Add Fraction Numbers

Adding Fractions

Add Whole Numbers Subtract Whole Numbers Multiply Whole Numbers Divide Whole Numbers
Add Fractions Subtract Fractions Multiply Fractions Divide Fractions
Add Decimal Numbers Subtract Decimal Numbers Multiply Decimal Numbers Divide Decimal Numbers
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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:

 

 

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

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

  3. Find the equivalent fractions with the LCD in the denominator.

  4. Add or subtract the numerators of the fractions.

  5. Simplify the resulting fraction.

 

 

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

 

  1. 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.

 

  1. Add the numerators of the fractions.

 

  1. 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:

  1. 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.

     

  2. Find the LCD for the fractions being added.

    1. 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

       

    2. 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.

       

    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.

     

  3. 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.

  4. 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.

  5. 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. MORE

Listen to an audio file on this topic HERE. MORE

Many electrician workbooks and practice exams are now available 
as digital downloads for immediate use. 
Click HERE to see what is available.

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