Write 10 3/7 as an improper fraction?
The Correct Answer and Explanation is:
To convert the mixed number (10 \frac{3}{7}) into an improper fraction, follow these steps:
Step 1: Understand the Components
A mixed number consists of a whole number and a proper fraction. In this case:
- The whole number is 10.
- The proper fraction is (\frac{3}{7}).
Step 2: Convert the Whole Number
To convert the whole number into a fraction, we multiply it by the denominator of the proper fraction. The denominator in this case is 7. Thus, we calculate:
[
10 \times 7 = 70
]
Step 3: Add the Numerator of the Proper Fraction
Next, we add the numerator of the proper fraction to the product from the previous step. The numerator is 3. Therefore, we add:
[
70 + 3 = 73
]
Step 4: Form the Improper Fraction
Now that we have the new numerator, we place it over the original denominator, which remains 7. Thus, the improper fraction is:
[
\frac{73}{7}
]
Conclusion
The improper fraction for the mixed number (10 \frac{3}{7}) is (\frac{73}{7}).
Explanation
Improper fractions are essential in mathematics because they provide a convenient way to perform calculations. An improper fraction has a numerator that is greater than or equal to its denominator, allowing for straightforward addition, subtraction, multiplication, and division.
In this example, converting (10 \frac{3}{7}) into (\frac{73}{7}) simplifies operations involving this number, particularly when adding or subtracting with other fractions or improper fractions. Understanding this conversion process is crucial for students as they progress in their mathematical education. It lays the groundwork for more complex topics, such as algebra and calculus, where manipulating fractions efficiently becomes increasingly important.
By recognizing how to convert mixed numbers to improper fractions, learners can enhance their problem-solving skills and tackle a broader range of mathematical challenges.