3/4 divided by 12 as a fraction
The Correct Answer and Explanation is :
The fraction (\frac{3}{4}) divided by 12 can be solved as follows:
[
\frac{3}{4} \div 12
]
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 12 is (\frac{1}{12}). So, we can rewrite the expression as:
[
\frac{3}{4} \times \frac{1}{12}
]
Now, multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{3 \times 1}{4 \times 12} = \frac{3}{48}
]
Next, simplify (\frac{3}{48}) by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[
\frac{3 \div 3}{48 \div 3} = \frac{1}{16}
]
So, (\frac{3}{4} \div 12 = \frac{1}{16}).
Explanation:
Dividing fractions or whole numbers involves understanding the relationship between division and multiplication. When you divide by a number, you can instead multiply by its reciprocal, which is simply flipping the numerator and denominator of that number (or turning a whole number like 12 into the fraction (\frac{1}{12})).
In this case, (\frac{3}{4}) is the fraction being divided by 12. Since dividing by 12 is the same as multiplying by (\frac{1}{12}), we convert the division into a multiplication problem. Multiplying fractions is straightforward: you multiply across the numerators and across the denominators.
Finally, we simplify the resulting fraction (\frac{3}{48}). The greatest common divisor of 3 and 48 is 3, so we divide both by 3 to get (\frac{1}{16}).
This solution highlights how fraction division and multiplication are closely related and how simplifying the final fraction leads to the correct and simplest answer.