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# How Do I Add Fractions

Fractions are the mathematics numbers which are expressed in ratio of two numbers. Fractions are used to compare between whole number and parts. These numbers can be a part of any group of object or a individual object. It is a part of whole number. Fractions cam be added, subtracted, multiply and divided. Fraction can be added by two methods: First is with like Denominators and another is with unlike Denominator.

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## Different Denominators

Let us have a look at the addition of fraction with different or unlike denominators. First find the lowest common denominator by given denominators. Finding the denominator process can be done by multiplying the denominators. Some of the easiest steps are given below as follows:
Step 1: Find the LCM.

Step 2: Divide LCM by denominator of first fraction and get the resultant.

Step 3: Multiply both numerator and denominator by the above resultant.

Step 4: Apply steps 2 and step 3 for other fractions also.

Step 5: Add the numerators as the denominators are same.

Step 6: Simplify if needed.
Problem:

Add $\frac{50}{9}$ and $\frac{30}{10}$ ?

Solution:

The given two fractions $\frac{50}{9}$ and $\frac{30}{10}$ are unlike fractions

Step 1: LCD of 9 and 10 => 90

Step 2: So, $\frac{50\times 10}{9\times 10}$ + $\frac{30\times 9}{10\times 9}$
Multiply and divide first fraction by 10 and second fraction by 9 to get same denominator.
= $\frac{500}{90}$ + $\frac{270}{90}$

Step 3: Since the denominators are same so, add numerators.

= $\frac{500+270}{90}$

The sum of 500 and 270 is 770

= $\frac{770}{90}$

After simplify we have $\frac{77}{9}$
Correct answer is $\frac{77}{9}$

## Adding Like Denominators

Here we are going to learn about addition of fraction with same or like denominators. If the given denominators are like or same then the addition of fraction is slightly change from the method of adding fractions with unlike denominators. Some of the easiest steps are given below as follows:
Step 1: Add numerators directly.

Step 2: The numerator from above step gives the numerator of resulting fraction.

Step 3: Denominator will remain same.

Step 4: If needed simplify the above.
Problem:

Add $\frac{42}{5}$ and $\frac{14}{5}$ ?

Solution:

The given two fractions $\frac{42}{5}$ and $\frac{14}{5}$ are unlike fractions

Step 1: Add the numerators together

42 + 14 = 56

Step 2: Keep the denominator same

= $\frac{56}{5}$

Step 3: Simplify

$\frac{56}{5}$  = 11.2 (or) we can express this as a mixed number

$\frac{56}{5}$ = $11\frac{1}{5}$

Hence $\frac{42}{5}$ + $\frac{14}{5}$

Correct answer is 11.2 (or) $11\frac{1}{5}$

## Adding Whole Numbers

As we have study before the fraction is the ratio of two number like $\frac{a}{b}$, where a and b are the two numbers. And we also know the whole numbers are nothing but the opposite of fraction. The addition of whole numbers and fraction can be done by some easiest method. The addition of whole numbers and fraction are mostly gives a fraction value. Below find an example to understand the process of whole number and fraction addition.
Problem:

Add the fraction value $\frac{1}{3}$ with the whole number 5.

Solution:

The steps to be followed to add the fraction value $\frac{1}{3}$ with the whole number 5 are as follows:

= $\frac{1}{3}$ + $5$

= $\frac{1}{3}$ + $5\times$ $\frac{3}{3}$ (multiply and divide the number 3 with the given whole number 5 to convert it into fraction value).

= $\frac{1}{3}$ + $\frac{15}{3}$

= $\frac{1+15}{3}$ (take the number 3 as the common divisor for both)

= $\frac{16}{3}$ (it is also a fraction value)
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