Question

How do you add `1/3 + 1/4`?

Answer 1

=`7/12`

Explanation:

When adding fractions, the denominators have to be the same before you can add the numerators.

Find equivalent fractions for both `1/3 and 1/4`

The lowest number which 3 and 4 can both divide into is 12

`1/3xx4/4 = 4/12 " and " 1/4 xx 3/3 = 3/12`

We can write this easier like this:
`1/3 +1/4`

=`(4+3)/12`

=`7/12 " ONLY add the numerators"`

Answer 2

`" "7/12`

Very detailed explanation given. With practice you could write this type of solution on 1 line ( some of them need more lines ).

Explanation:

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

A lot of this you have been told before but bear with me.

The proper names of the parts of a fraction are:

`" "("numerator")/("Denominator")`

but for the moment I do not want you think of a fraction using these names. Instead use:

`color(blue)(" "("Count")/("Size indicator"))`

Once their function and use is firmly fixed in your mind you should revert to using their proper names.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

The size indicator is how many of what you are counting would be needed to make a whole 1 of something.

So a size of 16 needs more to make a 1 than you would with a size 8. Consequently size 16 is smaller. So `1/16" is smaller than "1/8`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)(ul("Answering your question"))`

Given:`" " 1/3+1/4`

Both 3 and 4 can be diveded into 12 giving whole number answers. So change the 'sizes' to 12

`color(brown)("Consider "1/3)`

Multiply by 1 but in the form of `1=4/4` giving:

`" "1/3xx1" "->" "1/3xx4/4" "=" " (1xx4)/(3xx4)`

`" "color(brown)(=" "4/12" " larr" same value as "1/3)`
'....................................................................................................................
`color(brown)("Consider "1/4)`

Multiply by 1 but in the form of `1=3/3` giving:

`" "1/4xx1" "->" "1/4xx3/3" "=" "(1xx3)/(4xx3)`

`" "color(brown)(=3/12" "larr" same value as "1/4)`
''~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`" "1/3+1/4" " -=" "4/12+3/12`

`" "= (4+3)/12" "color(blue)(=" "7/12)`

`color(magenta)("Adding the counts does not change the 'size'")`