Write the product in the simplest form 3×1/6
The Correct Answer and Explanation is:
To multiply the expression (3 \times \frac{1}{6}), we follow the basic rules of multiplying a whole number by a fraction.
Step 1: Understanding the Multiplication of a Whole Number and a Fraction
When multiplying a whole number by a fraction, we can express the whole number as a fraction itself. The number 3 can be written as (\frac{3}{1}). Therefore, we rewrite the expression as follows:
[
3 \times \frac{1}{6} = \frac{3}{1} \times \frac{1}{6}
]
Step 2: Applying the Rule of Multiplying Fractions
To multiply fractions, we multiply the numerators together and the denominators together:
[
\text{Numerator: } 3 \times 1 = 3
]
[
\text{Denominator: } 1 \times 6 = 6
]
Putting these together, we have:
[
\frac{3 \times 1}{1 \times 6} = \frac{3}{6}
]
Step 3: Simplifying the Fraction
Now we need to simplify the fraction (\frac{3}{6}). To simplify, we look for the greatest common divisor (GCD) of the numerator (3) and the denominator (6). The GCD of 3 and 6 is 3. We divide both the numerator and the denominator by their GCD:
[
\frac{3 \div 3}{6 \div 3} = \frac{1}{2}
]
Final Answer
Thus, the product of (3 \times \frac{1}{6}) in its simplest form is
[
\boxed{\frac{1}{2}}
]
Explanation Recap
In summary, the process of multiplying a whole number by a fraction involves converting the whole number to a fraction, multiplying the numerators and denominators, and then simplifying the resulting fraction. This method is straightforward and relies on basic principles of arithmetic and fractions, ensuring that we achieve the correct result efficiently. The final answer, (\frac{1}{2}), represents the simplest form of the product.