4.10 Introduction and Key Insights

Adding and subtracting fractions and mixed numbers comes up in a variety of real-world applications. Let's return to your aunt's coffee shop. Your aunt has placed some online ads to reach even more customers, and several of the ads include coupons. One fine Saturday morning, one of your regular patrons presents two coupons. One reads, "half off". The second reads, "one-third off".

Assuming your aunt allows her customers to combine the coupons, how much of a reduction will they enjoy? Try to see if you can figure this out! (You can highlight below to see an answer.)

We need to add $\frac{1}{2}$ and $\frac{1}{3}$, which first requires a common denominator. We can write:

$\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$

Our frugal customer only has to pay one-sixth of the original price after you take off five-sixths!

One last thought about our coupon-combining diner: if their total bill was $30.36, how much do they owe after they apply both coupons? The answer is in the next section, since this calculation requires multiplying fractions.