Question

What is the simplified value of `7 8/9 - 5 3/5`?

Answer 1

`color(green)(103/45)` or `color(green)(2 13/45)` as a mixed number.

Explanation:

Make both mixed fractions improper fractions.

1.) Multiply the whole number by the denominator
2.) Add that to the numerator
3.) Put the whole thing over the original denominator

Example:

`a b/c = ((atimesc)+b)/c`

So, we end up getting:

`71/9 - 28/5`

We don't have common denominators. Multiply the fraction on the left by `5/5` and multiply the fraction on the right by `9/9` to get a common denominator of `45`.

`(71times5)/(9times5) - (28times9)/(5times9)`

`355/45` - `243/45`

Now we can subtract.

`(355-252)/45`

`=color(green)(103/45)`

That is your final solution!

Answer 2

`2 13/45`

Explanation:

Split the values into 2 parts. Whole numbers and fractions

`color(brown)("As "8/9" is bigger than "3/5" we can use 7-5")`

`color(blue)("Consider the whole numbers part")`

`" "color(green)(7-5=2)`

;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Consider the fraction part")`

`" "8/9-3/5`

A fraction is split up into 2 parts.

`" "("The count")/("The size indicator")->("numerator")/("denominator")`

`color(brown)("You can not directly add or subtract the 'counts' unless the size")` `color(brown)("indicators are the same.")`

`color(brown)("Multiply "8/9" by 1 but in the form of "1=5/5" giving:")`

`" "8/9xx5/5 = (8xx5)/(9xx5) = 40/45`

`color(brown)("Multiply "3/5" by 1 but in the form of "1=9/9" giving:")`

`" "3/5xx9/9 = (3xx9)/(5xx9) = 27/45`

`color(brown)("Putting all it together")`

`color(green)(" "8/9-3/5" " =" " 40/45-27/45" " =" " 13/45)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`" "bar(ul(|color(white)(2^2/2^2)7 8/9 - 5 3/5" " =" " 2 13/45color(white)(2/2)|))`