How do you add three mixed fractions?

Answer 1

Well, that's why we only use mixed fractions in solutions/answers because it is a hell to work with.

But, there are tricks to do it.

First, write mixed fractions as a combination of an integer and a proper fraction

By integer, we mean whole numbers, - 1000, -1, 0, 6, 20 etc.

By proper fraction, we mean a fraction p/q where both p and q are natural numbers, 1, 2, 3, 4, etc., they have no common factor and p <= q.

Now we have three in such form, let's say

a b/c, d e/f and g h/i

Now, write them by their definition

that is a b/c = a + b/c

so the sum of all 3 is

a + b/c + d + e/f +g + h/i

Addition is commutable and associative, so rearrange the operation

(a + d + g) + (b/c + e/f + h/i)

a + d + g are justing three integers, and the other half is adding proper fractions, easy as pie!

Let's say we get m = a + d + g and (o/p) = b/c + e/f + h/i,

then the answer is obvious m o/p

Oh, not so fast, we have to simplify o/p first --- first reduce it to lowest irreducible form, then write it in its mixed fraction form

say,

z x/y = o/p

then we combine them we get

(m + z) x/y is your solution.

A lot of symbols, might get lost.

Note: In higher calculations though, it is prefered never use mixed fractions operations because this trick will get very long. So the BEST way is to turn them into normal (non- proper/proper) fraction.