Question

Fill in the missing fractions to create a true equation.(1 point)
/5 − 1/2 =
3/

Answer 1

To fill in the missing fractions in the equation \(\frac{?}{5} - \frac{1}{2} = \frac{3}{?}\), we can denote the missing numerator as \(x\) for the left fraction and \(y\) for the right fraction, leading to the equation:

\[
\frac{x}{5} - \frac{1}{2} = \frac{3}{y}
\]

To solve this, we first find a common denominator for the left side:

The common denominator of 5 and 2 is 10. Therefore, we write:

\[
\frac{2x}{10} - \frac{5}{10} = \frac{3}{y}
\]

This simplifies to:

\[
\frac{2x - 5}{10} = \frac{3}{y}
\]

Next, we can cross-multiply:

\[
(2x - 5)y = 30
\]

Now, we need to find values for \(x\) and \(y\) that satisfy this equation.

Let's test a couple of reasonable values:

1. If we set \(y = 2\):

\[
(2x - 5) \times 2 = 30 \implies 2x - 5 = 15 \implies 2x = 20 \implies x = 10
\]

So, we fill in:

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

Calculating:

\(\frac{10}{5} = 2\), so:

\[
2 - \frac{1}{2} = 2 - 0.5 = 1.5 = \frac{3}{2}
\]

The equation holds true. Therefore, the final equation is:

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

Thus, the missing fractions are \(10\) and \(2\), yielding the complete and correct equation.