Problem 60 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{3}{7} \div \frac{1}{7}$$

Step-by-Step Solution

Answer

The simplified answer to the given fractional division is 3.

Step 1: Write Down the Problem

Write down the fractional division problem as it is written: \(\frac{3}{7} \div \(\frac{1}{7}\).

Step 2: Convert Division into Multiplication

Change the division problem into a multiplication problem by taking the reciprocal of the second fraction. Reciprocal of a fraction is obtained by swapping the numerator and the denominator. Hence, the reciprocal of \(\frac{1}{7}\) is \(\frac{7}{1}\). Our problem now turns into a multiplication problem: \(\frac{3}{7}×\(\frac{7}{1}\).

Step 3: Multiply Fractions

To multiply fractions, simply multiply the numerators together for the new numerator, and multiply the denominators together for the new denominator. Doing that gives us a new fraction: \(\frac{(3×7)}{(7×1)}\).

Step 4: Simplify the Result

Simplify the multiplication in the numerator and the denominator, as \(\frac{21}{7}\). This fraction can be further simplified by dividing the numerator and the denominator by their greatest common divisor, which is 7, to get: 3.

Step 5: Write Down the Final Answer

The final answer, after fully simplifying, is 3. This is the simplest form and cannot be reduced any further.