Question

which fraction is equivalent to \\(\frac{1}{2}\\)? \\(\frac{1}{3}\\) \\(\frac{3}{6}\\) \\(\frac{3}{8}\\) \\(\frac{2}{3}\\)

Explanation:

Step1: Recall equivalent fractions

Equivalent fractions are found by multiplying or dividing numerator and denominator by the same non - zero number. For a fraction $\frac{a}{b}$, an equivalent fraction is $\frac{a\times k}{b\times k}$ or $\frac{a\div k}{b\div k}$ where $k
eq0$.

Step2: Analyze each option

• For $\frac{1}{3}$: The numerator 1 and denominator 3 have no common factor (other than 1) with the numerator and denominator of $\frac{1}{2}$. $\frac{1}{3}

eq\frac{1}{2}$ since cross - multiplying: $1\times2 = 2$ and $1\times3=3$, $2
eq3$.

• For $\frac{3}{6}$: Simplify $\frac{3}{6}$ by dividing numerator and denominator by 3. $\frac{3\div3}{6\div3}=\frac{1}{2}$. So $\frac{3}{6}$ is equivalent to $\frac{1}{2}$.
• For $\frac{3}{8}$: Cross - multiply with $\frac{1}{2}$. $3\times2 = 6$ and $1\times8 = 8$, $6

eq8$, so $\frac{3}{8}
eq\frac{1}{2}$.

• For $\frac{2}{3}$: Cross - multiply with $\frac{1}{2}$. $2\times2=4$ and $1\times3 = 3$, $4

eq3$, so $\frac{2}{3}
eq\frac{1}{2}$.

Answer:

B. $\frac{3}{6}$ (assuming the options are labeled as A. $\frac{1}{3}$, B. $\frac{3}{6}$, C. $\frac{3}{8}$, D. $\frac{2}{3}$)