Adding and Subtracting Fractions

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Let’s go over the basics of how to add and subtract fractions. There are two different types of fractions that we usually encounter when we add or subtract them.

The first one, which is the Like Fractions, is easy because the bottom numbers (denominator) are alike. While the second one, Unlike Fractions, have different denominators. Thus, the process in adding or subtracting these types of fractions is different.

In Like Fractions, adding and subtracting them is easy, because you don’t need to do anything aside from adding or subtracting the upper number (nominator) while retaining (not doing anything for the bottom numbers (denominator). Please see the example below,

½ + ½ = 2/2
¾ + ¼ = 4/4

In contrast to Like Fractions, the only way to add them without doing division is to change them without changing its value. In order to do that, we need to find something called the least common denominator (LCD) -it’s really just the LCM of our denominators. Once you have the LCD, multiply it to each of the fraction so they both have the same denominators. Please see the example below:

= ½ + ⅛

LCD = 8 (Find out how we got the LCD, please click on this link)

8(½) = 4/8
8(⅛) = ⅛

½ + ⅛ = 4/8 + ⅛
4/8 + ⅛ = 5/8

Video by mathantics

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in this video we’re gonna learn the
basics about how to add fractions now a
lot of math books will teach you how to
add fractions before they teach you how
to multiply them but here at math antics
we think you should learn the other way
around you remember how easy it is to multiply
fractions right you just multiply the top numbers
together and you multiply the bottom
numbers together and you have your
answer so you might be wondering well
can’t we just do that with addition two
can’t we just add the top numbers
together and add the bottom numbers
together and get our answer well alright
let’s try it and see but I got a bad
feeling about this let’s try adding 1/2
to 1/2 so if we added the top numbers
we’d get 2 and if we added the bottom
numbers we’d get 4 but well that can’t
be right because 2 over 4 simplifies to
1/2 and if you add 1/2 and 1/2 you
should get a whole not 1/2 we must broke
some sort of math I’m out of here
ok here’s what we did wrong it turns out
that there’s some important math rules
called order of operations that say you
have to do multiplication and division
before you do addition and subtraction
now because fractions are just division
problems if you just added the top
numbers and added the bottom numbers
you’d be breaking those rules because
you would be doing the addition before
the division so what are we gonna do
instead well fortunately there’s a trick
that lets us work around the order of
operation rules and add fractions
without dividing but there’s a catch it
only works for fractions that have the
same bottom numbers the trick is if
fractions have the same bottom numbers
we can add them by just adding the top
numbers together and keeping the same
bottom number in our answer for example
to add 1/2 and 1/2 we just add the top
numbers and 1 plus 1 gives us 2 but we
don’t add the bottom numbers we just use
the same bottom number in the answer
which is 2 so 2 over 2 is a whole
fraction and that makes sense because if
you add 1/2 and 1/2 you get a whole
let’s see a few more examples like this
one five over 16 plus 2 over 16 again
since the bottom numbers are the same
it’s easy to add these fractions all we
do is add the top numbers together five
plus two equals seven and that’s a top
number of our answer then we just keep
16 as the bottom number of our answer so
5 over 16 plus 2 over 16 equals 7 over
16 pretty easy huh but what about
subtracting fractions does that work the
same way yep if the bottom numbers are
the same all you have to do is subtract
the top numbers and keep the same bottom
number in your answer here’s an example
of subtracting fractions with the same
bottom numbers 5 over 9 minus 2 over 9
first we subtract the top numbers 5
minus 2 equals 3 then we just write the
same bottom number and our answer 9 so 5
over 9 minus 2 over 9 is 3 over 9 yep
adding and subtracting fractions with
the same bottom numbers is easy and
there’s a special name for problems like
this it’s called adding or subtracting
like fractions the teacher once told me
that they’re called like fractions
because the bottom numbers are the same
or alike but I think it’s because they
secretly like each other just kidding
but seriously like fractions are easy to
add with the trick we just learned but
what happens if you want to add – unlike
fractions what do you do if you have
fractions with different bottom numbers
unfortunately the only way we can add
unlike fractions without doing the
division first is to change them so that
they do have the same bottom numbers in
other words we need to change our unlike
fractions into like fractions so we can
just use our trick in math language
that’s called finding a common
denominator now remember that a
denominator is just a fancy math word
for the bottom number of a fraction and
common just means that they’re the same
so how do we find a common denominator
so that we can add or subtract unlike
fractions that’s what we’re going to
learn in the next video but before you
move on be sure to do the exercises for
this section
learn more at math antics calm.

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