- To find an equivalent fraction with a denominator of 12, identify the factor that turns 4 into 12, which is 3.
- Multiply both the original numerator \(a\) and denominator 4 by 3 to maintain the ratio.
- The equivalent fraction is \(\frac{3a}{12}\).
- The missing numerator is \(\boxed{3a}\).
Explanation
- Finding the Equivalent Fraction
To find a fraction equivalent to \(\frac{a}{4}\) with a denominator of \(12\), we look for a missing numerator \(\square\) such that \[\frac{a}{4} = \frac{\square}{12}.\] An equivalent fraction is formed by multiplying the numerator and the denominator by the same non-zero constant. To transform the denominator from \(4\) to \(12\), we multiply by \(3\) because \(4 \times 3 = 12\). Applying the same operation to the numerator, we multiply \(a\) by \(3\), resulting in \(3a\). Thus, \(\frac{a}{4} = \frac{3a}{12}\). Additional equivalent fractions can be generated similarly, such as \(\frac{2a}{8}\) or \(\frac{4a}{16}\).
Examples
Imagine you are cutting a cake into equal portions. If you divide a cake into 4 equal slices and take \(a\) of them, you have \(\frac{a}{4}\) of the cake. If you were to divide the same cake into 12 equal slices instead, each original slice would be split into 3 smaller pieces. Therefore, taking \(a\) original slices is equivalent to taking \(3a\) smaller pieces. This demonstrates how equivalent fractions help us represent the same quantity in different ways, which is essential for tasks like adjusting recipes or comparing different measurement units.