You have to know that mixed numbers are a combination of a whole number and a proper fraction. Even though the plus signs aren't usually showing in mixed numbers (between the whole number and the proper fraction), there are actually added together.
4 |
7 |
4 |
7 |
If both fractions have the same denominator, they can be easily added by adding the whole numbers together, the numerators together, and the denominator remaining the same
4 |
7 |
1 |
7 |
4 |
7 |
1 |
7 |
4 |
7 |
1 |
7 |
4 + 1 |
7 |
5 |
7 |
Simplify the fraction if possible, in this example, the result already simplified.
For more details click here
There is another way to add mixed fractions, which can be used in all cases adding, subtracting, multiplying, and dividing
Convert both mixed fractions to improper fractions, then calculated like a proper fraction and finally simplify it.
To convert a mix fraction to improper fraction (improper fraction has the numerator bigger than denominator), keep the denominator the same, then for the numerator multiply the whole number by the denominator then added to the numerator
Example how to convert mixed fraction to improper fraction:
b |
c |
a x c + b |
c |
2 |
3 |
3 |
4 |
2 |
3 |
3 |
4 |
3 x 3 + 2 |
3 |
4 x 4 + 3 |
4 |
11 |
3 |
19 |
4 |
(11 x 4) + (19 x 3) |
3 x 4 |
101 |
12 |
5 |
12 |
more about improper fraction and how to simplify it click here
Adding mixed fractions with different denominators, we need to make the fractions have the same denominators and added like the previous example.
3 |
4 |
2 |
3 |
Add the whole numbers together, and make the proper fractions have the same denominator. more about adding proper fractions click here
3 |
4 |
2 |
3 |
3 |
4 |
2 |
3 |
3 |
4 |
2 |
3 |
3 x 3 |
4 x 3 |
2 x 4 |
3 x 4 |
17 |
12 |
Simplify the fraction if possible
For more details click here
17 |
12 |
5 |
12 |
5 |
12 |
Positive Fractions
-1 |
-2 |
1 |
-2 |
-1 |
2 |
1 |
2 |
Negative Fractions
-1 |
2 |
1 |
-2 |
-1 |
-2 |
1 |
2 |