Understanding and Solving Fractional Problems in Mathematics

Introduction

Fractions are fundamental to mathematics and often appear in real-life scenarios, such as comparing or measuring lengths. In this article, we will explore a specific example involving fractions, specifically a problem about cutting a ribbon. We'll break down the steps and strategy to solve this problem accurately. This will help you understand how to approach and solve similar problems on your own.

Problem Statement

The question here is: If you cut three-fifths of a meter of ribbon from a piece that is three-quarters of a meter long, what fraction of the ribbon is left? Let's solve this step-by-step to ensure clarity.

Step-by-Step Solution

Let's consider the length of the original piece of ribbon:

Total length of ribbon 3/4 meters. Length of ribbon cut 3/5 meters. Length of ribbon left ?

Step 1: Convert Fractions to a Common Denominator

Before we can subtract these fractions, we need to convert them to a common denominator. The least common multiple of 4 and 5 is 20.

(frac{3}{4} frac{3 times 5}{4 times 5} frac{15}{20}) (frac{3}{5} frac{3 times 4}{5 times 4} frac{12}{20})

Step 2: Subtract the Amount Cut from the Original Length

Now we subtract the fraction of the ribbon that was cut from the original length:

(frac{15}{20} - frac{12}{20} frac{15 - 12}{20} frac{3}{20})

So, the fraction of the ribbon that was left is (frac{3}{20}).

Conclusion

Therefore, the fraction of the ribbon left after cutting three-fifths of a meter from a piece that is three-quarters of a meter long is (frac{3}{20}) meters.

Alternative Solution

Another way to approach the problem is to directly consider the fractions involved:

Original piece of ribbon: (frac{3}{4}) meters. Piece cut: (frac{3}{5}) meters. Remaining piece: (frac{3}{4} - frac{3}{5}).

Repeating the steps as described earlier:

(frac{15}{20} - frac{12}{20} frac{15 - 12}{20} frac{3}{20})

Thus, the fraction of the ribbon that remains is (frac{3}{20}).

Conclusion

It's important to note that the problem specifically asks for the fraction left, rather than the remaining length. Hence, the answer is that two-fifths of the ribbon remains.

Alternative Calculation

If we consider the length of the remaining ribbon:

Total length 0.75 meters. Length cut 0.60 meters. Length left 0.15 meters.

This can be expressed as a fraction as well:

(frac{0.15}{0.75} frac{15}{75} frac{1}{5})

Key Takeaways

Fraction subtraction is a crucial skill that helps in solving real and abstract mathematical problems. When dealing with fractions, the key is to find a common denominator to simplify the subtraction process. Understanding the problem and identifying what is being asked is essential for correct answers.

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If you have any further questions or need assistance with similar problems, feel free to explore more examples and exercises. Understanding these concepts will enhance your problem-solving skills in mathematics.