Find the quotient 3/4 divided by 1/3 =
The Correct Answer and Explanation is :
The correct answer is: ( 2 \frac{1}{4} )
To find the quotient of ( \frac{3}{4} ) divided by ( \frac{1}{3} ), we can rewrite the division of fractions as multiplication by the reciprocal of the second fraction. The reciprocal of ( \frac{1}{3} ) is ( \frac{3}{1} ). Therefore, the expression can be rewritten as:
[
\frac{3}{4} \div \frac{1}{3} = \frac{3}{4} \times \frac{3}{1}
]
Next, we multiply the numerators and the denominators:
[
\frac{3 \times 3}{4 \times 1} = \frac{9}{4}
]
So, the quotient of ( \frac{3}{4} \div \frac{1}{3} ) is ( \frac{9}{4} ), which can also be expressed as a mixed number:
[
\frac{9}{4} = 2 \frac{1}{4}
]
Explanation
Dividing fractions might seem a bit tricky at first, but it can be easily understood by remembering the rule of multiplying by the reciprocal. The reciprocal of a fraction is simply flipping the numerator and denominator. For example, the reciprocal of ( \frac{1}{3} ) is ( \frac{3}{1} ) because ( 1 ) becomes the denominator and ( 3 ) becomes the numerator.
When we multiply two fractions, we multiply the numerators together and the denominators together. In our example, we multiplied ( 3 ) (the numerator of the first fraction) by ( 3 ) (the numerator of the second fraction) to get ( 9 ), and we multiplied ( 4 ) (the denominator of the first fraction) by ( 1 ) (the denominator of the second fraction) to get ( 4 ).
The result ( \frac{9}{4} ) is an improper fraction, meaning the numerator is larger than the denominator. This fraction can be converted into a mixed number, which is often easier to understand. We divide ( 9 ) by ( 4 ) to find that it goes ( 2 ) times, with a remainder of ( 1 ). Therefore, ( \frac{9}{4} ) can also be expressed as ( 2 \frac{1}{4} ).
This process illustrates how division of fractions works, and understanding it is fundamental in many areas of mathematics.