Question

which of the following fractions are equivalent to \\(\frac{24}{18}\\)? select all that apply. (1 point) \\(\frac{6}{3}\\) \\(\frac{4}{3}\\) \\(\frac{8}{6}\\) \\(\frac{14}{12}\\) \\(\frac{18}{24}\\)

Explanation:

First, simplify the given fraction $\frac{24}{18}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 6. So, $\frac{24\div6}{18\div6}=\frac{4}{3}$. Wait, no, wait, maybe I misread. Wait, the problem is which fractions are equivalent to $\frac{24}{18}$? Wait, no, maybe the original fraction is $\frac{24}{18}$? Wait, no, looking at the options, let's check each fraction:

First, simplify $\frac{24}{18}$: divide numerator and denominator by 6, we get $\frac{4}{3}$. Wait, no, 24÷6=4, 18÷6=3, so $\frac{24}{18}=\frac{4}{3}$. Now check each option:

1. $\frac{6}{2}$: simplify, 6÷2=3, 2÷2=1, so $\frac{3}{1}=3$, not equal to $\frac{4}{3}$.

2. $\frac{4}{3}$: that's the simplified form of $\frac{24}{18}$, so this is equivalent.

3. $\frac{8}{6}$: divide numerator and denominator by 2, we get $\frac{4}{3}$, so this is equivalent.

4. $\frac{14}{12}$: simplify, divide by 2, $\frac{7}{6}$, not equal to $\frac{4}{3}$.

5. $\frac{18}{24}$: simplify, divide by 6, $\frac{3}{4}$, not equal to $\frac{4}{3}$. Wait, but maybe I misread the original fraction. Wait, maybe the original fraction is $\frac{18}{24}$? Wait, the checkmarks are on $\frac{8}{6}$ and $\frac{18}{24}$? Wait, no, let's re-express. Wait, maybe the original fraction is $\frac{24}{18}$? Wait, no, let's do it correctly.

Wait, let's take the fraction to check as $\frac{24}{18}$. Let's simplify it: GCD of 24 and 18 is 6. So 24÷6=4, 18÷6=3. So $\frac{24}{18}=\frac{4}{3}$.

Now check each option:

- $\frac{6}{2}$: 6÷2=3, 2÷2=1, so 3, not equal to $\frac{4}{3}$.

- $\frac{4}{3}$: equal, so this is equivalent.

- $\frac{8}{6}$: 8÷2=4, 6÷2=3, so $\frac{4}{3}$, equivalent.

- $\frac{14}{12}$: 14÷2=7, 12÷2=6, so $\frac{7}{6}$, not equivalent.

- $\frac{18}{24}$: 18÷6=3, 24÷6=4, so $\frac{3}{4}$, not equivalent. Wait, but the checkmarks are on $\frac{8}{6}$ and $\frac{18}{24}$? Maybe I got the original fraction wrong. Wait, maybe the original fraction is $\frac{18}{24}$? Let's check that. $\frac{18}{24}$ simplifies to $\frac{3}{4}$ (divide by 6). Then:

- $\frac{6}{2}$: 3, not $\frac{3}{4}$.

- $\frac{4}{3}$: not $\frac{3}{4}$.

- $\frac{8}{6}$: simplifies to $\frac{4}{3}$, not $\frac{3}{4}$.

- $\frac{14}{12}$: $\frac{7}{6}$, not.

- $\frac{18}{24}$: same as original. Wait, maybe the original fraction is $\frac{24}{18}$ and the options are to find equivalents. Wait, the user's image shows checkmarks on $\frac{8}{6}$ and $\frac{18}{24}$? No, maybe I misread. Wait, let's do it again.

Wait, the problem is "Which of the following fractions are equivalent to $\frac{24}{18}$? Select all that apply."

Options:

1. $\frac{6}{2}$

2. $\frac{4}{3}$

3. $\frac{8}{6}$

4. $\frac{14}{12}$

5. $\frac{18}{24}$

Simplify $\frac{24}{18}$: divide numerator and denominator by 6: $\frac{24\div6}{18\div6}=\frac{4}{3}$.

Now check each option:

- $\frac{6}{2}$: 3, not $\frac{4}{3}$.

- $\frac{4}{3}$: equal, so yes.

- $\frac{8}{6}$: divide numerator and denominator by 2: $\frac{4}{3}$, so yes.

- $\frac{14}{12}$: divide by 2: $\frac{7}{6}$, not $\frac{4}{3}$.

- $\frac{18}{24}$: divide by 6: $\frac{3}{4}$, not $\frac{4}{3}$.

But the checkmarks in the image are on $\frac{8}{6}$ and $\frac{18}{24}$? Wait, maybe the original fraction is $\frac{18}{24}$? Let's check that. $\frac{18}{24}$ simplifies to $\frac{3}{4}$ (divide by 6: 18÷6=3, 24÷6=4). Now check options:

- $\frac{6}{2}$: 3, no.

- $\frac{4}{3}$: no.

- $\frac{8}{6}$: simplify to $\frac{4}{3}$, no.

- $\frac{14}{12}$: $\frac{7}{6}$, no.

- $\frac{18}{24}$: same as original, yes. But that doesn't match. Wait, maybe a typo. Wait, perhaps the original fraction is $\frac{24}{18}$, and the correct equivalents are $\frac{4}{3}$ and $\frac{8}{6}$.

Wait, let's do the cross-multiplication method. For two fractions $\frac{a}{b}$ and $\frac{c}{d}$ to be equivalent, $a\times d = b\times c$.

Check $\frac{24}{18}$ and $\frac{4}{3}$: 24×3=72, 18×4=72. So equal.

Check $\frac{24}{18}$ and $\frac{8}{6}$: 24×6=144, 18×8=144. So equal.

Check $\frac{24}{18}$ and $\frac{18}{24}$: 24×24=576, 18×18=324. Not equal.

So the correct equivalents are $\frac{4}{3}$ and $\frac{8}{6}$.

Answer:

The fractions equivalent to $\frac{24}{18}$ are $\frac{4}{3}$ and $\frac{8}{6}$. So the correct options are:

• $\frac{4}{3}$

• $\frac{8}{6}$