To determine which fraction is larger between [tex]\(\frac{2}{9}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex], and to plot a fraction equivalent to [tex]\(\frac{2}{9}\)[/tex], follow these steps:
### Step 1: Compare the Fractions
First, convert both fractions to decimal form for easier comparison.
- [tex]\(\frac{2}{9} \approx 0.2222\)[/tex]
- [tex]\(\frac{3}{8} = 0.375\)[/tex]
Comparing these decimal values:
- [tex]\(0.2222\)[/tex] is less than [tex]\(0.375\)[/tex]
So, [tex]\(\frac{3}{8}\)[/tex] is larger than [tex]\(\frac{2}{9}\)[/tex].
### Step 2: Plot an Equivalent Fraction to [tex]\(\frac{2}{9}\)[/tex]
To find an equivalent fraction to [tex]\(\frac{2}{9}\)[/tex], we can multiply the numerator and the denominator of [tex]\(\frac{2}{9}\)[/tex] by the same number. In this case, we'll use 8:
- Multiply both the numerator (2) and the denominator (9) by 8:
[tex]\[
\frac{2 \times 8}{9 \times 8} = \frac{16}{72}
\][/tex]
Thus, [tex]\(\frac{16}{72}\)[/tex] is an equivalent fraction to [tex]\(\frac{2}{9}\)[/tex].
### Summary of Solutions
- The fraction [tex]\(\frac{3}{8}\)[/tex] is larger than [tex]\(\frac{2}{9}\)[/tex].
- An equivalent fraction to [tex]\(\frac{2}{9}\)[/tex] is [tex]\(\frac{16}{72}\)[/tex].
By comparing decimal values and using equivalent fractions, we've determined the comparison and generated an equivalent fraction that represents the same value on the number line.
