Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
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.
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.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
