Subtract the fractions. Write your answer in simplest form.
$\frac{9}{10}-\frac{1}{5}=$
We are tasked with calculating the difference between two fractions: \(\frac{9}{10}\) and \(\frac{1}{5}\). To perform this subtraction, we need the two fractions to have a common denominator. The current denominators are 10 and 5. Finding a common denominator allows us to combine the numerators directly.
To find the least common denominator (LCD) for 10 and 5, we look for the smallest multiple shared by both numbers. Since 10 is a multiple of 5 (because \(5 \times 2 = 10\)), the least common denominator is 10. We can keep the first fraction, \(\frac{9}{10}\), as it is, and convert the second fraction, \(\frac{1}{5}\), so that it also has a denominator of 10. To do this, we multiply both the numerator and the denominator of \(\frac{1}{5}\) by 2:
\[\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}\]
Now that both fractions have the same denominator, we can subtract the second fraction from the first:
\[\frac{9}{10} - \frac{2}{10} = \frac{9 - 2}{10} = \frac{7}{10}\]
The resulting fraction is \(\frac{7}{10}\). To ensure it is in its simplest form, we check the greatest common divisor (GCD) of the numerator 7 and the denominator 10. Since 7 is a prime number and does not divide 10, the GCD is 1, meaning the fraction \(\frac{7}{10}\) is already in its simplest form.
The calculation \(\frac{9}{10} - \frac{1}{5}\) results in \(\frac{7}{10}\). Therefore, the final answer is \(\boxed{\frac{7}{10}}\).
Imagine you are baking a cake and your recipe calls for \(\frac{9}{10}\) of a cup of sugar, but you accidentally added \(\frac{1}{5}\) of a cup too much, or perhaps you want to know how much sugar is left after using a portion. Subtracting fractions helps in adjusting recipes, measuring ingredients, or managing resources in daily tasks. By converting to a common denominator, you can precisely determine the exact amount remaining, ensuring your measurements are always accurate and your results are consistent.