No improper fractions. I need to show all my work and no calculator

Question

The length of AB is 7(1/8) units. The length of BC is 5(2/7) units. Find AC.

Answer 1

The length of AB is 7(1/8) units. 

The length of BC is 5(2/7) units.

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A                 B                    C

From the above diagram we can clearly say thar

AC  =  AB + BC

       =   7(1/8)  +  5(2/7)

       =   7 + (1/8)  +  5 + (2/7)

       =   7 + 5 + (1/8) + (2/7)

       =   12 + (1/8) + (2/7)

       =   12 + [ (7X1) + (8 X 2) ] / 56               [ Since by taking LCM of denominators ]

       =   12 + (7 + 16) / 56

       =   12 + 23 / 56

AC  =   12(23 / 56)

Answer :

The length of AC is 12(23 / 56)units.