Is the sum of two mixed numbers always a mixed numbers? Why or why not?

true if both are positve, or if both are negative.

depends if one is + , the other -

e.g 8/5 - 9/7 = 11/35

but 15/4 - 3/2 = 9/4 , still a mixed number

To determine whether the sum of two mixed numbers is always a mixed number, we need to understand what a mixed number is.

A mixed number consists of a whole number and a fraction. For example, 3 1/2 is a mixed number where 3 is the whole number and 1/2 is the fraction part.

Now, when we add two mixed numbers, the result may or may not be a mixed number. It depends on the sum of the whole numbers and the sum of the fractions.

If the sum of the whole numbers is not a whole number, then the result will not be a mixed number. For example, if we add 3 1/2 and 2 3/4, the sum of the whole numbers is 5, which is a whole number.

However, if the sum of the whole numbers is a whole number and the sum of the fractions is less than 1, then the result will be a mixed number. For example, if we add 2 1/3 and 1 2/5, the sum of the whole numbers is 3 and the sum of the fractions is 5/15, which simplifies to 1/3. Therefore, the sum is 3 1/3, which is a mixed number.

In summary, the sum of two mixed numbers is not always a mixed number. It depends on the sum of the whole numbers and the sum of the fractions.