Question

select all the fractions that are equivalent to \\(\frac{2}{3}\\). use the area models to help. select all that apply. \\(\square\\) a. \\(\frac{2}{4}\\) \\(\square\\) b. \\(\frac{3}{6}\\) \\(\square\\) c. \\(\frac{4}{6}\\) \\(\square\\) d. \\(\frac{1}{2}\\) \\(\square\\) e. \\(\frac{8}{12}\\)

Explanation:

Step1: Simplify each option

Simplify fraction by dividing numerator and denominator by their GCD.

• Option A: $\frac{2}{4}=\frac{2\div2}{4\div2}=\frac{1}{2}

eq\frac{2}{3}$

• Option B: $\frac{3}{6}=\frac{3\div3}{6\div3}=\frac{1}{2}

eq\frac{2}{3}$

• Option C: $\frac{4}{6}=\frac{4\div2}{6\div2}=\frac{2}{3}$ (equal)
• Option D: $\frac{1}{2}

eq\frac{2}{3}$

• Option E: $\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}$ (equal)

Step2: Identify equivalent fractions

From simplification, $\frac{4}{6}$ (Option C) and $\frac{8}{12}$ (Option E) are equivalent to $\frac{2}{3}$.

Answer:

C. $\frac{4}{6}$, E. $\frac{8}{12}$