Question

Fill in the missing fraction to create a true equation blank/5 - 1/2 = 3/blank

Answer 1

To solve the equation \( \frac{\text{blank}}{5} - \frac{1}{2} = \frac{3}{\text{blank}} \), we will denote the missing value in the numerator of the first fraction as \( x \) and the missing value in the denominator of the third fraction as \( y \). This gives us the equation:

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

To solve for \( x \) and \( y \), we first find a common denominator for the left side of the equation. The common denominator between 5 and 2 is 10. Rewriting the left side:

\[
\frac{x}{5} = \frac{2x}{10}, \quad \frac{1}{2} = \frac{5}{10}
\]

Substituting these values we get:

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

Combining the fractions on the left side:

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

Cross-multiplying gives us:

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

Now we need to assign values to either \( x \) or \( y \) to find solutions. Let's assume \( y = 5 \):

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

Solving for \( x \):

\[
2x - 5 = 6 \\
2x = 11 \\
x = \frac{11}{2}
\]

Now substituting back, we have from our values:

\[
\frac{\frac{11}{2}}{5} - \frac{1}{2} = \frac{3}{5}
\]

This simplifies to:

\[
\frac{11}{10} - \frac{5}{10} = \frac{6}{10}, \; \text{or} \; \frac{3}{5}
\]

So substituting \( y = 5 \) works.

Thus, the answer to the missing fractions are:
\[
\frac{11}{2} \text{ for the first blank} \quad \text{and} \quad 5 \text{ for the second blank.}
\]