Add the fractions. Write your answer in simplest form.
$\frac{8}{12}+\frac{2}{12}$
The goal is to calculate the sum of two fractions, \(\frac{8}{12}\) and \(\frac{2}{12}\). These fractions share the same denominator, which is 12. Adding fractions with the same denominator is straightforward: we simply add the numerators while keeping the denominator unchanged. The sum is given by the expression:
\[\frac{8}{12} + \frac{2}{12} = \frac{8 + 2}{12} = \frac{10}{12}\]
To express the fraction \(\frac{10}{12}\) in its simplest form, we need to find the greatest common divisor (GCD) of the numerator 10 and the denominator 12. Both numbers are even, meaning they are divisible by 2.
Dividing both the numerator and the denominator by their GCD, which is 2, we get:
\[\frac{10 \div 2}{12 \div 2} = \frac{5}{6}\]
Since 5 and 6 have no common factors other than 1, the fraction \(\frac{5}{6}\) is in its simplest form.
Imagine you are baking cookies and the recipe requires \(\frac{8}{12}\) of a cup of sugar for the base and an additional \(\frac{2}{12}\) of a cup of sugar for the topping. To find the total amount of sugar needed, you add the two fractions \(\frac{8}{12} + \frac{2}{12}\). Adding these gives you \(\frac{10}{12}\) of a cup, which simplifies to \(\frac{5}{6}\) of a cup. This basic arithmetic helps ensure you have the correct measurements for your baking!