Question

which fractions are equivalent to \\(\frac{3}{6}\\)? choose all the correct answers. \\(\frac{3}{4}\\) \\(\frac{6}{9}\\) \\(\frac{4}{8}\\) \\(\frac{1}{3}\\) \\(\frac{4}{12}\\)

Explanation:

Step1: Simplify the given fraction

Simplify \(\frac{3}{6}\) by dividing numerator and denominator by their greatest common divisor, which is 3. So \(\frac{3\div3}{6\div3}=\frac{1}{2}\). Now we need to check which of the given fractions are equal to \(\frac{1}{2}\).

Step2: Check each fraction

• For \(\frac{3}{4}\): \(\frac{3}{4}

eq\frac{1}{2}\) (since \(3\times2 = 6
eq4\times1 = 4\)).

• For \(\frac{6}{9}\): Simplify \(\frac{6}{9}=\frac{6\div3}{9\div3}=\frac{2}{3}

eq\frac{1}{2}\) (since \(2\times2 = 4
eq3\times1 = 3\)).

• For \(\frac{4}{8}\): Simplify \(\frac{4}{8}=\frac{4\div4}{8\div4}=\frac{1}{2}\), so this is equivalent.
• For \(\frac{1}{3}\): \(\frac{1}{3}

eq\frac{1}{2}\) (since \(1\times2 = 2
eq3\times1 = 3\)).

• For \(\frac{4}{12}\): Simplify \(\frac{4}{12}=\frac{4\div4}{12\div4}=\frac{1}{3}

eq\frac{1}{2}\) (Wait, maybe I made a mistake. Wait, \(\frac{4}{12}\) simplifies to \(\frac{1}{3}\)? Wait no, \(\frac{4}{12}=\frac{4\div4}{12\div4}=\frac{1}{3}\)? Wait, no, 4 and 12 have a GCD of 4? Wait, 4 and 12: GCD is 4? 4 divides 4 (1 time) and 12 (3 times). So \(\frac{4}{12}=\frac{1}{3}\). Wait, but maybe the original fraction was \(\frac{3}{6}=\frac{1}{2}\). Wait, maybe I misread the last fraction. Wait, the last fraction is \(\frac{4}{12}\)? Wait, or maybe it's \(\frac{6}{12}\)? Wait, no, the user's image shows \(\frac{4}{12}\)? Wait, maybe a typo. Wait, alternatively, maybe the fraction is \(\frac{6}{12}\), but according to the given, it's \(\frac{4}{12}\). Wait, but let's re - check. Wait, \(\frac{3}{6}=\frac{1}{2}\). Let's check \(\frac{4}{8}\): \(\frac{4}{8}=\frac{1}{2}\) (correct). Wait, maybe another fraction: Wait, maybe the second fraction is \(\frac{6}{12}\)? No, the user's image shows \(\frac{6}{9}\), \(\frac{4}{8}\), \(\frac{1}{3}\), \(\frac{4}{12}\). Wait, maybe I made a mistake with \(\frac{4}{12}\). Wait, \(\frac{3}{6}=\frac{1}{2}\). Let's check \(\frac{4}{8}\): 4 divided by 8 is 0.5, which is \(\frac{1}{2}\). What about \(\frac{6}{12}\)? But in the given, it's \(\frac{4}{12}\). Wait, maybe the last fraction is \(\frac{6}{12}\), but according to the user's input, it's \(\frac{4}{12}\). Wait, perhaps there's a mistake in the problem, but based on the given fractions:

Wait, let's re - evaluate:

\(\frac{3}{6}=\frac{1}{2}\)

• \(\frac{3}{4}\): 3/4 = 0.75≠0.5
• \(\frac{6}{9}=\frac{2}{3}\approx0.666

eq0.5\)

• \(\frac{4}{8}=\frac{1}{2}=0.5\) (correct)
• \(\frac{1}{3}\approx0.333

eq0.5\)

• \(\frac{4}{12}=\frac{1}{3}\approx0.333

eq0.5\)

Wait, but maybe the original fraction was \(\frac{3}{6}=\frac{1}{2}\), and the correct fraction is \(\frac{4}{8}\). Wait, maybe there's another fraction. Wait, maybe the first fraction is \(\frac{3}{6}\), and the fraction \(\frac{6}{12}\) is equivalent, but in the given, it's \(\frac{4}{12}\). So based on the given options, the only fraction equivalent to \(\frac{3}{6}\) is \(\frac{4}{8}\). Wait, but maybe I misread the fractions. Let's assume that the fractions are \(\frac{3}{4}\), \(\frac{6}{12}\) (instead of \(\frac{6}{9}\)), but no, the user's image shows \(\frac{6}{9}\). So according to the given, the correct fraction is \(\frac{4}{8}\).

Answer:

The fraction equivalent to \(\frac{3}{6}\) is \(\frac{4}{8}\) (the third square from the left, with the fraction \(\frac{4}{8}\)).