67/45 : 5/90

To simplify the expression \( \frac{67}{45} : \frac{5}{90} \), you can rewrite the division as multiplication by the reciprocal:

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

Now, multiply the fractions:

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

Perform the multiplications:

• Numerator: \( 67 \times 90 = 6030 \)
• Denominator: \( 45 \times 5 = 225 \)

So we have:

\[ \frac{6030}{225} \]

Next, simplify the fraction \( \frac{6030}{225} \). First, find the greatest common divisor (GCD) of 6030 and 225.

Calculating the GCD, we find:

• The prime factorization of 6030: \( 2 \times 3 \times 5 \times 67 \)
• The prime factorization of 225: \( 3^2 \times 5^2 \)

The common factors are \( 3 \) and \( 5 \), and the GCD is \( 15 \).

Now, divide both the numerator and the denominator by their GCD:

\[ \frac{6030 \div 15}{225 \div 15} = \frac{402}{15} \]

Next, we can simplify \( \frac{402}{15} \) further if we divide both the numerator and the denominator by 3:

\[ \frac{402 \div 3}{15 \div 3} = \frac{134}{5} \]

Thus, the simplified result is:

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

If you wish to express this as a decimal:

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

So, the final answer is:

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