Question

X : \frac{1}{4} = 2\frac{2}{5} : \frac{2}{5}

Answer 1

Ответ:

$x \div \frac{1}{4} = 2 \frac{2}{5} \div \frac{2}{5} \\ \frac{x}{4} = \frac{12}{5} \div \frac{2}{5} \\ \frac{x}{4} = \frac{12}{5} \times \frac{5}{2} \\ \frac{x}{4} = 6 \\ x = 6 \times 4 \\ x = 24$

Answer 2

To solve the proportion $X : \frac{1}{4} = 2\frac{2}{5} : \frac{2}{5}$, you can follow these steps:

1. Convert the mixed number to an improper fraction: $2\frac{2}{5}$ as an improper fraction is $\frac{12}{5}$.

2. Rewrite the proportion: $X : \frac{1}{4} = \frac{12}{5} : \frac{2}{5}$.

3. Invert and multiply: $X = \frac{1}{4} \times \frac{5}{2} \times 12$.

   $X = \frac{5}{8} \times 12$.

   $X = \frac{60}{8}$.

   $X = 7.5$.

So, the solution to the proportion is $X = 7.5$.