What is $\frac{7}{8}-13 / 48$ written in simplest terms?
To solve the expression \(\frac{7}{8} - \frac{13}{48}\), we need to subtract two fractions. The primary requirement for subtracting fractions is to have a common denominator. The current denominators are 8 and 48. Since 48 is a multiple of 8 (specifically, \(8 \times 6 = 48\)), we can use 48 as the common denominator for both fractions.
Now, we convert \(\frac{7}{8}\) into an equivalent fraction with a denominator of 48. Multiplying the numerator and the denominator by 6, we get:
\[\frac{7}{8} = \frac{7 \times 6}{8 \times 6} = \frac{42}{48}\]
Now that both fractions share the same denominator, we can proceed with the subtraction:
\[\frac{42}{48} - \frac{13}{48} = \frac{42 - 13}{48}\]
Performing the subtraction in the numerator, we find:
\[42 - 13 = 29\]
So the resulting fraction is \(\frac{29}{48}\).
Finally, we check if the fraction \(\frac{29}{48}\) can be simplified further. We examine if 29 and 48 share any common factors other than 1. Since 29 is a prime number and does not divide 48 (because \(29 \times 1 = 29\) and \(29 \times 2 = 58\)), the fraction is already in its simplest form. Thus, the result is \(\frac{29}{48}\).
Understanding how to subtract fractions is essential for daily tasks like measuring ingredients for a recipe or managing time. For instance, if you have a recipe that requires \(\frac{7}{8}\) of a cup of flour, but you accidentally spill \(\frac{13}{48}\) of a cup, you need to subtract these amounts to know how much flour you have remaining. Performing this subtraction using a common denominator ensures that you can measure your ingredients accurately and follow the recipe correctly.