67/45 : 5/90
To solve the expression \( \frac{67}{45} \div \frac{5}{90} \), you can rewrite the division as multiplication by the reciprocal:
\[ \frac{67}{45} \div \frac{5}{90} = \frac{67}{45} \times \frac{90}{5} \]
Next, simplify the multiplication:
Multiply the numerators: \[ 67 \times 90 = 6030 \]
Multiply the denominators: \[ 45 \times 5 = 225 \]
Now, your fraction is:
\[ \frac{6030}{225} \]
Next, simplify \( \frac{6030}{225} \). To do this, find the greatest common divisor (GCD) of 6030 and 225:
- Factor 6030: \( 6030 = 2 \times 3 \times 5 \times 67 \)
- Factor 225: \( 225 = 15 \times 15 = 3^2 \times 5^2 \)
The GCD of 6030 and 225 is \( 15 \) (using the factors of both numbers).
Now divide both the numerator and the denominator by the GCD:
\[ \frac{6030 \div 15}{225 \div 15} = \frac{402}{15} \]
You can simplify \( \frac{402}{15} \) further by dividing by \( 3 \):
\[ \frac{402 \div 3}{15 \div 3} = \frac{134}{5} \]
Thus, \( \frac{67}{45} \div \frac{5}{90} = \frac{134}{5} \). If you want it in decimal form:
\[ \frac{134}{5} = 26.8 \]
So, the final answer is:
\(\frac{134}{5}\) or \(26.8\).
