiply the numerator with the whole number, then add to the numerator:

`(9)/(4) / x = (5)/(4) / (18)/(5)`

Now simplify, to get rid of the numbers that are dividing:

`((9)/(4) ) (x)/(( x) ((5)/(18))) = ((5)/(4))(x) / (((18)/(5))( (5)/(18) )`

Cancel same numbers that are multiplying and dividing:

`(9)/(4) / (5)/(18)  = (5)/(4) (x)`

Clear X:

`x = ((9)/(4)) ((4)/(5) )/ (5)/(18)`

Simplify

`x = ( (9)/(5) ) ( (18)/(5) )`

you will get the following improper fraction:
`(162)/(25\\)`

and for the mixed fraction you will have
`6(12)/(25)`