Problem 61 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{6} \div \frac{5}{3}$$

Step-by-Step Solution

Answer

The answer is \( \frac{7}{10} \).

Step 1: Identify the Reciprocal

Take note that when dividing fractions, rather than actually dividing, you can multiply by the reciprocal (or simply 'flip') of the second fraction. That means, replace the division sign with multiplication and flip the second fraction. So the task becomes to solve \( \frac{7}{6} \times \frac{3}{5} \).

Step 2: Multiply Numerators and Denominators

Now simply multiply the numerators with each other and the denominators with each other. This gives \( \frac{7 \times 3}{6 \times 5} = \frac{21}{30} \).

Step 3: Simplify the Result

Finally, simplify the answer to its lowest terms by finding the greatest common divisor (gcd) of 21 and 30, which is 3. Divide both numerator and denominator by the gcd. This gives \( \frac{21}{30} = \frac{21 ÷ 3}{30 ÷ 3} = \frac{7}{10} \).