To solve the expression [tex]\(\frac{8}{9} \div \frac{2}{3} \times \frac{15}{28}\)[/tex], we need to follow the order of operations, which dictates that we perform division before multiplication. Here are the steps involved:
1. Perform the division:
Divide [tex]\(\frac{8}{9}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]. Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, we need to multiply [tex]\(\frac{8}{9}\)[/tex] by [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
\frac{8}{9} \div \frac{2}{3} = \frac{8}{9} \times \frac{3}{2}
\][/tex]
When multiplying fractions, we multiply the numerators together and the denominators together:
[tex]\[
\frac{8 \times 3}{9 \times 2} = \frac{24}{18}
\][/tex]
Simplify the fraction [tex]\(\frac{24}{18}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 6:
[tex]\[
\frac{24 \div 6}{18 \div 6} = \frac{4}{3}
\][/tex]
So, [tex]\(\frac{8}{9} \div \frac{2}{3} = \frac{4}{3}\)[/tex].
2. Perform the multiplication:
Now, multiply [tex]\(\frac{4}{3}\)[/tex] by [tex]\(\frac{15}{28}\)[/tex]:
[tex]\[
\frac{4}{3} \times \frac{15}{28}
\][/tex]
Again, multiply the numerators together and the denominators together:
[tex]\[
\frac{4 \times 15}{3 \times 28} = \frac{60}{84}
\][/tex]
Simplify the fraction [tex]\(\frac{60}{84}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which in this case is 12:
[tex]\[
\frac{60 \div 12}{84 \div 12} = \frac{5}{7}
\][/tex]
3. Results:
- The result of the division [tex]\(\frac{8}{9} \div \frac{2}{3}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex] or approximately 1.3333.
- The result of the entire expression [tex]\(\frac{8}{9} \div \frac{2}{3} \times \frac{15}{28}\)[/tex] is [tex]\(\frac{5}{7}\)[/tex] or approximately 0.7143.
So, [tex]\(\frac{8}{9} \div \frac{2}{3} \times \frac{15}{28}\)[/tex] equals [tex]\(\frac{5}{7}\)[/tex] or, in decimal form, approximately 0.7143.
