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

3 Answers
Jan 8, 2017

(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

Jul 7, 2017

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

Aug 17, 2017

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