Question

How do write in simplest form given `-2/5+17/20`?

Answer 1

`9/20`

Explanation:

To do the simplification we require the denominators of the fractions to be the same.

To make the denominator of the first fraction 20, multiply numerator/denominator by 4, equivalent to multiplying by 1.

`-2/5xx4/4=-8/20`

We now have.

`-8/20+17/20`

Now we just add the numerators.

`rArr-8/20+17/20=(-8+17)/20=9/20`

Answer 2

`9/20`

Explanation:

`color(blue)("The structure of a fraction is:")`

`color(green)(("count")/("size indicator") " "color(brown)(vec("mathematical names"))" " ("numerator")/("denominator"))`

You can not 'directly' add or subtract counts unless the size indicators are the same.

`color(brown)("Multiply by 1 and you do not change the underlying value of ")` `color(brown)("something. However, 1 comes in many forms.")`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Make all the size indicators (denominators) the same then subtract the counts (numerators).

`[ -2/5color(magenta)(xx1)]+17/20" "->" "[ -2/5color(magenta)(xx4/4)]+17/20`

`""-(2xx4)/(5xx4)" "+17/20" "->" "-8/20" "+17/20`

`color(white)(.)`

`" "(17-8)/20" " =" " 9/20`