Algebra Den

Addition of Mixed Fractions

Explanation
Addition of Mixed Fractions can be done by two separate methods :
Method 1 = Conversion of Mixed Fraction into Improper Fraction.
Method 2 = Addition of Whole Numbers and Fractions separately.

For Example Add 1 ²/₅ and 1 ⁴/₅

Method 1 = Conversion of Mixed Fraction into Improper Fraction. (This conversion is available under Fractions -- Conversion of Fractions)
1 ²/₅ = 7/5 and;
1 ⁴/₅ = 9/5
Now, add the improper fraction and we get:
= (7/5) + (9/5)
Here, the denominators of both the fractions are same, so we apply -- Addition of Fraction with Same Denominator {This topic can be studied from the above link --- Addition(Same Denominator)}
= (7+9) / 5
Solve Parentheses and we get:
= 16 / 5
Now, you can also convert the Improper Fraction into Mixed Fraction (This conversion is available under Fractions -- Conversion of Fractions)
16 / 5 = 3 ¹/₅

Method 2 = Addition of Whole Numbers and Fractions separately.
Addition of Whole Numbers = 1 + 1     = 2
Fractions = (2/5) + (4/5)
Here, the denominators of both the fractions are same, so we apply -- Addition of Fraction with Same Denominator {This topic can be studied from the above link --- Addition(Same Denominator)}
= (2+4) / 5     = 6/5

Now, Add Whole Number and Fraction and we get: (Topic available above)
= 2 + (6/5)
= (2/1) + (6/5) (because 2 = 2/1)
= {(2 × 5) + 6} / 5
Solve Parentheses and we get:
= {10 + 6} / 5
Solve Braces and we get:
= 16 / 5
Now, you can also convert the Improper Fraction into Mixed Fraction (This conversion is available under Fractions -- Conversion of Fractions)
16 / 5 = 3 ¹/₅