Write in simplest form. 1/6 divided by 6 divided by 6
The Correct Answer and Explanation is:
To solve the expression ( \frac{1}{6} \div 6 \div 6 ), we need to follow the rules of division for fractions. Here are the steps:
Step 1: Understanding Division of Fractions
When dividing fractions, instead of dividing by a number, we multiply by its reciprocal. The reciprocal of a number is simply 1 divided by that number. For example, the reciprocal of 6 is ( \frac{1}{6} ).
The expression ( \frac{1}{6} \div 6 \div 6 ) can be rewritten step-by-step using the reciprocal rule of division.
Step 2: Rewrite the Expression
We start with:
[
\frac{1}{6} \div 6 \div 6
]
First, rewrite the first division as multiplication by the reciprocal:
[
\frac{1}{6} \div 6 = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
]
Now, we have:
[
\frac{1}{36} \div 6
]
Again, we apply the reciprocal rule:
[
\frac{1}{36} \div 6 = \frac{1}{36} \times \frac{1}{6} = \frac{1}{216}
]
Step 3: Final Answer
The final result of ( \frac{1}{6} \div 6 \div 6 ) is ( \frac{1}{216} ).
Step 4: Simplify the Answer
In this case, ( \frac{1}{216} ) is already in its simplest form. We cannot simplify it any further because the numerator is 1 and the denominator, 216, is not divisible by 1 (except for itself).
Conclusion
The expression ( \frac{1}{6} \div 6 \div 6 ) simplifies to ( \frac{1}{216} ). The key to solving this problem is recognizing that division by a number is the same as multiplying by its reciprocal, and applying this rule step by step.