What is 24/10 in simplest form
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{24}{10} ), we need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD).
Step 1: Find the GCD
The GCD of two numbers is the largest number that can divide both without leaving a remainder. For the numbers 24 and 10, we can determine the GCD as follows:
- Factors of 24: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- Factors of 10: The factors of 10 are 1, 2, 5, and 10.
The common factors of 24 and 10 are 1 and 2. Therefore, the GCD is 2.
Step 2: Divide the Numerator and Denominator by the GCD
Now, we can simplify ( \frac{24}{10} ) by dividing both the numerator and the denominator by the GCD:
[
\frac{24 \div 2}{10 \div 2} = \frac{12}{5}
]
Step 3: Final Result
The fraction ( \frac{24}{10} ) in simplest form is ( \frac{12}{5} ).
Understanding the Simplification Process
Simplifying fractions is an essential skill in mathematics, as it allows for easier calculations and clearer communication of numerical relationships. A simplified fraction expresses the same value as the original fraction but in a more straightforward way.
In real-world applications, simplified fractions can be easier to work with. For instance, when dealing with measurements in cooking or construction, using simpler fractions can lead to less confusion and more accurate results. Additionally, understanding how to find the GCD helps develop number sense and enhances overall mathematical reasoning.
In summary, to simplify ( \frac{24}{10} ), we found the GCD, divided both the numerator and the denominator by that GCD, resulting in ( \frac{12}{5} ), which is the simplest form of the original fraction.