Question
Write 2/5∶ 2 in the form of 1 ∶ 𝑛.
Answers
GPT-4o mini
To express the ratio \( \frac{2}{5} : 2 \) in the form \( 1 : n \), we first need to express it as a single ratio.
Starting with the ratio \( \frac{2}{5} : 2 \), we can convert it to a single fraction. This is done by dividing \( \frac{2}{5} \) by \( 2 \):
\[
\frac{2}{5} : 2 = \frac{2}{5} \div 2 = \frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}
\]
Next, we want to express this in the form \( 1 : n \). We can rewrite \( \frac{1}{5} \) as:
\[
1 : 5
\]
Thus, both the left side and the right side of the ratio represents the same relationship, which can be expressed as:
\[
1 : 5
\]
Therefore, the final ratio in the form \( 1 : n \) is
\[
1 : 5
\]
So, \( n = 5 \).
Starting with the ratio \( \frac{2}{5} : 2 \), we can convert it to a single fraction. This is done by dividing \( \frac{2}{5} \) by \( 2 \):
\[
\frac{2}{5} : 2 = \frac{2}{5} \div 2 = \frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}
\]
Next, we want to express this in the form \( 1 : n \). We can rewrite \( \frac{1}{5} \) as:
\[
1 : 5
\]
Thus, both the left side and the right side of the ratio represents the same relationship, which can be expressed as:
\[
1 : 5
\]
Therefore, the final ratio in the form \( 1 : n \) is
\[
1 : 5
\]
So, \( n = 5 \).