Final answer:
To evaluate \(\frac{2}{5} + \frac{3}{4}\) using equivalent fractions, find a common denominator of 20, convert each fraction, and then add them together to get \(\frac{23}{20}\).
Step-by-step explanation:
The equation to evaluate \(\frac{2}{5} + \frac{3}{4}\) using equivalent fractions involves finding a common denominator so that the two fractions can be added. To find a common denominator, we look for the least common multiple (LCM) of the two denominators, which in this case is 20. Therefore, we need to convert \(\frac{2}{5}\) and \(\frac{3}{4}\) to equivalent fractions with a denominator of 20.
To convert \(\frac{2}{5}\) to a fraction with a denominator of 20, multiply both the numerator and the denominator by 4, so we get \(\frac{2 \times 4}{5 \times 4} = \frac{8}{20}\). To convert \(\frac{3}{4}\) to a fraction with a denominator of 20, multiply both the numerator and the denominator by 5, so we get \(\frac{3 \times 5}{4 \times 5} = \frac{15}{20}\). Now, with a common denominator, the fractions can be added together directly:
\(\frac{8}{20} + \frac{15}{20} = \frac{8 + 15}{20} = \frac{23}{20}\).
Thus, using equivalent fractions to evaluate the sum of \(\frac{2}{5}\) and \(\frac{3}{4}\) would look like:
\(\frac{2}{5} + \frac{3}{4} = \frac{2 \times 4}{5 \times 4} + \frac{3 \times 5}{4 \times 5} = \frac{8}{20} + \frac{15}{20} = \frac{23}{20}\).