Try Again $\newline$ One or more of your answers are incorrect. $\newline$ First, rewrite $\newline$ $\frac{4}{5}$ and $\newline$ $\frac{9}{11}$ so that they have a common denominator. Then, use $\newline$ $<$ , $=$ , or $\newline$ $>$ to order $\newline$ $\frac{4}{5}$ and $\newline$ $\frac{9}{11}$ .

View step-by-step help

Home

Math Problems

Algebra 2

Power rule

Full solution

Q. Try Again

\newline

One or more of your answers are incorrect.

\newline

First, rewrite

\newline

\frac{4}{5}

and

\newline

\frac{9}{11}

so that they have a common denominator. Then, use

\newline

<

=

, or

\newline

>

to order

\newline

\frac{4}{5}

and

\newline

\frac{9}{11}

Find LCD: Find the least common denominator (LCD) for the fractions $(\frac{4}{5})$ and $(\frac{9}{11})$ . To find the LCD, we look for the least common multiple (LCM) of the denominators $5$ and $11$ . Since $5$ and $11$ are both prime numbers and have no common factors other than $1$ , the LCM of $5$ and $11$ is simply their product. $\text{LCD} = 5 \times 11 = 55$
Rewrite fractions: Rewrite each fraction with the common denominator of $55$ . For $(\frac{4}{5})$ , we need to find a number that when multiplied by $5$ gives us $55$ . That number is $11$ . So, we multiply both the numerator and the denominator of $(\frac{4}{5})$ by $11$ to get the equivalent fraction with a denominator of $55$ . $(\frac{4}{5}) \times (\frac{11}{11}) = (\frac{4\times11}{5\times11}) = \frac{44}{55}$ For $(\frac{9}{11})$ , we need to find a number that when multiplied by $11$ gives us $55$ . That number is $5$ . So, we multiply both the numerator and the denominator of $(\frac{9}{11})$ by $5$ to get the equivalent fraction with a denominator of $55$ . $(\frac{$9$}{$11$}) \times (\frac{$5$}{$5$}) = (\frac{$9$\times$5$}{$11$\times$5$}) = \frac{$45$}{$55$}
Compare fractions: Compare the two fractions with the common denominator.$\newline$Now that both fractions have the same denominator, we can compare their numerators directly.$\newline$$\frac{44}{55}$ compared to $\frac{45}{55}$$\newline$Since $44$ is less than $45$, we can conclude that $\frac{4}{5}$ is less than $\frac{9}{11}$.
Write final comparison: Write the final comparison using the appropriate inequality symbol. $(\frac{4}{5}) < (\frac{9}{11})$