# How do you evaluate #\frac { \frac { 1} { 2} + \frac { 2} { 3} } { 1\frac { 1} { 5} }#?

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To evaluate ( \frac { \frac { 1} { 2} + \frac { 2} { 3} } { 1\frac { 1} { 5} } ), follow these steps:

- Convert the mixed number ( 1\frac { 1} { 5} ) to an improper fraction: ( \frac {6} {5} ).
- Rewrite the expression as ( \frac { \frac { 1} { 2} + \frac { 2} { 3} } { \frac {6} {5} } ).
- Find a common denominator for the fractions in the numerator: ( \frac { \frac {3} {6} + \frac {4} {6} } { \frac {6} {5} } ).
- Combine the fractions in the numerator: ( \frac { \frac {7} {6} } { \frac {6} {5} } ).
- Invert the divisor and multiply: ( \frac { \frac {7} {6} } { \frac {6} {5} } \times \frac {5} {6} ).
- Multiply the numerators and denominators: ( \frac {7 \times 5} {6 \times 6} ).
- Calculate the result: ( \frac {35} {36} ).

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