The fraction 24/28 in simplest form is _.
The Correct Answer and Explanation is :
The fraction ( \frac{24}{28} ) in simplest form is ( \frac{6}{7} ).
Explanation
To simplify a fraction, we divide the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). In this case, we start by finding the GCD of 24 and 28.
Step 1: Find the GCD of 24 and 28
- First, list the factors of each number:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 28: 1, 2, 4, 7, 14, 28
- The largest common factor between 24 and 28 is 4.
Thus, the GCD of 24 and 28 is 4.
Step 2: Divide by the GCD
Now that we know the GCD is 4, we can divide both the numerator and the denominator of ( \frac{24}{28} ) by 4:
[
\frac{24 \div 4}{28 \div 4} = \frac{6}{7}
]
Step 3: Verify that ( \frac{6}{7} ) is in Simplest Form
To ensure that ( \frac{6}{7} ) is the simplest form, check that 6 and 7 have no common factors other than 1, which they don’t. Therefore, ( \frac{6}{7} ) is indeed the fraction in simplest form.
Why Simplifying Fractions Matters
Simplifying fractions is essential for a few reasons:
- Ease of Understanding: A simplified fraction, like ( \frac{6}{7} ), is easier to interpret and compare with other fractions.
- Consistency: Simplified forms are standard in mathematics, so using the simplest version allows for consistent communication.
- Application in Calculations: Simplified fractions make arithmetic operations more straightforward, reducing the risk of errors in complex calculations.
In conclusion, simplifying ( \frac{24}{28} ) to ( \frac{6}{7} ) demonstrates a basic mathematical process that is useful across many areas, ensuring clarity and efficiency in working with fractions.