Solve the Fraction Division: 5/9 ÷ 7/18 Step by Step

To solve $\frac{5}{9} \div \frac{7}{18}$, we will proceed with the following steps:

• Step 1: Identify the dividend and divisor: $\frac{5}{9}$ and $\frac{7}{18}$.
• Step 2: Find the reciprocal of the divisor. The reciprocal of $\frac{7}{18}$ is $\frac{18}{7}$.
• Step 3: Multiply the dividend by the reciprocal of the divisor: $\frac{5}{9} \times \frac{18}{7}.$
• Step 4: Multiply the numerators: $5 \times 18 = 90$.
• Step 5: Multiply the denominators: $9 \times 7 = 63$.
• Step 6: The resulting fraction from the multiplication is $\frac{90}{63}.$
• Step 7: Simplify $\frac{90}{63}$. The greatest common divisor (GCD) of 90 and 63 is 9. Divide both the numerator and the denominator by 9: $\frac{90 \div 9}{63 \div 9} = \frac{10}{7}.$
• Step 8: Convert $\frac{10}{7}$ into a mixed number. Since $10$ divided by $7$ is $1$ with a remainder of $3$, this is $1\frac{3}{7}.$

So, the solution to the problem is $1\frac{3}{7}$.