Divide and write in simplest form 5/6 divided by 3

Divide and write in simplest form 5/6 divided by 3

The Correct Answer and Explanation is:

To divide the fraction ( \frac{5}{6} ) by the whole number 3, we can follow these steps:

1. Convert the Whole Number to a Fraction: We start by converting the whole number 3 into a fraction. Any whole number can be expressed as a fraction by placing it over 1. Thus, 3 can be written as ( \frac{3}{1} ).
2. Set Up the Division of Fractions: When dividing fractions, we use the rule that states to divide by a fraction, you multiply by its reciprocal. Therefore, dividing ( \frac{5}{6} ) by ( \frac{3}{1} ) can be rewritten as multiplying by the reciprocal of ( \frac{3}{1} ), which is ( \frac{1}{3} ). This gives us:
   [
   \frac{5}{6} \div \frac{3}{1} = \frac{5}{6} \times \frac{1}{3}
   ]
3. Multiply the Numerators and Denominators: Now we multiply the numerators together and the denominators together:
   [
   \frac{5 \times 1}{6 \times 3} = \frac{5}{18}
   ]
4. Simplifying the Result: In this case, ( \frac{5}{18} ) is already in its simplest form because 5 and 18 have no common factors other than 1.

Explanation of the Steps

• Why Convert to a Fraction?: The reason we convert the whole number to a fraction is to make it easier to apply the rules of fraction division. This is particularly useful when dealing with mixed numbers or when whole numbers are involved.
• Understanding the Reciprocal: The reciprocal of a number is simply 1 divided by that number. For any fraction ( \frac{a}{b} ), its reciprocal is ( \frac{b}{a} ). This concept is critical in fraction operations, especially division.
• Multiplying Fractions: The process of multiplying fractions involves straightforward multiplication of the numerators and denominators. This is a fundamental property of fractions, and understanding it helps simplify various mathematical operations.
• Simplifying: Always check if the resulting fraction can be simplified. In this case, 5 is a prime number, and 18 is not divisible by 5, so the fraction remains ( \frac{5}{18} ).

Thus, the final answer to ( \frac{5}{6} \div 3 ) is:
[
\boxed{\frac{5}{18}}
]