67/45 : 5/90

To solve the expression \( \frac{67}{45} : \frac{5}{90} \), we first convert the division of fractions into multiplication by taking the reciprocal of the second fraction:

\[ \frac{67}{45} \div \frac{5}{90} = \frac{67}{45} \times \frac{90}{5} \]

Now we can simplify the expression. We can simplify \( \frac{90}{5} \):

\[ \frac{90}{5} = 18 \]

So now we have:

\[ \frac{67}{45} \times 18 \]

Next, we can multiply:

\[ \frac{67 \times 18}{45} \]

Calculating \( 67 \times 18 \):

\[ 67 \times 18 = 1206 \]

Now, we have:

\[ \frac{1206}{45} \]

Next, we can simplify this fraction. We should find the greatest common divisor (GCD) of 1206 and 45.

Calculating the GCD:

1206 can be divided by 3 (1 + 2 + 0 + 6 = 9, which is divisible by 3) giving:

\[ 1206 \div 3 = 402 \]

45 is also divisible by 3:

\[ 45 \div 3 = 15 \]

So we can simplify \( \frac{1206}{45} \) by dividing both numerator and denominator by 3:

\[ \frac{402}{15} \]

Next, we divide \( 402 \) by \( 3 \) again to get:

\[ 402 \div 3 = 134 \]

So now we have:

\[ \frac{134}{5} \]

This is a simplified form of the original expression. If you want to convert it to a mixed number or decimal:

\[ \frac{134}{5} = 26.8 \]

So the final answer is:

\[ \frac{134}{5} \text{ or } 26.8 \]