Evaluate the following expression:
$\frac{7}{8}-\frac{2}{3}=$
The objective is to calculate the difference between two fractions: \(\frac{7}{8}\) and \(\frac{2}{3}\). These fractions have different denominators, 8 and 3. To perform the subtraction, we need to convert both fractions to an equivalent form using a common denominator. The least common multiple (LCM) of 8 and 3 is the smallest positive integer that is divisible by both. Since 8 and 3 have no common factors other than 1, their least common multiple is \(8 \times 3 = 24\).
Now we convert each fraction to an equivalent fraction with a denominator of 24.
For the first fraction, \(\frac{7}{8}\), we multiply both the numerator and the denominator by 3:
\[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \]
For the second fraction, \(\frac{2}{3}\), we multiply both the numerator and the denominator by 8:
\[ \frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} \]
With both fractions now having the same denominator, we can subtract the second from the first by subtracting their numerators and keeping the common denominator:
\[ \frac{21}{24} - \frac{16}{24} = \frac{21 - 16}{24} \]
Subtracting the numerators, we get \(21 - 16 = 5\). Thus:
\[ \frac{21 - 16}{24} = \frac{5}{24} \]
The final result is \(\frac{5}{24}\).
In daily life, managing fractions is essential for tasks like baking or measuring ingredients. For example, if a recipe calls for \(\frac{7}{8}\) of a cup of flour, but you only have a measuring cup that is \(\frac{2}{3}\) of a cup, you might need to determine the difference to know how much more or less you need. Subtracting \(\frac{7}{8} - \frac{2}{3}\) helps you understand the exact portion size needed to adjust your recipe correctly.