Adding Fractions

In addition of fractions having similar denominators, just add the numerators and remain the denominator as it is. If the sum can be reduced to lowest terms then do so.

But in the case of fractions having unlike denominators, the least common denominator (LCD) should be get first then change the fractions into equivalent fractions with the LCD as the denominator. If the sum can still be reduced to lowest terms then do so.

If a proper or improper fraction is added with a mixed number, it is easier to convert the mixed number first into an improper fraction then use the steps and conditions mentioned above. Same situation applies with addends which are all mixed numbers.

Fraction Addition Examples

Example 1:
 `1/2`

Explanation:

Since the denominators are the same, just add the numerators and keep the same denominator.
`1/8 + 3/8 = (1+3)/8 = 4/8`
Reducing the sum to lowest terms;
`4/8 = (2 × 2)/(2 × 2 × 2) = 1/2`
Therefore, 1/8 + 3/8 = 1/2

Example 2:
 `7/6` or `1 1/6`

Explanation:

Since the fractions have unlike denominators, find the LCD.

3 = 3
6 = 2 × 3
LCD = 2 × 3

Converting the fractions into equivalent fractions with 6 as the denominator;
`1/3 × 2/2 = 2/6`
`5/6 × 1/1 = 5/6`
Since the fractions have similar denominators, add the numerators and remain the LCD as it is.
`2/6 + 5/6 = (2+5)/6 = 7/6 or 1 1/6`
Therefore, `1/3 + 5/6 = 7/6 or 1 1/6`

Example 3:
 `21/10 or 2 1/10`

Explanation:

Convert the mixed number into an improper fraction.
Multiply the whole number by the denominator.
`1 × 5 = 5`
Add the product to the numerator of the proper fraction.
`5 + 2 = 7`
The numerator of the improper fraction is `7`.
The denominator remains to be `5`.
The improper fraction form for `1 2/5` is `7/5`.
Since the fractions have unlike denominators, find the LCD.

5 = 5
10 = 2 × 5
LCD = 2 × 5 = 10

Converting the fractions into equivalent fractions with 10 as the denominator;

`7/10 × 1/1 = 7/10`
`7/5 × 2/2 = 14/10`
Since the fractions have similar denominators, add the numerators and remain the LCD as it is.
`7/10 + 14/10 = 21/10 or 2 1/10`
Therefore, `7/10 + 1 2/5 = 2 1/10`





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