Find the difference. Write your answer in simplest form.
$\frac{5}{6}-\frac{4}{5}$
To calculate the difference between the two fractions \(\frac{5}{6}\) and \(\frac{4}{5}\), we must first express them with a common denominator. This makes it possible to subtract the numerators directly.
The denominators of the fractions are 6 and 5. To find a common denominator, we calculate the least common multiple (LCM) of 6 and 5. Since 6 and 5 share no common factors other than 1, their least common multiple is simply their product:
\[6 \times 5 = 30\]
Thus, 30 is the least common denominator.
Next, we convert each fraction to an equivalent fraction with a denominator of 30.
For \(\frac{5}{6}\):
\[\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\]
For \(\frac{4}{5}\):
\[\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}\]
Now that both fractions share the same denominator, we subtract the second numerator from the first:
\[\frac{25}{30} - \frac{24}{30} = \frac{25 - 24}{30} = \frac{1}{30}\]
The resulting fraction \(\frac{1}{30}\) cannot be simplified further as 1 and 30 share no common factors other than 1. The final answer is \(\boxed{\frac{1}{30}}\).
Subtracting fractions is a common task in real life, such as when following a recipe. If a recipe calls for \(\frac{5}{6}\) of a cup of flour and you only have \(\frac{4}{5}\) of a cup, calculating the difference \(\frac{5}{6} - \frac{4}{5} = \frac{1}{30}\) helps you determine exactly how much more flour you need to complete the measurement. Mastering this simple operation ensures accuracy in cooking, construction, and any situation involving parts of a whole.