27/25 : 54/45

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 \( 9 : 10 \).