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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Answers:
1. \(\frac{7}{10}\)
2. \(\frac{5}{14}\)
3. \(\frac{3}{8}\)
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