Find an equivalent fraction:
$\frac{3}{8} = \frac{3}{8} \times \frac{?}{?} = \frac{?}{16}$
We are given the fraction \(\frac{3}{8}\) and asked to find an equivalent fraction with a denominator of \(16\). An equivalent fraction is formed by multiplying the numerator and the denominator of a given fraction by the same non-zero number \(k\). That is, if we have a fraction \(\frac{a}{b}\), multiplying it by \(\frac{k}{k}\) results in \(\frac{a \times k}{b \times k}\), which represents the same value. Our goal is to determine the multiplier \(k\) such that the denominator of the new fraction is \(16\).
The original denominator is \(8\), and the target denominator is \(16\). To find the multiplier \(k\), we solve the equation \(8 \times k = 16\). Dividing both sides by \(8\), we get:
\[k = \frac{16}{8} = 2.\]
Therefore, to transform the original denominator into \(16\), we must multiply both the numerator and the denominator by \(2\).
Now that we have identified the multiplier \(k = 2\), we apply it to both parts of the original fraction \(\frac{3}{8}\):
\[\frac{3}{8} \times \frac{2}{2} = \frac{3 \times 2}{8 \times 2} = \frac{6}{16}.\]
Thus, the equivalent fraction with a denominator of \(16\) is \(\frac{6}{16}\).
The fraction \(\frac{3}{8}\) is equal to \(\frac{3}{8} \times \frac{2}{2}\), which equals \(\frac{6}{16}\). The missing numbers are \(2\) in the multiplier and \(6\) as the new numerator. Therefore, the equivalent fraction is \(\boxed{\frac{6}{16}}\).
Equivalent fractions are used frequently in daily life for tasks like cooking and measurements. For example, if a recipe calls for \(\frac{3}{8}\) of a cup of flour, but your measuring cup is marked in sixteenths of a cup, you can use equivalent fractions to convert the measurement. By knowing that \(\frac{3}{8} = \frac{6}{16}\), you can easily measure exactly 6 out of 16 marks on your measuring cup to get the right amount of flour. Understanding this concept allows for easy adjustments in recipes, construction, and any scenario involving parts of a whole.