In this section, we’ll look at some real-world problems, which involve adding and subtracting fractions. When solving real-world problems, it’s important to first define terms. What information does the problem give us? What information does the problem ask us to find out? Once we know where we are and where we want to go, we can figure out how to get there.

Example

Benito works in a bakery and has baked the world’s longest loaf of cinnamon bread. His loaf measures feet. He cuts a piece that measures feet long, and gives it to his friend Pamela. He then cuts another piece feet long for his friend Serena. How much bread does he have left?

Let’s take careful inventory of the information that the problem gives us. We know that the whole loaf of bread is feet long. Pamela gets a piece feet long, that is her piece and Serena gets a piece feet long. This is the given information.

What do we want to find out? We want to know the length of the bread after he cuts Pamela and Serena’s pieces (loaf after cutting ). Let’s write an equation to show the relationship between the values:

Whole loaf – Pamela’s piece – Serena’s piece = loaf after cutting

When we substitute the given values, we have the following equation.

Now, we simply solve from left to right. First, find a common denominator between the fractions in and . Let’s use 8, so we solve .

Next, we can simplify the problem.

The lowest common denominator for the fractions is going to be 24. We simplify the problem further.

I can already see that I will have to convert the mixed numbers to improper fractions. Simplify again.

Next, we just convert the answer to a mixed number and write in simplest terms.

Solution: feet or about feet

Now let’s go back to the introduction problem and help Jesse with his peach problem.

Real Life Example Completed

Plenty of Peaches

Here is the original problem once again. Read it and underline any important information.

Jesse has decided to make peach pie for...