Perform the indicated operation. Simplify if possible.
$\frac{4}{m}+5$
$\frac{4}{m}+5=$ $\square$ (Simplify your answer.)
Answer (1)
Rewrite the whole number 5 as a fraction with denominator m: 5 = m 5 m .
Add the two fractions: m 4 + m 5 m .
Combine the numerators over the common denominator: m 4 + 5 m .
The simplified expression is: m 4 + 5 m .
Explanation
Understanding the Problem We are asked to add a fraction and a whole number. The expression is m 4 + 5 . Our goal is to simplify this expression into a single fraction.
Rewriting the Whole Number as a Fraction To add a fraction and a whole number, we need to rewrite the whole number as a fraction with the same denominator as the given fraction. In this case, we want to express 5 as a fraction with denominator m . We can do this by multiplying 5 by m m , which is equal to 1, so it doesn't change the value of 5: 5 = 5 × m m = m 5 m
Adding the Fractions Now we can add the two fractions: m 4 + 5 = m 4 + m 5 m Since the fractions have the same denominator, we can add the numerators: m 4 + m 5 m = m 4 + 5 m
Final Answer The expression m 4 + 5 m is now simplified, as there are no common factors between the numerator and the denominator.
Examples
Understanding how to add fractions and whole numbers is useful in many everyday situations. For example, if you are baking a cake and a recipe calls for 2 1 cup of flour, but you want to make 5 cakes, you need to calculate 5 + 2 1 . By rewriting 5 as 2 10 , you can easily add the fractions: 2 10 + 2 1 = 2 11 cups of flour. This skill is also useful in managing time, distances, and quantities in various real-life scenarios.
