To solve [tex]\(\frac{20}{33} \div \frac{30}{77}\)[/tex], follow these steps:
1. Understand Division of Fractions:
Dividing one fraction by another is equivalent to multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
[tex]\[
\frac{20}{33} \div \frac{30}{77} = \frac{20}{33} \times \frac{77}{30}
\][/tex]
2. Multiply the Numerators:
Multiply the numerators of the two fractions together:
[tex]\[
20 \times 77 = 1540
\][/tex]
3. Multiply the Denominators:
Multiply the denominators of the two fractions together:
[tex]\[
33 \times 30 = 990
\][/tex]
4. Form the New Fraction:
Combine the results of the multiplication to form a new fraction:
[tex]\[
\frac{1540}{990}
\][/tex]
5. Simplify the Fraction:
Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of 1540 and 990 and dividing the numerator and the denominator by this GCD.
However, the final simplified fraction can be directly expressed in decimal form, derived from the intermediate calculations.
By following these steps, you'll find that the division of [tex]\(\frac{20}{33}\)[/tex] by [tex]\(\frac{30}{77}\)[/tex] results in approximately:
[tex]\[
\frac{20}{33} \div \frac{30}{77} \approx 1.5555555555555556
\][/tex]
So, [tex]\(\frac{20}{33} \div \frac{30}{77} \approx 1.5556\)[/tex] when rounded to four decimal places.
