Question

Identify the missing lie denominator in the subtraction expression 3/5 - 1/?

Answer 1

To find the missing denominator in the expression \( \frac{3}{5} - \frac{1}{?} \), we need to determine a value that makes the subtraction meaningful.

Let's denote the missing denominator as \( x \). The key is to get a common denominator in order to perform the subtraction. The common denominator for \( \frac{3}{5} \) and \( \frac{1}{x} \) would be \( 5x \).

Rewriting both fractions with the common denominator:

\[
\frac{3}{5} = \frac{3x}{5x}
\]

\[
\frac{1}{x} = \frac{5}{5x}
\]

Now, the subtraction becomes:

\[
\frac{3x}{5x} - \frac{5}{5x} = \frac{3x - 5}{5x}
\]

To make \( \frac{1}{x} \) a valid fraction such that the subtraction can be executed, the term \( 1/x \) must not result in a negative value when \( \frac{3}{5} \) is subtracted from it.

Since we are looking for the simplest fraction that leads to a meaningful subtraction, let’s approach it via setting \( \frac{3}{5} - \frac{1}{2} \):

1. Here, apply the same common denominator of 10:

\[
\frac{3}{5} = \frac{6}{10}
\]

\[
\frac{1}{2} = \frac{5}{10}
\]

So:

\[
\frac{3}{5} - \frac{1}{2} = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}
\]

In that particular case, your \( x \) can be \( 2 \).

However, the problem demands deriving from \( \frac{1}{?} \) that directly corresponds. This means \( ? = 2 \) because:

\[
\frac{3}{5} - \frac{1}{2} = \text{subtraction resolves correctly as shown above, making denominator the part of original fraction }
\]

Thus the missing denominator \( ?\) we determine is \( \mathbf{2} \).