Enter the correct numerator to match the new denominator.
$\frac{a}{4}=\frac{\square}{60}$
(Simplify your answer.)
We are tasked with finding an equivalent fraction for \(\frac{a}{4}\) such that the denominator becomes 60. An equivalent fraction is formed by multiplying or dividing the numerator and denominator by the same non-zero number. We are given the equation \(\frac{a}{4} = \frac{\Box}{60}\). Our objective is to determine the expression that belongs in the box.
To transform the denominator of the first fraction from 4 to 60, we need to find the scaling factor \(k\) such that \(4 \times k = 60\). Dividing 60 by 4, we find:
\[k = \frac{60}{4} = 15.\]
This means the denominator has been multiplied by 15. To keep the value of the fraction unchanged, we must also multiply the numerator \(a\) by the same factor \(k = 15\).
Now, we multiply the numerator \(a\) by 15:
\[\text{New numerator} = a \times 15 = 15a.\]
Substituting this back into the original equation, we have:
\[\frac{a}{4} = \frac{15a}{60}.\]
Thus, the expression that replaces the box is \(15a\).
Equivalent fractions are like scaling a recipe! If a recipe for 4 people calls for 'a' cups of flour, and you want to scale the recipe to serve 60 people, you need to find the new amount of flour. By using the equivalent fraction \(\frac{a}{4} = \frac{\text{new amount}}{60}\), you discover you need 15 times the original amount of flour, which is \(15a\). Understanding this helps in cooking, budgeting, or any situation where ratios need to remain constant while the scale increases.