Question

How do you simplify `(5/6)/(1 1/4)`?

Answer 1

`(5/6)/(1 1/4)=2/3`

Explanation:

Let us first convert mixed fraction `1 1/4` into improper fraction

`1 1/4=1+1/4=4/4+1/4=5/4`

Now dividing by a fraction `a/b` is equivalent to multiplying by its reciprocal `b/a`

Hence `(5/6)/(1 1/4)`

= `(5/6)/(5/4)`

= `5/6xx4/5`

= `cancel5/(cancel6^3)xx(cancel4^2)/cancel5`

= `2/3`

Answer 2

`2/3`

Explanation:

To divide and multiply, you need to work with common fractions, so change any mixed number into an improper fraction.

`1 1/4 = (4xx1 +1)/4 = 5/4`

There is a useful technique for dividing fractions given in this form:

`(color(green)(a/b))/(color(magenta)(c/d)) = color(green)(a/b) div color(magenta)(c/d) = a/b color(magenta)(xx d/c) = (ad)/(bc)`

`:.(color(red)(5)/color(blue)(6))/(color(blue)(5)/color(red)(4)) = color(red)(5xx4)/(color(blue)(6xx5))" "larr` now simplify

`(cancel5xxcancel4^2)/(cancel6^3xxcancel5) = 2/3`

Answer 3

Use the complex fraction theorem

Explanation:

`(5/6)/ ( 1 1/4) = (5/6)/(5/4) " "larr( 1 1/4 = 4/4 + 1/4 = 5/4)`

Using the multiplicative inverse and the multiplication property of equality multiply both the top fraction and the bottom fraction by the reciprocal of the bottom fraction `4/5`

`(5/6 xx 4/5)/ (5/4 xx 4/5 )" "larr" " 5/4 xx 4/5 = 1" "` leaving

`5/6 xx 4/5`

`= 20/30`

`= 2/3`