Subtract the fractions. Write your answer in simplest form.
$\frac{11}{12}-\frac{3}{6}$
The problem requires us to subtract the fraction \(\frac{3}{6}\) from \(\frac{11}{12}\) and express the result in its simplest form. We have two fractions with different denominators, 12 and 6. To perform the subtraction, we first need to find a common denominator for both fractions.
To find the common denominator, we look at the denominators 12 and 6. Since 12 is a multiple of 6 (because \(6 \times 2 = 12\)), we can use 12 as our least common denominator. We convert the second fraction \(\frac{3}{6}\) into an equivalent fraction with a denominator of 12 by multiplying both the numerator and the denominator by 2:
\[\frac{3}{6} = \frac{3 \times 2}{6 \times 2} = \frac{6}{12}\]
Now that both fractions have the same denominator, we can subtract them by subtracting their numerators:
\[\frac{11}{12} - \frac{6}{12} = \frac{11 - 6}{12} = \frac{5}{12}\]
The resulting fraction is \(\frac{5}{12}\).
Finally, we check if the fraction \(\frac{5}{12}\) can be simplified further. The greatest common divisor (GCD) of 5 and 12 is 1, which means the fraction is already in its simplest form. Thus, the final result is \(\frac{5}{12}\).
Imagine you are baking a recipe that calls for \(\frac{11}{12}\) of a cup of flour. You have already used \(\frac{3}{6}\) of a cup. To find out how much more flour you need, you subtract the amount used from the total amount required: \(\frac{11}{12} - \frac{3}{6} = \frac{5}{12}\). This shows that you need exactly \(\frac{5}{12}\) of a cup of flour to complete your recipe.