Question

which fractions are equivalent to \\(\frac{4}{10}\\)? choose all the correct answers. \\(\frac{2}{8}\\) \\(\frac{8}{10}\\) \\(\frac{1}{6}\\) \\(\frac{40}{100}\\) \\(\frac{2}{5}\\)

Explanation:

Step1: Simplify $\frac{4}{10}$

Simplify the given fraction by dividing numerator and denominator by their GCD (2). So, $\frac{4\div2}{10\div2}=\frac{2}{5}$. Also, we can check equivalent fractions by cross - multiplying.

Step2: Check $\frac{2}{8}$

Cross - multiply: $4\times8 = 32$ and $2\times10 = 20$. Since $32
eq20$, $\frac{2}{8}$ is not equivalent to $\frac{4}{10}$.

Step3: Check $\frac{8}{10}$

Cross - multiply: $4\times10 = 40$ and $8\times10 = 80$. Since $40
eq80$, $\frac{8}{10}$ is not equivalent to $\frac{4}{10}$.

Step4: Check $\frac{1}{6}$

Cross - multiply: $4\times6 = 24$ and $1\times10 = 10$. Since $24
eq10$, $\frac{1}{6}$ is not equivalent to $\frac{4}{10}$.

Step5: Check $\frac{40}{100}$

Simplify $\frac{40}{100}$ by dividing numerator and denominator by 20: $\frac{40\div20}{100\div20}=\frac{2}{5}$, which is equivalent to $\frac{4}{10}$ (since $\frac{4}{10}=\frac{2}{5}$). Also, cross - multiply: $4\times100 = 400$ and $40\times10 = 400$. Since $400 = 400$, $\frac{40}{100}$ is equivalent to $\frac{4}{10}$.

Step6: Check $\frac{2}{5}$

We already simplified $\frac{4}{10}$ to $\frac{2}{5}$, so $\frac{2}{5}$ is equivalent to $\frac{4}{10}$. Cross - multiply: $4\times5 = 20$ and $2\times10 = 20$. Since $20 = 20$, $\frac{2}{5}$ is equivalent to $\frac{4}{10}$.

Answer:

$\frac{40}{100}$, $\frac{2}{5}$