Question

How do you divide `1\frac { 2} { 5} \div 1\frac { 1} { 4}`?

Answer 1

See a solution process below:

Explanation:

Step 1) Convert the mixed numbers into improper fractions:

`1 2/5 -: 1 1/4 => (1 + 2/5) -: (1 + 1/4) =>`

`([5/5 xx 1] + 2/5) -: ([4/4 xx 1] + 1/4) =>`

`(5/5 + 2/5) -: (4/4 + 1/4) =>`

`7/5 -: 5/4`

Step 2) Rewrite the expression as:

`(7/5)/(5/4)`

Step 3) 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)(7)/color(blue)(5))/(color(green)(5)/color(purple)(4)) => (color(red)(7) xx color(purple)(4))/(color(blue)(5) xx color(green)(5)) => 28/25`