What is the quotient of 1/4 divided by 4
The Correct answer and Explanation is :
The correct answer is: {1}{16}
To find the quotient of ( \frac{1}{4} ) divided by ( 4 ), we can express the operation as follows:
[
\frac{1}{4} \div 4
]
Dividing by a whole number can be rewritten as multiplying by the reciprocal of that number. The reciprocal of ( 4 ) is ( \frac{1}{4} ). Therefore, we can convert the division into multiplication:
[
\frac{1}{4} \div 4 = \frac{1}{4} \times \frac{1}{4}
]
Now, we multiply the two fractions:
[
\frac{1 \times 1}{4 \times 4} = \frac{1}{16}
]
Thus, the quotient of ( \frac{1}{4} ) divided by ( 4 ) is ( \frac{1}{16} ).
Explanation:
When dividing fractions, it’s essential to understand the concept of reciprocals. A reciprocal of a number is simply ( \frac{1}{\text{number}} ). In this case, since we are dividing by ( 4 ), we take its reciprocal, which is ( \frac{1}{4} ). This means that instead of dividing ( \frac{1}{4} ) by ( 4 ), we are effectively scaling ( \frac{1}{4} ) by how much ( \frac{1}{4} ) of ( 4 ) is.
The multiplication of two fractions involves multiplying their numerators together and their denominators together. Here, we multiply ( 1 ) (from the first fraction) by ( 1 ) (from the second fraction), resulting in ( 1 ) as the new numerator. In the denominator, ( 4 \times 4 ) gives us ( 16 ). Therefore, the resulting fraction is ( \frac{1}{16} ).
In practical terms, if you have a whole (like a pie) and you want to divide it into ( 4 ) equal parts, each part is ( \frac{1}{4} ). Now, if you take ( 4 ) of those ( \frac{1}{4} ) pieces, you are taking one of those parts and dividing it into ( 4 ) more equal pieces. This gives you a much smaller piece, which can be represented as ( \frac{1}{16} ) of the whole pie.