To simplify the ratio ( \frac{27/25}{54/45} ), we can rewrite it as follows:
[
\frac{27}{25} \div \frac{54}{45}
]
This division of fractions can be handled by multiplying by the reciprocal of the second fraction:
[
\frac{27}{25} \times \frac{45}{54}
]
Now we can simplify the fractions. First, let's factor where possible.
- The fraction ( \frac{45}{54} ) can be simplified. Both the numerator and denominator can be divided by 9:
- ( 45 \div 9 = 5 )
- ( 54 \div 9 = 6 )
Thus, ( \frac{45}{54} = \frac{5}{6} ).
Now substituting this back, we have:
[
\frac{27}{25} \times \frac{5}{6}
]
Now multiply the numerators and the denominators:
[
\frac{27 \times 5}{25 \times 6} = \frac{135}{150}
]
Next, we simplify ( \frac{135}{150} ). Both the numerator and the denominator can be divided by 15:
- ( 135 \div 15 = 9 )
- ( 150 \div 15 = 10 )
So, ( \frac{135}{150} = \frac{9}{10} ).
Thus, the simplified form of ( \frac{27/25}{54/45} ) is
[
\frac{9}{10}
] or in ratio form, it can be expressed as ( 9 : 10 ).
