To solve the ratio ( 13 \frac{1}{2} : 7 \frac{7}{12} ), let's first convert these mixed numbers into improper fractions.
Convert ( 13 \frac{1}{2} ):
- ( 13 \frac{1}{2} = 13 + \frac{1}{2} = \frac{26}{2} + \frac{1}{2} = \frac{27}{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
]
