Find the missing number __- \( 7=12: 21 \)

To solve the equation \( \_\_ - 7 = 12 : 21 \), we first need to interpret the expression \( 12 : 21 \). The colon typically represents a ratio, which can also be expressed as a fraction. So, we can rewrite \( 12 : 21 \) as: \[ \frac{12}{21} \] Next, we simplify the fraction \( \frac{12}{21} \): \[ \frac{12}{21} = \frac{4}{7} \quad \text{(dividing both the numerator and denominator by 3)} \] Now, we can substitute this back into the equation: \[ \_\_ - 7 = \frac{4}{7} \] To isolate the missing number (let's call it \( x \)), we add 7 to both sides: \[ x = \frac{4}{7} + 7 \] To add these, we need a common denominator. We can express 7 as a fraction with a denominator of 7: \[ 7 = \frac{7 \times 7}{7} = \frac{49}{7} \] Now we can add the two fractions: \[ x = \frac{4}{7} + \frac{49}{7} = \frac{4 + 49}{7} = \frac{53}{7} \] Thus, the missing number is: \[ \frac{53}{7} \] If you want a decimal approximation, \( \frac{53}{7} \approx 7.57 \). So, the final answer is: \[ \frac{53}{7} \]