Problem 59 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{4} \div \frac{1}{4}$$

Step-by-Step Solution

Answer

The simplified result of \(\frac{3}{4} \div \frac{1}{4}\) is 3.

Step 1: Identify the Reciprocal of the Fraction

The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. Therefore, the reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\).

Step 2: Rewrite the Problem Using Multiplication

The division problem \(\frac{3}{4} \div \(\frac{1}{4}\) can be rewritten as a multiplication problem with the reciprocal of the second fraction. Therefore, we get \(\frac{3}{4} \times \(\frac{4}{1}\).

Step 3: Perform the Multiplication

To multiply fractions, we multiply the numerators together and the denominators together. this will give us \(\frac{3 \times 4}{4 \times 1} = \frac{12}{4}\).

Step 4: Simplify if Possible

The resulting fraction \(\frac{12}{4}\) can be simplified by dividing both numerator and denominator by their greatest common divisor, which is 4. Therefore, we get \(\frac{12 \div 4}{4 \div 4} = \frac{3}{1}\), which is most simply expressed as 3.