Evaluate:
$\frac{4}{5}-\frac{1}{4}$
The objective is to compute the value of the expression \(\frac{4}{5} - \frac{1}{4}\). This involves subtracting two fractions with different denominators. To subtract fractions, we must first express them with a common denominator. The least common denominator (LCD) for two fractions is the least common multiple (LCM) of their denominators. Here, the denominators are 5 and 4. Since 5 and 4 are relatively prime, their least common multiple is simply their product, \(5 \times 4 = 20\).
To perform the subtraction \(\frac{4}{5} - \frac{1}{4}\), we convert each fraction to have a denominator of 20.
For the first fraction, \(\frac{4}{5}\), we multiply both the numerator and the denominator by 4:
\[\frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}\]
For the second fraction, \(\frac{1}{4}\), we multiply both the numerator and the denominator by 5:
\[\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}\]
Now that both fractions have the same denominator, we can subtract the second fraction from the first:
\[\frac{16}{20} - \frac{5}{20} = \frac{16 - 5}{20}\]
Subtracting the numerators, we get \(16 - 5 = 11\). Thus, the final value is:
\[\frac{16 - 5}{20} = \frac{11}{20}\]
Subtracting fractions is a common task in everyday life, such as when following a recipe. If a recipe calls for \(\frac{4}{5}\) of a cup of flour and you already used \(\frac{1}{4}\) of a cup, you need to determine how much more flour is required. By calculating \(\frac{4}{5} - \frac{1}{4} = \frac{11}{20}\), you know precisely how much more flour to measure, ensuring your proportions remain accurate for the perfect dish.