13 1/2:7 7/12

To solve the ratio \( 13 \frac{1}{2} : 7 \frac{7}{12} \), let's first convert these mixed numbers into improper fractions.

1. Convert \( 13 \frac{1}{2} \):

   • \( 13 \frac{1}{2} = 13 + \frac{1}{2} = \frac{26}{2} + \frac{1}{2} = \frac{27}{2} \)

2. Convert \( 7 \frac{7}{12} \):

   • \( 7 \frac{7}{12} = 7 + \frac{7}{12} = \frac{84}{12} + \frac{7}{12} = \frac{91}{12} \)

Now the ratio can be rewritten as: \[ \frac{27}{2} : \frac{91}{12} \]

To simplify this ratio, we can express it as a fraction: \[ \frac{27/2}{91/12} = \frac{27}{2} \times \frac{12}{91} \]

Now, multiply: \[ = \frac{27 \times 12}{2 \times 91} = \frac{324}{182} \]

Next, we simplify \( \frac{324}{182} \) by finding the greatest common divisor (GCD). The GCD of 324 and 182 is 2.

Dividing both the numerator and the denominator by 2: \[ = \frac{162}{91} \]

Thus, the simplified ratio \( 13 \frac{1}{2} : 7 \frac{7}{12} \) is: \[ \frac{162}{91} \]

You can also express it as: \[ 162 : 91 \]

So, the final answer is: \[ 162 : 91 \]