Divide 3/4 divided by 6
The Correct Answer and Explanation is :
The correct answer is: (\frac{1}{8})
To divide (\frac{3}{4}) by (6), you can rewrite the problem using the concept of multiplication by the reciprocal. Dividing by a number is equivalent to multiplying by its reciprocal. The reciprocal of (6) is (\frac{1}{6}). Thus, the operation can be expressed as:
[
\frac{3}{4} \div 6 = \frac{3}{4} \times \frac{1}{6}
]
Next, you multiply the fractions:
[
\frac{3}{4} \times \frac{1}{6} = \frac{3 \times 1}{4 \times 6} = \frac{3}{24}
]
Now, simplify (\frac{3}{24}). Both the numerator and the denominator can be divided by (3):
[
\frac{3 \div 3}{24 \div 3} = \frac{1}{8}
]
Thus, the final answer is:
[
\frac{3}{4} \div 6 = \frac{1}{8}
]
Explanation:
Dividing fractions may seem challenging at first, but once you understand the method of using reciprocals, it becomes straightforward. In this case, dividing (\frac{3}{4}) by (6) required the transformation of the division into multiplication.
The reciprocal is simply the fraction flipped upside down, which is a fundamental property of fractions. When multiplying fractions, you multiply the numerators together and the denominators together. This method applies regardless of the size of the numbers involved.
After multiplying, you arrive at (\frac{3}{24}). Simplifying this fraction is crucial for presenting the answer in its most reduced form. To simplify, you find the greatest common divisor (GCD) of the numerator and denominator. For (3) and (24), the GCD is (3), which allows you to reduce the fraction easily.
The final result, (\frac{1}{8}), is a simple fraction that reflects the relationship between (\frac{3}{4}) and (6). Understanding these concepts is vital in mathematics, as they form the foundation for more complex operations involving fractions and division.