What is equivalent to 1/3 with a denominator of 6?
The Correct Answer and Explanation is:
To find a fraction equivalent to ( \frac{1}{3} ) with a denominator of 6, we need to determine what the numerator would be when the fraction is expressed with that specific denominator.
First, let’s recall the property of equivalent fractions: two fractions are equivalent if they represent the same part of a whole, which can be established by cross-multiplying or by ensuring that the ratio of the numerators to the denominators remains constant.
Starting with ( \frac{1}{3} ), we want to find an equivalent fraction with a denominator of 6. To do this, we can set up a proportion:
[
\frac{1}{3} = \frac{x}{6}
]
where ( x ) is the unknown numerator that we are trying to find. To solve for ( x ), we can cross-multiply:
[
1 \times 6 = 3 \times x
]
This simplifies to:
[
6 = 3x
]
Next, we solve for ( x ) by dividing both sides of the equation by 3:
[
x = \frac{6}{3} = 2
]
Thus, the equivalent fraction to ( \frac{1}{3} ) with a denominator of 6 is ( \frac{2}{6} ).
To confirm our result, we can simplify ( \frac{2}{6} ) back to see if it equals ( \frac{1}{3} ). We do this by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[
\frac{2 \div 2}{6 \div 2} = \frac{1}{3}
]
This verification shows that our calculation is correct. Therefore, the fraction ( \frac{2}{6} ) is indeed equivalent to ( \frac{1}{3} ).
In summary, the equivalent fraction of ( \frac{1}{3} ) with a denominator of 6 is ( \frac{2}{6} ). Understanding how to find equivalent fractions is crucial in various mathematical applications, such as adding fractions with different denominators or simplifying complex expressions.