What is the simplest form of 1/6 divided by 2
The Correct Answer and Explanation is :
To simplify ( \frac{1}{6} \div 2 ), we first need to understand the operation of division with fractions. When dividing a fraction by a whole number, we can convert the whole number into a fraction.
In this case, we can express 2 as a fraction:
[
2 = \frac{2}{1}
]
Now we rewrite the division of fractions as a multiplication of the first fraction by the reciprocal of the second fraction:
[
\frac{1}{6} \div 2 = \frac{1}{6} \times \frac{1}{2}
]
Next, we multiply the numerators together and the denominators together:
[
\frac{1 \times 1}{6 \times 2} = \frac{1}{12}
]
Thus, the simplest form of ( \frac{1}{6} \div 2 ) is ( \frac{1}{12} ).
Explanation
- Understanding Fractions and Division: A fraction represents a part of a whole. The division of fractions can be thought of as asking how many times the divisor (in this case, 2) fits into the dividend (which is ( \frac{1}{6} )). Instead of directly dividing, we multiply by the reciprocal.
- Reciprocal: The reciprocal of a fraction is obtained by swapping its numerator and denominator. For a whole number, like 2, its reciprocal is ( \frac{1}{2} ).
- Multiplication of Fractions: When multiplying fractions, the operation is straightforward. You simply multiply the numerators together and the denominators together, which allows us to find the product directly.
- Final Result: After performing the multiplication, we arrive at the simplified fraction ( \frac{1}{12} ). This result indicates that if you have one-sixth of something and you want to divide it into two equal parts, each part will be one-twelfth of the whole.
In summary, dividing a fraction by a whole number involves converting the whole number into a fraction and then using multiplication with its reciprocal, leading to a simplified result of ( \frac{1}{12} ).