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

2 Answers
Jun 15, 2016

=#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"#

Jun 15, 2016

#" "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'")#