To determine which fractions are equivalent to [tex]\(\frac{2}{3}\)[/tex], we need to find fractions that have the same value when simplified. Fractions are equivalent if they represent the same portion of a whole. This can be achieved by multiplying the numerator and the denominator of the given fraction by the same number.
Here’s a step-by-step approach to find some fractions equivalent to [tex]\(\frac{2}{3}\)[/tex]:
1. Start with the given fraction:
[tex]\[
\frac{2}{3}
\][/tex]
2. Multiply the numerator and the denominator by 2:
[tex]\[
2 \times 2 = 4 \quad \text{and} \quad 3 \times 2 = 6
\][/tex]
So, the fraction becomes:
[tex]\[
\frac{4}{6}
\][/tex]
3. Multiply the numerator and the denominator by 3:
[tex]\[
2 \times 3 = 6 \quad \text{and} \quad 3 \times 3 = 9
\][/tex]
So, the fraction becomes:
[tex]\[
\frac{6}{9}
\][/tex]
4. Multiply the numerator and the denominator by 4:
[tex]\[
2 \times 4 = 8 \quad \text{and} \quad 3 \times 4 = 12
\][/tex]
So, the fraction becomes:
[tex]\[
\frac{8}{12}
\][/tex]
Hence, the fractions that are equivalent to [tex]\(\frac{2}{3}\)[/tex] are:
[tex]\[
\frac{4}{6}, \frac{6}{9}, \text{ and } \frac{8}{12}
\][/tex]
