5/16 : ( 13:18 - 3/8 ) =

To solve \( \frac{5}{16} : \left( 13:18 - \frac{3}{8} \right) \), we first need to clarify the operations involved. It looks like the expression can be interpreted in terms of fractions and a subtraction of a fraction. 1. **Convert the ratio to a fraction**: The ratio \( 13:18 \) can be expressed as \( \frac{13}{18} \). 2. **Now substitute it into the expression**: The expression becomes: \[ \frac{5}{16} : \left( \frac{13}{18} - \frac{3}{8} \right) \] 3. **Find a common denominator** to subtract \( \frac{13}{18} - \frac{3}{8} \): The least common multiple of 18 and 8 is 72. - Convert \( \frac{13}{18} \) to a fraction with a denominator of 72: \[ \frac{13}{18} = \frac{13 \times 4}{18 \times 4} = \frac{52}{72} \] - Convert \( \frac{3}{8} \) to a fraction with a denominator of 72: \[ \frac{3}{8} = \frac{3 \times 9}{8 \times 9} = \frac{27}{72} \] 4. **Now perform the subtraction**: \[ \frac{52}{72} - \frac{27}{72} = \frac{52 - 27}{72} = \frac{25}{72} \] 5. **Now, replace back into the original expression**: We have: \[ \frac{5}{16} : \frac{25}{72} \] 6. **Dividing by a fraction is the same as multiplying by its reciprocal**: \[ \frac{5}{16} \times \frac{72}{25} \] 7. **Now multiply the fractions**: \[ = \frac{5 \times 72}{16 \times 25} = \frac{360}{400} \] 8. **Simplify the fraction**: Both the numerator and the denominator can be divided by 40: \[ = \frac{360 \div 40}{400 \div 40} = \frac{9}{10} \] Therefore, the final answer is: \[ \frac{9}{10} \]