10/45 simplified

less than a minute read 19-10-2024

Simplifying Fractions: Understanding 10/45

Fractions represent parts of a whole. Simplifying a fraction means finding an equivalent fraction with smaller numbers, making it easier to understand and compare. Let's delve into how to simplify the fraction 10/45.

Finding the Greatest Common Factor (GCD)

The key to simplifying fractions is finding the Greatest Common Factor (GCD) of the numerator and denominator. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder.

Here's how to find the GCD of 10 and 45:

List the factors of each number:
- Factors of 10: 1, 2, 5, 10
- Factors of 45: 1, 3, 5, 9, 15, 45
Identify the common factors:
- Common factors of 10 and 45: 1, 5
The greatest common factor is 5.

Simplifying 10/45

Divide both the numerator and denominator by the GCD (5):
- 10 ÷ 5 = 2
- 45 ÷ 5 = 9
The simplified fraction is 2/9.

Why is this important?

Simplifying fractions helps us in many ways:

Easier to understand: 2/9 is easier to visualize and grasp than 10/45.
Comparison: Comparing 2/9 to other fractions becomes simpler.
Calculations: Simplifying before performing calculations can often make the process easier.

Practical Application

Imagine you have a pizza cut into 45 slices. You have 10 slices, represented by the fraction 10/45. Simplifying this fraction to 2/9 tells you that you have 2 out of every 9 slices of the pizza.

Conclusion

Simplifying fractions is an essential skill in mathematics. By finding the greatest common factor and dividing both the numerator and denominator by it, we can reduce fractions to their simplest form. This makes fractions easier to understand, compare, and work with.