Which fraction is equivalent to 1/6?
The Correct Answer and Explanation is :
To find fractions equivalent to ( \frac{1}{6} ), we can use the concept of equivalent fractions, which involves multiplying both the numerator and the denominator of a fraction by the same non-zero number. This preserves the value of the fraction, even though its appearance changes.
Basic Concept of Equivalent Fractions:
An equivalent fraction is one that represents the same quantity as another fraction, even if the numbers look different. To create an equivalent fraction, both the numerator (the top number) and the denominator (the bottom number) are multiplied by the same number, which is often called the “multiplying factor.” This ensures that the ratio between the numerator and denominator remains unchanged.
For example, if we want to find fractions equivalent to ( \frac{1}{6} ), we can multiply both the numerator and the denominator by the same number, such as 2, 3, or 4.
Steps to Find Equivalent Fractions:
- Multiply by 2:
[
\frac{1}{6} \times \frac{2}{2} = \frac{2}{12}
]
This gives the fraction ( \frac{2}{12} ), which is equivalent to ( \frac{1}{6} ). - Multiply by 3:
[
\frac{1}{6} \times \frac{3}{3} = \frac{3}{18}
]
So, ( \frac{3}{18} ) is another equivalent fraction to ( \frac{1}{6} ). - Multiply by 4:
[
\frac{1}{6} \times \frac{4}{4} = \frac{4}{24}
]
Hence, ( \frac{4}{24} ) is also an equivalent fraction. - Generalization:
The principle of finding equivalent fractions applies universally. You can multiply both the numerator and the denominator by any non-zero integer, and the result will be an equivalent fraction.
Why Do Equivalent Fractions Work?
Equivalent fractions work because they represent the same proportion or ratio of the numerator to the denominator. For example, ( \frac{1}{6} ) and ( \frac{2}{12} ) both represent the same part of a whole: one-sixth. When you scale both the numerator and denominator by the same factor, you are essentially dividing the same total into more parts but keeping the proportion the same.
Conclusion:
Therefore, fractions like ( \frac{2}{12}, \frac{3}{18}, \frac{4}{24} ), and others are all equivalent to ( \frac{1}{6} ), because they represent the same ratio or proportion.