What is 2 3/5 + 2 4/5 + 1 1/2?

Steps to Solve

1. Convert Mixed Numbers to Improper Fractions

   • For ( 2 \frac{3}{5} ):
     $$ 2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} $$
   • For ( 2 \frac{4}{5} ):
     $$ 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} $$
   • For ( 1 \frac{1}{2} ):
     $$ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} $$

2. Find a Common Denominator

   • The denominators are ( 5 ) and ( 2 ).
   • The least common multiple of ( 5 ) and ( 2 ) is ( 10 ).

3. Convert Fractions to Have the Common Denominator

   • Convert ( \frac{13}{5} ):
     $$ \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} $$
   • Convert ( \frac{14}{5} ):
     $$ \frac{14}{5} = \frac{14 \times 2}{5 \times 2} = \frac{28}{10} $$
   • Convert ( \frac{3}{2} ):
     $$ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} $$

4. Add the Converted Fractions

   • Now we add:
     $$ \frac{26}{10} + \frac{28}{10} + \frac{15}{10} = \frac{26 + 28 + 15}{10} = \frac{69}{10} $$

5. Convert the Improper Fraction Back to a Mixed Number

   • Calculate:
     $$ 69 \div 10 = 6 \quad \text{(the quotient)} $$
     $$ 69 - (10 \times 6) = 9 \quad \text{(the remainder)} $$
   • Thus, we have:
     $$ \frac{69}{10} = 6 \frac{9}{10} $$