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

To add or subtract fractions that already share a denominator in a word problem, work only with the numerators and leave the denominator alone, then simplify or convert to a mixed number if the question asks. Below: the method step by step, two worked problems, and practice questions.

To add or subtract fractions with the same denominator in a word problem, work with the numerators and keep the denominator unchanged, then check whether the answer should be simplified or written as a mixed number. The problems below apply that to real situations, each with a full worked solution.

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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