Question

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

Answer 1

See a solution process below:

Explanation:

Because in the standard order of operations the division is evaluated before subtraction we can rewrite this expression as:

`(1/2)/(1/5) - 1/4`

We can then use this rule for dividing fractions to evaluate the division operation:

`(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)(1)/color(blue)(2))/(color(green)(1)/color(purple)(5)) - 1/4 = (color(red)(1) xx color(purple)(5))/(color(blue)(2) xx color(green)(1)) - 1/4 = 5/2 - 1/4`

Next, in order to subtract the two fractions we must put them over common denominators by multiplying, where necessary, by the appropriate form of `1`:

`5/2 - 1/4 => (2/2 xx 5/2) - 1/4 => 10/4 - 1/4`

We can now subtract the numerators over the common denominator:

`10/4 - 1/4 = (10 - 1)/4 = 9/4`