# Life’s Fractional Challenges: How to Solve Word Problems on Adding and Subtracting Fractions with Different Denominators

Everyday scenarios often involve fractions, and sometimes, these fractions have different denominators. Whether it's splitting a dessert, allocating time for activities, or measuring ingredients, understanding how to add and subtract these fractions is crucial. In this post, we’ll tackle real-life word problems that involve adding and subtracting fractions with different denominators, guiding you through each solution.

## Step-by-step Guide:

1. Decoding the Problem:

Begin by reading the word problem thoroughly. Identify the fractions involved and their respective denominators.

2. Visualizing the Scenario:

Imagine the situation described in the problem. This visualization aids in understanding the problem and determining the required operation.

3. Determining the Least Common Denominator (LCD):

Identify the smallest number into which all the denominators can divide. This LCD ensures that the fractions are comparable.

4. Adjusting the Fractions to the LCD:

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

5. Performing the Operation:

Depending on the problem, either add or subtract the numerators of the fractions to get the final answer.

### Example 1:

Jenny baked a cake and ate $$\frac{1}{4}$$ of it on Monday. On Tuesday, she ate another $$\frac{1}{6}$$ of the cake. How much of the cake is left?

Solution:

First, find the total fraction of the cake Jenny ate: $$\frac{1}{4} + \frac{1}{6}$$. The LCD is 12. Adjusting the fractions:

– $$\frac{1}{4}$$ becomes $$\frac{3}{12}$$.

– $$\frac{1}{6}$$ becomes $$\frac{2}{12}$$.

Jenny ate $$\frac{5}{12}$$ of the cake in total. Therefore, $$\frac{7}{12}$$ of the cake is left.

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### Example 2:

Sam ran $$\frac{1}{3}$$ of a marathon on the first day and $$\frac{1}{4}$$ on the second day. How much of the marathon is still left for him to run?

Solution:

First, find the total fraction of the marathon Sam ran: $$\frac{1}{3} + \frac{1}{4}$$. The LCD is 12. Adjusting the fractions:

– $$\frac{1}{3}$$ becomes $$\frac{4}{12}$$.

– $$\frac{1}{4}$$ becomes $$\frac{3}{12}$$.

Sam ran $$\frac{7}{12}$$ of the marathon in total. Therefore, $$\frac{5}{12}$$ of the marathon is still left.

### Practice Questions:

1. Lisa drank $$\frac{1}{5}$$ of a juice bottle in the morning and $$\frac{1}{10}$$ in the evening. How much juice is left in the bottle?

2. During a school trip, students spent $$\frac{2}{7}$$ of the day at the zoo and $$\frac{1}{14}$$ at the amusement park. How much of the day was spent on other activities?

3. Mike read $$\frac{3}{8}$$ of a book on Monday and $$\frac{1}{4}$$ on Tuesday. How much of the book has he not read yet?

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1. $$\frac{7}{10}$$

2. $$\frac{5}{14}$$

3. $$\frac{3}{8}$$

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