Algebra using mixed numbers

Question

this is the question=

The sum of three mixed numbers is 22 4/5

Two of the numbers are 9 2/3 and 5 5/6

What is the third number?

the answer is as a improper fraction

Answer 1

A+B+C = 22 4/5. Rewrite as a fraction: (22*5+4)/5 = 114/5

Let A = 9 2/3. Rewrite as a fraction: (9*3 + 2)/3 = 29/3

Let B = 5 5/6. Rewrite as a fraction: (5*6 + 5)/6 = 35/6

Notice that A has the denominator 3 and B has the denominator 6. 6 is 2*3, so multiply A by 2/2 to get 29/3*2/2 = 58/6.

A+B = 58/6+35/6 = 93/6.

C = 114/5 - 93/6

The denominators need to be made common. 5*6 = 30 is a common denominator.

C = 114/5*6/6 - 93/5*5/5 = 684/30 - 465/30 = (684-465)/30 = 219/30

Convert C = 219/30 to a mixed number: 219/30 = 7 9/30 = 7 3/10

As a crude check on calculation, add the whole number parts of A, B and C: 9+5+7 = 21 and the sum of the fractional parts should add to 1 4/5