What is the quotient of 2/3 divided by 4 in simples form

What is the quotient of 2/3 divided by 4 in simples form

The Correct Answer and Explanation is:

To find the quotient of (\frac{2}{3}) divided by (4), we can follow these steps:

Step 1: Set Up the Division

Dividing a fraction by a whole number can be expressed as:

[
\frac{2}{3} \div 4
]

Step 2: Convert the Whole Number to a Fraction

To perform the division, we can convert the whole number (4) into a fraction. Any whole number (n) can be expressed as (\frac{n}{1}). Therefore, we have:

[
4 = \frac{4}{1}
]

Step 3: Rewrite the Division as Multiplication

Now, we can rewrite the division of fractions as multiplication by the reciprocal of the divisor. The reciprocal of (\frac{4}{1}) is (\frac{1}{4}). Thus, the equation becomes:

[
\frac{2}{3} \div \frac{4}{1} = \frac{2}{3} \times \frac{1}{4}
]

Step 4: Multiply the Fractions

To multiply fractions, we multiply the numerators together and the denominators together:

[
\frac{2 \times 1}{3 \times 4} = \frac{2}{12}
]

Step 5: Simplify the Result

Next, we simplify (\frac{2}{12}) by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of (2) and (12) is (2). We can divide both the numerator and the denominator by (2):

[
\frac{2 \div 2}{12 \div 2} = \frac{1}{6}
]

Conclusion

Thus, the quotient of (\frac{2}{3}) divided by (4) in simplest form is:

[
\frac{1}{6}
]

Explanation

This method demonstrates the fundamental principles of dividing fractions and highlights the importance of understanding reciprocals in fraction operations. By expressing a whole number as a fraction and applying the rule for dividing fractions (multiplying by the reciprocal), we maintain the clarity of the operation. Simplifying fractions by identifying and dividing by their GCD ensures the result is in its simplest form, making it easier to interpret and use in further calculations. Overall, this process exemplifies the straightforward nature of fraction arithmetic when executed step by step.