Adding Fractions
Adding Fractions
A calculator is the perfect tool to add fractions together. Each fraction is
converted to a decimal by entering the numerator (top number) dividing by the
denominator (bottom number) then adding any whole number which is part of the
expression.
So 1/2 plus 3/4 becomes .5 plus .75 equals 1.25
Here
is more on fractions which may be interesting.
What would our world be like without fractions? Our language would certainly
change!
You could never tell a friend to break a cookie in "half" to share
with you. You could only tell them to break it into two pieces. A glass
containing water could never be described as "half full." How could
you describe this glass? There would be no such thing as "half past the
hour" with timekeeping. You could never say you are "halfway"
there when traveling.
Obviously, fractions are truly an important part of our language. They are
equally important for mathematics.
Some people feel it is very hard to work with fractions. Here are some
helpful hints to make fractions easier to understand.
Fractions were used by many early civilizations. This included the Babylonians,
Chinese, Egyptians, Greeks, and Hindus
(in India). Many times, they only used fractions for very specific mathematical
equations. Today, fractions are a very important part of the study of
mathematics.
A fraction can be written as . N stands for
numerator (always the number on top of the line). D is the denominator (always
on bottom). An important point to remember is that the denominator can never be
zero.
Adding fractions is not difficult. If two fractions have the same
denominator, then it is an easy math problem. In that case, you only need to add
the numerators.
Subtracting the same fractions can be just as easy if both fractions have the
same denominator.
It is only slightly more difficult when the denominators are different.
You must find the "least common denominator" by rewriting both
fractions so they have the same denominator. You must create equivalent
fractions. To do this, you can multiply your denominators. 3 X 5 = 15
This means that 15 is your new "least common denominator." The
fraction now becomes .
How does this happen? Multiply the denominator (3) and numerator (1) both by
the second denominator (5). When you multiply both the denominator and numerator
by the same number you don't change the value of the fraction and you wouldn't
want to do that.
Your second fraction must also be multiplied  in this case, times 3 (since 5
X 3 = 15).
Now, we are able to add the fractions since they both have the same
denominator.
When adding the fractions being added must have the same denominator. When
denominators are different, you will need to convert each fraction into an
equivalent fraction by finding the least common denominator (LCD) for the
fractions. The two new fractions should have the same denominator, making them
easy to add or subtract. (Determining the LCD of a set of fractions was reviewed
in the unit Comparing
Fractions.)
Rule for Addition of Fractions
When adding fractions, you must make sure that the fractions
being added have the same denominator. If they do not, find the
LCD for the fractions and put each in its equivalent form. Then,
simply add the numerators of the fractions.



This rule can be broken down into several steps:


Determine whether the
fractions have the same denominator.
If the denominators are the same, move to step 4.

If the denominators
are different, find the LCD for the fractions being added.
(This process is explained in detail in the previous
unit.)

Find the equivalent
fractions with the LCD in the denominator.

Add or subtract the
numerators of the fractions.

Simplify the
resulting fraction.

If we have the fractions 1/6 and 2/6, and wish to add them, we follow our
steps:


Determine whether the
fractions have the same denominator. If the denominators are the
same, move to step 4.

The fractions 1/6 and 2/6 have the same denominator, so we can move
to step 4.



Add the numerators of
the fractions.




Simplify the
resulting fraction.
This fraction can be simplified to 1/2.


Visually, this would look like:
Now let's try an example.
Example of Adding Fractions
What is the sum of 3/4 and 1/3?
The answer is 13/12.
Following the steps:

Determine whether the
fractions have the same denominator.
If the denominators are the same, move to step 4.
First, you should notice that the two fractions do not have the same
denominator. This means we need to find the LCD for the two fractions.

Find the LCD for the
fractions being added.

Write the prime
factors for the denominator of each fraction.

The prime
factors of 4 are: 2 and 2.

The prime factor of 3
is: 3

Note all prime factors
that occur. For each prime factor that occurs, determine in which
denominator it occurs the most. Write down the prime factor the number
of times it occurs in that one denominator.
The prime factors that occur are 2, 2, and 3.

Calculate the LCD of your
fractions. To do this, multiply the factors selected in step 2b.
2 x 2 x 3= 12,
12 is our LCD.

Find the equivalent fractions
that have the LCD in the denominator.
Let's
start with 3/4. The prime factor missing from this denominator is a
3. So, 3 is the multiplier for 3/4.


For the
fraction 1/3, the prime factors that are missing are 2 and 2. Since
2 x 2= 4, 4 is the multiplier for the fraction 1/3.



Add the numerators of the
fractions.
Now that
we have found the fractions that are equivalent to the ones we are
adding, and these have the same denominator, we can add the
fractions together.


We can see that the fraction
we are adding are 9/12 and 4/12, which equals 13/12.

Simplify the resulting
fraction.
The answer of 13/12 is in its simplest form.
Calculator Practice
Fractions like a half and a fourth are in use by everyone all
the time. Practice without a pencil and scratch paper builds brain
connections. The exercises given are intended to be used as a learning tool to
improve mathematical manipulation, and also as practice in the accurate use of a
calculator.
Find a practice worksheet HERE.
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Listen to an audio file on this topic HERE.
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