1) Adding fractions involves making the denominators the same by finding a common denominator, then simply adding the numerators. 2) Subtracting fractions also involves making the denominators the same, then subtracting the numerators. 3) When the denominators are different, the least common multiple (LCM) of the denominators is used to convert the fractions to equivalent fractions with a common denominator to allow addition or subtraction of the numerators.

1. ADDITION OF FRACTION
Adding fraction is very easy. You have to remember just one thing. The denominator always
must be the same. For the example, my mother has a watermelon with eight slices. Three
pieces is three eighths of watermelon. So, four pieces is four eighths of watermelon. Let’s try
and add three over eight and four over eight. Let’s count them. One. Two. Three. Four. Five.
Six. Seven. It’s seven, seven over eight. So, three over eight plus four over eight is equal to
seven over eight. Wasn’t that easy? We are just adding the numerators. But we have to mave
sure that the denominators must be the same.
Let’s take a look at one more example. Take a pizza with seven slices. Two piece is two over
seven of pizza and three pieces is three over seven of pizza. Now, let’s add the two. Let’s
count. One. Two. Three. Four. Five. It’s five. So, we get five over seven. So, we see that two
over seven plus three over seven is equal to two plus three over seven which equals five over
seven. Did you noticed what’s happening? We are just adding the numerators and we can
only do this when the denominators are the same.
Now let’s do one without pictures. Two over nine plus four over nine. Since the
denominators are the same, we can simply add the numerator. Therefore, two plus four as the
numerator and the denominator remains nine. Hence, the answer is six over nine. If we
reduce six over nine, we get two over three which is the answer.
Let’s try and add two fractions which have different denominators. Let’s add three over five
and one over three. We can add the numerator only if the denominators are the same. So how
do we make the denominators same? We will use the Least Common Multiply. The LCM of
five and three is fifteen. So fifteen, which is the LCM, is our new denominator. Change the
first number, three over five, so that it has fifteen as the denominator. So, three over five will
become three multiplied by three over five multiplied by three which is equal to nine over
fifteen.
And then, change the second number, one over three, so that it has fifteen as the denominator.
So, one over three will become one multiplied by five over three multiplied by five which is
equal to five over fifteen.
Now, we can simply do the calculation. Three over five plus one over three equals nine over
fifteen plus five over fifteen which is equal to nine plus five over fifteen equals fourteen over
fifteen. So, the answer is fourteen over fifteen.

2. SUBTRACTION OF FRACTION
Just like additon, subtraction of fraction is very easy. You just have to remember one thing.
The denominators always must be the same. Let’s take a look at an example. Take a cake
with ten slices. Let’s try to subtract eight over ten and five over ten. Eight over ten equals
eight pieces of the cake. Take away five over ten that is five pieces of the cake. We are left
with three pieces. So, eight over ten minus five over ten equals three over ten. Look what we
really did. We are just subtracted the numerators
Now, take a look at an example without pictures. Eleven over fourteen minus six over
fourteen equals how much? The numerator will be eleven minus six which is equal to five
and the denominator will be fourteen. Hence, the answer will be five over fourteen.
Now, let’s try and subtract two fractions with different denominators. For example, take three
over five minus a half. We have to find the common of the denominators which is the LCM.
The LCM of five and two is ten. So ten, which is the LCM is our new denominator. Change
the first number, three over five, so that it has ten as the denominator. So, three over five will
become three multiplied by two over five multiplied by two which is equal to six over ten.
And then, change the second number, a half, so that it has ten as the denominator. So, a half
will become one multiplied by five over two multiplied by five which is equal to five over
ten.
And the numbers will be six over ten minus five over ten equals one over ten.
Let’s do one more example. Six over eight minus two over three. The LCM will be twenty
four. We have to change both number so that it has twenty four as the denominators. Change
the first number, six over eight will become six multiplied by three over eight multiplied by
three equals eighteen over twenty four. And then, change the second number, two over three
will become two multiplied by eight over three multiplied by eight equals sixteen over twenty
four. Thus, we can simply do the calculation. Six over eight minus two over three equals
eighteen over twenty four minus sixteen over twenty four which is equal to eighteen minus
sixteen over twenty four equals two over twenty four. We can reduce two over twenty four
to one over twelve which is the answer.