What is the sum of mixed fractions?

Adding mixed fractions might seem tricky, but it becomes straightforward with a few steps. Let’s break it down with an example.

1. Convert Mixed Fractions to Improper Fractions
   A mixed fraction consists of a whole number and a fraction. To add them, first convert each mixed fraction to an improper fraction. An improper fraction has a numerator larger than its denominator.

Example

Consider the mixed fractions $2frac{1}{3}$ and $1frac{2}{5}$

For $2frac{1}{3}$:

1. Multiply the whole number by the denominator: $2 times 3 = 6$
2. Add the numerator to this product: $6 + 1 = 7$
3. Place this sum over the original denominator: $frac{7}{3}$

For $1frac{2}{5}$:

1. Multiply the whole number by the denominator: $1 times 5 = 5$
2. Add the numerator to this product: $5 + 2 = 7$
3. Place this sum over the original denominator: $frac{7}{5}$

2. Find a Common Denominator
   To add these fractions, they need a common denominator. The least common multiple (LCM) of the denominators 3 and 5 is 15.

   Convert the fractions to have this common denominator:

   $frac{7}{3}$ becomes $frac{7 times 5}{3 times 5} = frac{35}{15}$

   $frac{7}{5}$ becomes $frac{7 times 3}{5 times 3} = frac{21}{15}$

3. Add the Fractions
   Now add the numerators while keeping the common denominator:

   $frac{35}{15} + frac{21}{15} = frac{56}{15}$

4. Convert Back to a Mixed Fraction
   Finally, convert the improper fraction back to a mixed fraction.

   $frac{56}{15}$ can be divided as $56 div 15 = 3$ remainder $11$

   So, $frac{56}{15}$ is $3frac{11}{15}$

Conclusion

By converting mixed fractions to improper fractions, finding a common denominator, adding them, and then converting back to mixed fractions, we can easily find the sum of mixed fractions. Practice with different examples to get the hang of it!

Citations

1. 1. Khan Academy – Adding Mixed Numbers
2. 2. Math is Fun – Mixed Fractions
3. 3. Cool Math – Adding Mixed Numbers