Alright, let's solve this step-by-step:
First, we need to compare two fractions: [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{5}{9}\)[/tex].
### Step 1: Ensure both fractions have a common denominator
One way to compare two fractions is to convert them to have a common denominator. This makes it easier to see which fraction is greater.
To find a common denominator, we look for the Least Common Multiple (LCM) of the denominators of both fractions, which are 3 and 9.
- The denominators are 3 and 9.
- The LCM of 3 and 9 is 9, because 9 is the smallest number that both 3 and 9 can divide into without leaving a remainder.
### Step 2: Convert fractions to have the common denominator
Next, we'll convert [tex]\(\frac{2}{3}\)[/tex] to have a denominator of 9:
- Multiply both the numerator and the denominator of [tex]\(\frac{2}{3}\)[/tex] by 3.
[tex]\[
\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\][/tex]
So, [tex]\(\frac{2}{3}\)[/tex] converts to [tex]\(\frac{6}{9}\)[/tex].
The other fraction [tex]\(\frac{5}{9}\)[/tex] already has the denominator of 9, so we don't need to change it.
### Step 3: Compare the two fractions
Now we can directly compare the two fractions because they have the same denominator:
- [tex]\(\frac{6}{9}\)[/tex]
- [tex]\(\frac{5}{9}\)[/tex]
Since both fractions now have the same denominator, we can simply compare the numerators: 6 and 5.
[tex]\[
6 > 5
\][/tex]
Therefore, [tex]\(\frac{6}{9} > \frac{5}{9}\)[/tex].
### Step 4: Conclude
From this comparison, we can conclude that:
[tex]\[
\frac{2}{3} > \frac{5}{9}
\][/tex]
Hence, the comparison [tex]\( \frac{2}{3} \times > \frac{5}{9} \)[/tex] is true. The fraction [tex]\(\frac{2}{3}\)[/tex] is indeed greater than [tex]\(\frac{5}{9}\)[/tex].
