Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine which of the given statements is true, we will evaluate each statement step-by-step.
1. First statement: [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex]
Let's compare the two fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{10}{12}\)[/tex]:
[tex]\[ \frac{10}{12} = \frac{5 \times 2}{6 \times 2} = \frac{5}{6} \][/tex]
So, [tex]\(\frac{5}{6} = \frac{10}{12}\)[/tex]. Thus, the statement [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex] is false.
2. Second statement: [tex]\(\frac{1}{4} > \frac{1}{3}\)[/tex]
Let's compare the two fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex] by finding a common denominator. The lowest common denominator of 4 and 3 is 12.
[tex]\[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \][/tex]
[tex]\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \][/tex]
Thus, [tex]\(\frac{3}{12} < \frac{4}{12}\)[/tex]. Therefore, [tex]\(\frac{1}{4} < \frac{1}{3}\)[/tex], making the statement [tex]\(\frac{1}{4} > \frac{1}{3}\)[/tex] false.
3. Third statement: [tex]\(\frac{6}{9} = \frac{1}{3}\)[/tex]
Let's simplify [tex]\(\frac{6}{9}\)[/tex]:
[tex]\[ \frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} \][/tex]
Comparing [tex]\(\frac{2}{3}\)[/tex] with [tex]\(\frac{1}{3}\)[/tex], we can see that they are not equal. Therefore, the statement [tex]\(\frac{6}{9} = \frac{1}{3}\)[/tex] is false.
4. Fourth statement: [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex]
Let's compare the two fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]:
First, convert [tex]\(\frac{4}{5}\)[/tex] to have a denominator of 15:
[tex]\[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \][/tex]
Now, we compare [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[ \frac{13}{15} > \frac{12}{15} \][/tex]
So, the statement [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex] is true.
Therefore, the only true statement is the fourth one: [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex].
1. First statement: [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex]
Let's compare the two fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{10}{12}\)[/tex]:
[tex]\[ \frac{10}{12} = \frac{5 \times 2}{6 \times 2} = \frac{5}{6} \][/tex]
So, [tex]\(\frac{5}{6} = \frac{10}{12}\)[/tex]. Thus, the statement [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex] is false.
2. Second statement: [tex]\(\frac{1}{4} > \frac{1}{3}\)[/tex]
Let's compare the two fractions [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex] by finding a common denominator. The lowest common denominator of 4 and 3 is 12.
[tex]\[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \][/tex]
[tex]\[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \][/tex]
Thus, [tex]\(\frac{3}{12} < \frac{4}{12}\)[/tex]. Therefore, [tex]\(\frac{1}{4} < \frac{1}{3}\)[/tex], making the statement [tex]\(\frac{1}{4} > \frac{1}{3}\)[/tex] false.
3. Third statement: [tex]\(\frac{6}{9} = \frac{1}{3}\)[/tex]
Let's simplify [tex]\(\frac{6}{9}\)[/tex]:
[tex]\[ \frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} \][/tex]
Comparing [tex]\(\frac{2}{3}\)[/tex] with [tex]\(\frac{1}{3}\)[/tex], we can see that they are not equal. Therefore, the statement [tex]\(\frac{6}{9} = \frac{1}{3}\)[/tex] is false.
4. Fourth statement: [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex]
Let's compare the two fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex]:
First, convert [tex]\(\frac{4}{5}\)[/tex] to have a denominator of 15:
[tex]\[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \][/tex]
Now, we compare [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[ \frac{13}{15} > \frac{12}{15} \][/tex]
So, the statement [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex] is true.
Therefore, the only true statement is the fourth one: [tex]\(\frac{13}{15} > \frac{4}{5}\)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.