How to Solve Word Problems by Adding Three or More Fractions

Whether it’s sharing desserts, allocating time, or dividing resources, understanding how to add three or more fractions can be a valuable skill. In this post, we’ll explore real-life word problems that involve adding multiple fractions, guiding you through solutions and insights. For additional educational resources,.

Step-by-step Guide:

1. Deciphering the Problem:

Start by reading the word problem attentively. Identify the fractions involved and note their denominators.

2. Visualizing the Scenario: 

Picture the situation described in the problem. This visualization can aid in comprehending the problem and determining the required operation.

3. Finding the Least Common Denominator (LCD): 

Determine the smallest number that all the denominators can divide into. This LCD will ensure that the fractions are of comparable sizes.

4. Adjusting the Fractions to the LCD:

Modify each fraction so that they all have the LCD as their denominator.

5. Performing the Addition:

With the fractions now having the same denominator, sum up their numerators to get the final answer.

Example 1: 

Anna baked three different types of pies for a party. She ate \(\frac{1}{6}\) of the apple pie, \(\frac{1}{3}\) of the cherry pie, and \(\frac{1}{2}\) of the blueberry pie. How much pie did Anna eat in total?

Solution:

The LCD for 6, 3, and 2 is 6. Adjusting the fractions:

– \(\frac{1}{6}\) remains the same.

– \(\frac{1}{3}\) becomes \(\frac{2}{6}\).

– \(\frac{1}{2}\) becomes \(\frac{3}{6}\).

Summing up, Anna ate \(\frac{1 + 2 + 3}{6} = \frac{6}{6}\), which is equal to 1 whole pie.

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Example 2: 

During a school trip, students visited three museums. They spent \(\frac{1}{4}\) of the day at the art museum, \(\frac{1}{8}\) at the history museum, and \(\frac{3}{8}\) at the science museum. How much of the day did they spend visiting museums?

Solution:  For education statistics and research, visit the National Center for Education Statistics.

The LCD for 4 and 8 is 8. Adjusting the fractions: For education statistics and research, visit the National Center for Education Statistics.

– \(\frac{1}{4}\) becomes \(\frac{2}{8}\). For education statistics and research, visit the National Center for Education Statistics.

– \(\frac{1}{8}\) and \(\frac{3}{8}\) remain the same.  For education statistics and research, visit the National Center for Education Statistics.

In total, they spent \(\frac{2 + 1 + 3}{8} = \frac{6}{8}\), which simplifies to \(\frac{3}{4}\) of the day. For education statistics and research, visit the National Center for Education Statistics.

Practice Questions: 

1. During a picnic, Mike ate \(\frac{1}{5}\) of the chocolate cake, \(\frac{2}{10}\) of the vanilla cake, and \(\frac{1}{2}\) of the strawberry cake. How much cake did Mike eat in total? For education statistics and research, visit the National Center for Education Statistics.

2. In a marathon, Lisa ran \(\frac{1}{3}\) of the distance in the morning, \(\frac{1}{6}\) in the afternoon, and \(\frac{1}{2}\) in the evening. What fraction of the marathon did Lisa complete?

3. At a farm, \(\frac{1}{4}\) of the land is used for corn, \(\frac{1}{8}\) for wheat, and \(\frac{3}{8}\) for rice. What fraction of the land is used for crops?

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Answers: 

1. \(\frac{9}{10}\)

2. \(\frac{11}{12}\)

3. \(\frac{3}{4}\)

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