Simplifying Fractions: A Step-by-Step Guide
When it comes to simplifying fractions, it’s essential to understand the concept of dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, we’re going to simplify the fraction 411 divided by 10.
Step 1: Identify the Numerator and Denominator
In the fraction 411⁄10, 411 is the numerator, and 10 is the denominator.
Step 2: Find the Greatest Common Divisor (GCD)
To simplify the fraction, we need to find the GCD of 411 and 10. The GCD is the largest number that divides both numbers without leaving a remainder.
| Factors of 411 | Factors of 10 |
|---|---|
| 1, 3, 137, 411 | 1, 2, 5, 10 |
As we can see, the only common factor is 1, which means the GCD of 411 and 10 is 1.
Step 3: Simplify the Fraction
Since the GCD is 1, we cannot simplify the fraction further by dividing both the numerator and denominator by their GCD. However, we can still express the fraction as a decimal or mixed number.
Converting the Fraction to a Decimal
To convert the fraction to a decimal, we divide the numerator by the denominator:
411 ÷ 10 = 41.1
Converting the Fraction to a Mixed Number
To convert the fraction to a mixed number, we divide the numerator by the denominator and express the remainder as a fraction:
411 ÷ 10 = 41 remainder 1
So, the mixed number is 41 1⁄10.
Conclusion
In this example, we learned how to simplify the fraction 411 divided by 10. We found the GCD of the numerator and denominator, which was 1, and then converted the fraction to a decimal and mixed number.
📝 Note: When simplifying fractions, it's essential to check if the GCD is greater than 1 to ensure the fraction is in its simplest form.
What is the greatest common divisor (GCD) of 411 and 10?
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The GCD of 411 and 10 is 1.
How do you simplify a fraction?
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To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
What is the decimal equivalent of the fraction 411⁄10?
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The decimal equivalent of the fraction 411⁄10 is 41.1.
