# Adding Mixed Numbers

## Adding Mixed Numbers - How it Works - Video

### Example 1

Example 1:

In adding mixed numbers the key is to make sure denominator for both numbers is the same when adding mixed numbers. In this case the the denominators are 6 and 6. So now, we can add the whole numbers, 2 + 5 = 7. Next we can add the numerators, 1 + 4 = 5. The final result is 7 and 5/6.

### Example 2

Example 2:

In adding mixed numbers the key is to make sure denominator for both numbers is the same when adding mixed numbers. In this case the the denominators are 5 and 5. So now, we can add the whole numbers, 3 + 5 = 8. Next we can add the numerators, 4 + 3 = 7. Now have the fraction 7/5, since 7 is greater then 5, we have to make the improper fraction into a mixed number. So 7/5 equals 1 and 2/5. Now we can the whole numbers, 8 + 1 = 9. The final result is 9 and 2/5.

### Example 3

Example 3:

In adding mixed numbers the key is to make sure denominator for both numbers is the same when adding mixed numbers. In this case the the denominators are 4 and 5. We can add the whole numbers, 2 + 4 = 6 and set that aside. Since the denominators are different, we have to find a common denominator of 4 and 5. The LCM (Least Common Multiple) is 20. You can choose 40 or any other common multiple, but you will have to reduce in the last step.

We have 3/4 and we need x/20. So we in order to get 20, we multiply 4 by 5. Since we did it to denominator, we have to do it the numerator, as well. This gives us 3 x 5 = 15. So now we have 15/20.

We have 2/5 and we need x/20. So we in order to get 20, we multiply 5 by 4. Since we did it to denominator, we have to do it the numerator, as well. This gives us 2 x 4 = 8. So now we have 8/20.

Now, we can add the two numerators of 15/20 and 8/20, and that is 15 + 8 = 23. Now we have 23/20 and we must convert the improper fraction into a mixed number. So 23/20 equals 1 and 3/20. Now we can the whole numbers, 6 + 1 = 7. The final result is 7 and 3/20.

### Example 4a

Example 4a:

In adding mixed numbers the key is to make sure denominator for both numbers is the same when adding mixed numbers. In this case the the denominators are 9 and 3. We can add the whole numbers, 4 + 3 = 7 and set that aside. Since the denominators are different, we have to find a common denominator of 3 and 9. The LCM (Least Common Multiple) is 9. But in this case we multiply the numbers of 9 and 3 to find a common multiple of 27.

We have 7/9 and we need x/27. So we in order to get 27, we multiply 9 by 3. Since we did it to denominator, we have to do it the numerator, as well. This gives us 7 x 3 = 21. So now we have 21/27.

We have 2/3 and we need x/27. So we in order to get 27, we multiply 3 by 9. Since we did it to denominator, we have to do it the numerator, as well. This gives us 2 x 9 = 18. So now we have 18/27.

Now, we can add the two numerators of 21/27 and 18/27, and that is 21 + 18 = 39. Now we have 39/21 and we must convert the improper fraction into a mixed number. So 39/27 equals 1 and 12/27. Now we have to reduce the 12/27 to 4/9 by diving each number by 3. Now we can the whole numbers, 7 + 1 = 8. The final result is 1 and 4/9.

### Example 4b

Example 4b:

In adding mixed numbers the key is to make sure denominator for both numbers is the same when adding mixed numbers. In this case the the denominators are 9 and 3. We can add the whole numbers, 4 + 3 = 7 and set that aside. Since the denominators are different, we have to find a common denominator of 3 and 9. The LCM (Least Common Multiple) is 9. You can choose 18, 27, or any other common multiple, but you will have to reduce in the last step.

We have 7/9 and we need x/9. In this case, we already have that denominator, so we don't have to do anything and we can keep it as 7/9.

We have 2/3 and we need x/9. So we in order to get 9, we multiply 3 by 3. Since we did it to denominator, we have to do it the numerator, as well. This gives us 2 x 3 = 6. So now we have 6/9.

Now, we can add the two numerators of 7/9 and 6/9, and that is 7 + 6 = 13 Now we have 13/9 and we must convert the improper fraction into a mixed number. So 13/9 equals 1 and 4/9. Now we can the whole numbers, 7 + 1 = 8. The final result is 1 and 4/9.

## Live Worksheet

Here is the link if you prefer.