For each fraction, find an equivalent fraction that has a denominator of 20:
To find an equivalent fraction for a given fraction \(\frac{a}{b}\) with a new denominator \(D\), we need to find a number \(k\) such that \(b \times k = D\). Once we find \(k\), the equivalent fraction is given by \(\frac{a \times k}{b \times k} = \frac{a \times k}{D}\). We are given two fractions to convert: \(\frac{3}{5}\) and \(\frac{3}{4}\), both to a denominator of 20.
For the fraction \(\frac{3}{5}\), we want to find a numerator \(n\) such that \(\frac{3}{5} = \frac{n}{20}\). We need to determine the value of \(k\) such that \(5 \times k = 20\). Dividing 20 by 5, we find \(k = 4\). Multiplying the numerator by this same constant, we get \(n = 3 \times 4 = 12\). Thus, the equivalent fraction is \(\frac{12}{20}\).
For the fraction \(\frac{3}{4}\), we want to find a numerator \(n\) such that \(\frac{3}{4} = \frac{n}{20}\). We need to determine the value of \(k\) such that \(4 \times k = 20\). Dividing 20 by 4, we find \(k = 5\). Multiplying the numerator by this same constant, we get \(n = 3 \times 5 = 15\). Thus, the equivalent fraction is \(\frac{15}{20}\).
The equivalent fractions with a denominator of 20 are \(\frac{12}{20}\) and \(\frac{15}{20}\). Therefore, the final answers are:
Imagine you are baking cookies and have a recipe that calls for \(\frac{3}{5}\) of a cup of sugar and \(\frac{3}{4}\) of a cup of flour. Your measuring cup has 20 small markings. By converting these fractions to have a common denominator of 20, you can easily measure out \(\frac{12}{20}\) of a cup for the sugar and \(\frac{15}{20}\) of a cup for the flour, making it much simpler to follow your recipe accurately.