Evaluate:
$\frac{7}{12} + \frac{1}{8}$
To find the sum of \(\frac{7}{12}\) and \(\frac{1}{8}\), we first need to ensure that the fractions have a common denominator. The denominators are 12 and 8. To add these fractions, we identify the Least Common Multiple (LCM) of 12 and 8. The multiples of 12 are 12, 24, 36, ... and the multiples of 8 are 8, 16, 24, 32, .... The smallest common multiple is 24.
Now, we convert each fraction so that they have a denominator of 24.
For the first fraction, \(\frac{7}{12}\), we multiply both the numerator and the denominator by 2:
\[\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}\]
For the second fraction, \(\frac{1}{8}\), we multiply both the numerator and the denominator by 3:
\[\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}\]
Finally, we add the two fractions by summing their numerators and keeping the common denominator:
\[\frac{14}{24} + \frac{3}{24} = \frac{14+3}{24} = \frac{17}{24}\]
The fraction \(\frac{17}{24}\) is already in its simplest form because 17 is a prime number and is not a divisor of 24. The final result is \(\boxed{\frac{17}{24}}\).
Imagine you are mixing two different quantities of ingredients for a recipe, where one part is measured as \(\frac{7}{12}\) of a cup and the other is \(\frac{1}{8}\) of a cup. To determine the total amount of the ingredient needed, you calculate \(\frac{7}{12} + \frac{1}{8}\). This is a practical example of how finding a common denominator allows you to combine measurements effectively to ensure your recipe is successful.