Adding mixed numbers is quite easy.

We know that mixed number consists of integer part and fractional part.

To add mixed numbers three steps are needed:

1. Convert each mixed number to improper fraction.
3. Convert improper fraction to mixed number if needed (and if possible).

Example 1. Find 1 3/5+2 4/9.

Convert each mixed number into improper fraction: 1 3/5=8/5 and 2 4/9=22/9.

Now add fractions: 8/5+22/9=(8*9)/(5*9)+(22*5)/(9*5)=72/45+110/45=182/45.

Convert fraction to mixed number: 182/45=4 2/45.

Answer: 4 2/45.

Next example.

Example 2. Find -2 1/6+3 1/2.

Convert each mixed number into improper fraction: -2 1/6=-13/6 and 3 1/2=7/2.

Now add fractions: -13/6+7/2=-13/6+(7*3)/(2*3)=-13/6+21/6=8/6.

Reduce fraction: 8/6=4/3.

Convert fraction to mixed number: 4/3=1 1/3.

Answer: 4/3=1 1/3.

Next example.

Example 3. Find 2+5 8/11.

Since first number has no fractional part, we can easier add numbers.

Add integer parts: 2+5=7 and fractional part leave the same.

Warning. This works only when we add either both positive numbers or both negative numbers.

Answer: 7 8/11=85/11.

Now, take pen and paper and do following exercises.

Exercise 1. Find 5 1/6+3 7/8.

Answer: 217/24=9 1/24.

Next exercise.

Exercise 2. Find 7 4/9+(-2 5/6).

Answer: 83/18=4 11/18.

Next exercise.

Exercise 3. Find -5 1/6+(-3 7/8).

Answer: -217/24=-9 1/24.

Next exercise.

Exercise 4. Find 3 5/6+5/7.

3 5/6+5/7=23/6+5/7=161/42+30/42=191/42=4 23/42.

Answer: 191/42=4 23/42.

Next exercise.

Exercise 5. Find -5 1/6+7.

Here we just can't add fractional parts to obtain 2 1/6. This is not correct, because one of the addends is negative and another is positive.

We do it as always.

-5 1/6+7=-31/6+42/6=11/6=1 5/6.

Answer: 11/6=1 5/6.

If you are not sure whether it is possible to add integer parts, use the three-step method. It guarantees correct answer.