Question

Проверьте правильность пропорции (двумя способами) 2 : 10 = 3 : 15 2 : 5 = 3 : 8 1 : 5 = 0,2 : 1 0,5 : 0,125 = 0,4 : 0,25 14 : 2,8 = 6,2 : 1,24 0,4 : 3,2 = 0,25 : 2

Answer 1

$\frac{2}{10} = \frac{3}{15} \\ \frac{6}{30} = \frac{6}{30}$
$\frac{2}{5} = \frac{3}{8} \\ \frac{16}{40} =? \frac{15}{40} ... \frac{16}{40} > \frac{15}{40}$
$\frac{1}{5} = \frac{1}{5}$
$\frac{4}{1} > \frac{1.6}{1}$
дальше не знаю

Answer 2

Proportions Verification

To verify the correctness of the given proportions, let's calculate the ratios using two different methods.

Method 1: Cross-multiplication

To check the proportion 2 : 10 = 3 : 15, we can cross-multiply the terms and check if they are equal:

2 * 15 = 10 * 3

30 = 30

The cross-multiplication method confirms that the proportion is correct.

Now, let's check the proportion 2 : 5 = 3 : 8:

2 * 8 = 5 * 3

16 = 15

The cross-multiplication method shows that the proportion is incorrect.

Finally, let's check the proportion 1 : 5 = 0.2 : 1:

1 * 1 = 5 * 0.2

1 = 1

The cross-multiplication method confirms that the proportion is correct.

Method 2: Division

Another way to verify proportions is by dividing the terms and checking if the ratios are equal.

For the proportion 2 : 10 = 3 : 15:

2 / 10 = 0.2

3 / 15 = 0.2

The division method confirms that the proportion is correct.

For the proportion 2 : 5 = 3 : 8:

2 / 5 = 0.4

3 / 8 = 0.375

The division method shows that the proportion is incorrect.

For the proportion 1 : 5 = 0.2 : 1:

1 / 5 = 0.2

0.2 / 1 = 0.2

The division method confirms that the proportion is correct.

In summary:

- The proportion 2 : 10 = 3 : 15 is correct. - The proportion 2 : 5 = 3 : 8 is incorrect. - The proportion 1 : 5 = 0.2 : 1 is correct.