Problem 54 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{7}{8} \div \frac{2}{3}$$

Step-by-Step Solution

Answer

The simplified result of \( \frac{7}{8} \div \frac{2}{3} \) is \( \frac{21}{16} \).

Step 1: Rewrite the Division Operation

Firstly, rewrite the division between fractions as multiplication by taking the reciprocal (or multiplicative inverse) of the divisor. This means that \( \frac{7}{8} \div \frac{2}{3} \) should be rewritten as \( \frac{7}{8} * \frac{3}{2} \).

Step 2: Multiply the Fractions

When multiplying fractions, simply multiply the numerators (top numbers) together and do the same with the denominators (bottom numbers). The multiplication operation yields \( \frac{7*3}{8*2} \) resulting in \( \frac{21}{16} \).

Step 3: Simplify the Fraction

The resulting fraction \( \frac{21}{16} \) is already in its simplest form as 21 and 16 share no common divisors other than 1.