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Adding Fractions

Fractions as we know are used to denote some part out of the whole one. And it’s very necessary, to know how to apply the 4 mathematical operations (addition, subtraction, multiplication and division) on fractions.

We will first consider the addition of fractions, which will form the base for applying the other operations on fractions.

  • The procedure to add two fractions are, firstly, to check whether the fractions are in mixed form or not.
  • If they are mixed fraction, we will convert them into simple fractions by multiplying the denominator of the mixed fraction by its initial number and then adding the numerator to that multiplied number.
  • Secondly, if all the fractions are in simple form, the next thing to check is their denominators. Either denominators can be alike or they could be different.
  • When denominators are same, to add fractions, the resulting sum of the fractions will have the same denominator and the numerator will consist of the sum of the individual numerator of each fraction.
  • If denominators of fractions are different, the first step would be to find the least common denominator (LCD) of the fractions, secondly, changing each fraction by multiplying its numerator and denominator by the same concerned multiple to get that LCD.
  • Once, we will get the same denominators of each fraction, we will follow the same procedure mentioned above, where the sum of fractions, will be the same denominator (LCD) and the resulting numerator will be the sum of individual numerators of each fraction.

Solved examples: -

1.Add $\frac{2}{3}+\frac{8}{3}$
To add fractions with common denominators, we simply add their numerators and put it over the common denominator
We get $\frac{2+8}{3}= \frac{10}{3}$.

2.Add $\frac{5}{4}+\frac{25}{20}$
$\frac{25}{20}$ can be simplified to $\frac{5}{4}$ by dividing both the numerator and the denominator by 5.
Therefore we get the equation as $\frac{5}{4}$ + $\frac{5}{4}$ and this is equal to $\frac{5+5}{4}$ = $\frac{10}{4}$.
Now we can divide both the numerator and the denominator by 2, which makes the fraction as $\frac{5}{2}$.

3.Add $\frac{7}{5}+\frac{1}{2}$
This is the case of fractions with different denominators
First find the least common denominator. Here we have 2 and 5, so the least common denominator will be 10.
Now we multiply the numerator and denominator of $\frac{7}{5}$ by 2 to get 10 in the denominator, we get  
 $\frac{7}{5} \times \frac{2}{2}$ = $\frac{14}{10}$.
Similarly with $\frac{1}{2}$, we multiply both 1 and 2 by 5 to get 10 in the bottom of the fraction.
$\frac{1}{2} \times \frac{5}{5}$ = $\frac{5}{10}$
Thus it will be $\frac{14}{10}+\frac{5}{10}$ which can be added to give $\frac{19}{10}$.

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