How to Solve Real-Life Puzzles: Word Problems on Adding and Subtracting Fractions with Like Denominators

In this post, we’ll work through some word problems that revolve around adding and subtracting fractions with the same denominator, offering solutions and insights along the way.

Step-by-step Guide:

1. Understanding the Problem: 

Begin by reading the word problem carefully. Identify the fractions involved and ensure they have the same denominator.

2. Visualizing the Scenario: 

Imagine the situation described in the problem. This will help in understanding what’s being asked and how to approach the solution.

3. Performing the Operation: 

Depending on whether the problem asks for addition or subtraction, combine or take away the numerators of the fractions while keeping the denominator the same.

4. Simplifying the Answer: 

After performing the operation, always check if the resulting fraction can be simplified further.

Example 1: 

Lucy baked a pie and ate \(\frac{1}{4}\) of it on Monday. On Tuesday, she ate another \(\frac{1}{4}\). How much of the pie has Lucy eaten in total?

Solution: 

Lucy ate \(\frac{1}{4} + \frac{1}{4} = \frac{2}{4}\) of the pie, which simplifies to \(\frac{1}{2}\). Lucy has eaten half of the pie in total.

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Example 2: 

John has \(\frac{3}{5}\) of a chocolate bar. He gives \(\frac{2}{5}\) to his friend. How much of the chocolate bar does John have left?

Solution:

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John has \(\frac{3}{5} – \frac{2}{5} = \frac{1}{5}\) of the chocolate bar left.

Practice Questions: 

1. Emma read \(\frac{3}{8}\) of a book on Saturday and \(\frac{1}{8}\) on Sunday. How much of the book has she read in total?

2. Mike had \(\frac{5}{6}\) of a pizza. He ate \(\frac{2}{6}\) for dinner. How much pizza does he have left?

3. Sarah practiced piano for \(\frac{2}{7}\) hours on Monday and \(\frac{3}{7}\) hours on Tuesday. How many hours did she practice in total?

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Answers: 

1. \(\frac{4}{8}\) or \(\frac{1}{2}\)

2. \(\frac{3}{6}\) or \(\frac{1}{2}\)

3. \(\frac{5}{7}\) hours

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