Question

which fractions are equivalent to \\(\frac{1}{2}\\)? choose all the correct answers. \\(\frac{4}{5}\\) \\(\frac{3}{6}\\) \\(\frac{6}{7}\\) \\(\frac{5}{10}\\) \\(\frac{7}{8}\\) \\(\frac{8}{12}\\)

Explanation:

Step1: Recall equivalent fraction rule

A fraction $\frac{a}{b}$ is equivalent to $\frac{1}{2}$ if $a\times2 = b$ (or simplifying the fraction gives $\frac{1}{2}$).

Step2: Check $\frac{4}{5}$

$4\times2 = 8$, $8
eq5$. Not equivalent.

Step3: Check $\frac{3}{6}$

Simplify: $\frac{3\div3}{6\div3}=\frac{1}{2}$. Equivalent.

Step4: Check $\frac{6}{7}$

$6\times2 = 12$, $12
eq7$. Not equivalent.

Step5: Check $\frac{5}{10}$

Simplify: $\frac{5\div5}{10\div5}=\frac{1}{2}$. Equivalent.

Step6: Check $\frac{7}{8}$

$7\times2 = 14$, $14
eq8$. Not equivalent.

Step7: Check $\frac{8}{12}$

Simplify: $\frac{8\div4}{12\div4}=\frac{2}{3}
eq\frac{1}{2}$. Wait, re - check: $8\times2 = 16$, $16
eq12$. Wait, earlier mistake. Wait, $\frac{8}{12}=\frac{2}{3}$, not equivalent. Wait, original check: for $\frac{3}{6}$, $3/6 = 1/2$; $\frac{5}{10}=1/2$; wait, let's re - check $\frac{8}{12}$: divide numerator and denominator by 4, get $\frac{2}{3}$, not 1/2. So correct ones are $\frac{3}{6}$ and $\frac{5}{10}$. Wait, also, wait $\frac{8}{12}$: 8 divided by 4 is 2, 12 divided by 4 is 3, so 2/3. But wait, maybe I made a mistake. Wait, the problem is to find fractions equivalent to 1/2. So for a fraction $\frac{n}{d}$, $n=\frac{d}{2}$. So:

• $\frac{4}{5}$: $5/2 = 2.5

eq4$

• $\frac{3}{6}$: $6/2 = 3$, so 3/6 is equivalent.
• $\frac{6}{7}$: $7/2 = 3.5

eq6$

• $\frac{5}{10}$: $10/2 = 5$, so 5/10 is equivalent.
• $\frac{7}{8}$: $8/2 = 4

eq7$

• $\frac{8}{12}$: $12/2 = 6

eq8$

Wait, so the correct ones are $\frac{3}{6}$ and $\frac{5}{10}$.

Answer:

$\frac{3}{6}$, $\frac{5}{10}$