Enter the correct numerator to match the new denominator.
$\frac{-8}{13}=\frac{\square}{39}$
We are given the equation \(\frac{-8}{13} = \frac{x}{39}\). Our goal is to find the numerator \(x\) that makes the two fractions equivalent. To maintain equivalence, if we multiply the denominator of a fraction by a certain number, we must multiply its numerator by the same number.
First, we observe the relationship between the two denominators, \(13\) and \(39\). We determine the factor by which \(13\) was multiplied to get \(39\):
\[39 \div 13 = 3\]
Thus, the denominator is scaled by a factor of \(3\). To keep the fraction equivalent, we must multiply the numerator \(-8\) by this same factor:
\[x = -8 \times 3\]
Performing the multiplication, we find:
\[x = -24\]
We have found that \(x = -24\). We can check the equivalence of the fractions by verifying:
\[\frac{-24}{39} = \frac{-24 \div 3}{39 \div 3} = \frac{-8}{13}\]
Since the fractions are equivalent, our solution is correct. The value of the numerator is \(\boxed{-24}\).
Equivalent fractions are used in many real-life situations, such as cooking or managing shared resources. For instance, if a recipe calls for \(\frac{8}{13}\) of a cup of a specific ingredient, but you only have measuring cups marked with 39ths, you would need to calculate that you need \(\frac{24}{39}\) of a cup. Understanding how to scale fractions helps ensure that ratios remain constant, whether you are scaling a recipe, adjusting proportions for a design project, or distributing workloads fairly.