Find an equivalent fraction of the following 1-8 with denominator 24
The Correct Answer and Explanation is:
To find an equivalent fraction for a given fraction with a denominator of 24, we start with the fraction ( \frac{1}{8} ) and find a way to express it in terms of the new denominator.
Step-by-Step Process
- Understand Equivalent Fractions: Equivalent fractions are fractions that represent the same value or proportion of a whole, even though their numerators and denominators are different. For instance, ( \frac{1}{2} ) and ( \frac{2}{4} ) are equivalent because they both represent the same part of a whole.
- Identify the New Denominator: In this case, we want the denominator to be 24. We need to find a way to convert ( \frac{1}{8} ) into a fraction with 24 as the denominator.
- Finding the Conversion Factor: To determine the conversion factor, we divide the new denominator by the original denominator:
[
\text{Conversion Factor} = \frac{24}{8} = 3
] - Multiply the Numerator and Denominator: To maintain the equality of the fraction, we multiply both the numerator and the denominator of ( \frac{1}{8} ) by this conversion factor (3):
[
\frac{1 \times 3}{8 \times 3} = \frac{3}{24}
] - Verification: To verify that ( \frac{3}{24} ) is indeed equivalent to ( \frac{1}{8} ), we can simplify ( \frac{3}{24} ):
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[
\frac{3 \div 3}{24 \div 3} = \frac{1}{8}
]
This confirms that both fractions are equivalent.
Conclusion
Thus, an equivalent fraction of ( \frac{1}{8} ) with a denominator of 24 is ( \frac{3}{24} ). This process of finding equivalent fractions is essential in mathematics, especially when adding, subtracting, or comparing fractions, as having a common denominator allows for easier calculation. Understanding the relationship between numerators and denominators ensures that we can manipulate fractions correctly while preserving their values.