Mixed Numbers Addition and Subtraction Word Problems

A Step-By-Step Guide to Solving Mixed Numbers Addition and Subtraction Word Problems

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Whether you're in school or in the real world, the ability to solve word problems involving mixed numbers is a handy tool to have in your mathematical arsenal. In this article, we'll take a step-by-step look at how to solve addition and subtraction word problems involving mixed numbers.

Step 1: Understand the Problem

The first step in any word problem is to understand what the problem is asking. Read the problem carefully. Make sure you understand what you need to find, what you already know, and what the mixed numbers in the problem represent.

For example:

"James baked \(5 \frac{1}{2}\) pies for a party. He baked an additional \(1 \frac{1}{4}\) pies. How many pies did he bake in total?"

Here, we know that James initially baked \(5 \frac{1}{2}\) pies and then baked \(1 \frac{1}{4}\) pies more. The problem asks for the total number of pies baked.

Step 2: Plan your Approach

Once you understand the problem, plan your approach. For an addition problem like our example, you need to add the mixed numbers together. For a subtraction problem, you would subtract one mixed number from another.

Step 3: Convert Mixed Numbers into Improper Fractions

Before you can add or subtract mixed numbers, it's often easiest to convert them into improper fractions.

Remember that a mixed number is made up of a whole number and a fraction. To convert it into an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. The result is the numerator of the improper fraction, with the same denominator as the original fraction.

Using the example problem, we convert \(5 \frac{1}{2}\) to \(\frac{11}{2}\) and \(1 \frac{1}{4}\) to \(\frac{5}{4}\).

Step 4: Find a Common Denominator

Addition and subtraction of fractions require a common denominator. To find one, you can simply multiply the two denominators together, but it's usually better to find the least common denominator to simplify your calculations.

For our example, the denominators are 2 and 4. The least common denominator is 4.

Step 5: Add or Subtract the Fractions

Once you have common denominators, you can add or subtract the numerators. The denominator remains the same.

In our example, we adjust our fractions to have the common denominator (\(\frac{11}{2}\) becomes \(\frac{22}{4}\) and \(\frac{5}{4}\) stays as it is) and then add the fractions to get \(\frac{27}{4}\).

Step 6: Convert Back to a Mixed Number

After performing the operation, convert your answer back to a mixed number, if necessary, by dividing the numerator by the denominator.

So, \(\frac{27}{4}\) becomes \(6 \frac{3}{4}\).

Step 7: Interpret the Answer

Finally, answer the problem's question with your result. In our example, "James baked \(6 \frac{3}{4}\) pies in total."

Through these steps, we can demystify the process of solving word problems involving addition and subtraction of mixed numbers. Like any skill, practice is key - so keep solving problems, and you'll be a pro before you know it!

Exercises 

1) Jackson read \(3 \frac{1}{2}\) books last week and \(2 \frac{3}{4}\) books this week. How many books did he read in total?

2) A carpenter used \(5 \frac{1}{4}\) feet of wood for one project and \(3 \frac{2}{3}\) feet for another. How much wood did he use in total?

3) Julia baked \(4 \frac{1}{2}\) pies for a party. After the party, there were \(1 \frac{3}{4}\) pies left. How many pies were eaten at the party?

4) Mike ran \(7 \frac{3}{4}\) miles on Monday and \(5 \frac{1}{2}\) miles on Tuesday. How many miles did he run in total?

5) A recipe requires \(3 \frac{1}{2}\) cups of flour and \(2 \frac{1}{4}\) cups of sugar. How many cups of these ingredients are needed in total?

6) A seamstress used \(6 \frac{1}{3}\) yards of fabric for a dress and \(4 \frac{2}{3}\) yards for a skirt. How much fabric did she use in total?

7) A shop sold \(8 \frac{1}{2}\) pounds of apples in the morning and \(4 \frac{3}{4}\) pounds in the afternoon. How many pounds of apples were sold in total?

8) A painter used \(7 \frac{1}{4}\) gallons of paint for the living room and \(3 \frac{1}{2}\) gallons for the bedroom. How much paint did he use in total?

9) A hiker walked \(9 \frac{2}{3}\) miles in the morning and \(5 \frac{3}{4}\) miles in the afternoon. How far did he walk in total?

10) A factory produced \(10 \frac{1}{4}\) tons of goods in January and \(7 \frac{2}{3}\) tons in February. How much did it produce in total?