Question

How do you simplify `3 2/3 + 1 1/4 - 2 5/12`?

Answer 1

Method broken down into a lot of detail. Once you get used to these you can do a lot of it in your head and rattle the answer off in a couple of lines.

`2 1/2`

Explanation:

`color(blue)("The teaching bit!")`

Stating the obvious: When adding and subtracting you are dealing with counts.

A fractions structure is such that we have:

`("count")/("size indicator of what you are counting")->("numerator")/("denominator")`

You can not DIRECTLY add or subtract counts unless the size indicators are the same. This is why 2+3 works as really it is `2/1+3/1` The size indicator of their `ul("unit size")` are the same.

Consider `3/16` the count is 3 and the unit size is `1/16`

So you have 3 of unit size `1/16 = 3xx1/16=3/16`
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`color(blue)("Answering the question")`

In the end I make them all have the same 'unit size' (denominator)

Consider `3 2/3 larr" Detailed explanation"`

Write as `3+2/3` this is the same as

`color(green)([3color(red)(xx1)]+2/3`

`color(green)([3/1color(red)(xx3/3)]+2/3`

`color(green)([(3color(red)(xx3))/(1color(red)(xx3))]+2/3`

`[9/3]+2/3=11/3`
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Consider `1 1/4`

Using the same method as above this is `5/4`
................................................................
Consider `2 5/12`

Using the same method this is `29/12`
....................................................................
Putting it all together

`11/3+5/4-29/12`

Again using the above approach we have

`44/12+15/12-29/12" "=" "(44+15-29)/12`

`=30/12`

`=(30-:6)/(12-:6)`

`= 5/2 color(white)("ddd") rarr color(white)("ddd")(2+2+1)/2`

`= 2/2+2/2+1/2" " =" " 2 1/2`