Write 5/6 as an equivalent fraction with a denominator of 12.
The Correct Answer and Explanation is :
The correct answer is: ( \frac{10}{12} )
To convert the fraction ( \frac{5}{6} ) into an equivalent fraction with a denominator of 12, we need to find a fraction that represents the same value but has a denominator of 12 instead of 6.
Step 1: Understand Equivalent Fractions
Equivalent fractions are fractions that may look different but represent the same value or proportion of a whole. For instance, ( \frac{1}{2} ) and ( \frac{2}{4} ) are equivalent because they both represent half of a whole.
Step 2: Determine the Conversion
To find an equivalent fraction, we can use the following formula:
[
\text{Equivalent Fraction} = \frac{a \times n}{b \times n}
]
Where:
- ( \frac{a}{b} ) is the original fraction (in this case, ( \frac{5}{6} )),
- ( n ) is the number we multiply the numerator and denominator by to get the desired denominator.
Step 3: Identify the Multiplier
Here, our original denominator is 6, and we want to convert it to 12. We can find the multiplier by dividing the new denominator (12) by the original denominator (6):
[
n = \frac{12}{6} = 2
]
Step 4: Apply the Multiplier
Now that we have our multiplier, we can find the equivalent fraction:
[
\text{Numerator} = 5 \times 2 = 10
]
[
\text{Denominator} = 6 \times 2 = 12
]
Conclusion
Thus, ( \frac{5}{6} ) is equivalent to ( \frac{10}{12} ). To verify, we can simplify ( \frac{10}{12} ) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[
\frac{10 \div 2}{12 \div 2} = \frac{5}{6}
]
This confirms that ( \frac{10}{12} ) is indeed equivalent to ( \frac{5}{6} ), demonstrating that we have successfully converted the fraction to have a denominator of 12.