Problem 65 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$6 \frac{3}{5} \div 1 \frac{1}{10}$$

Step-by-Step Solution

Answer

The answer is 6.

Step 1: Convert the mixed fractions to improper fractions

Firstly, convert both 6 3/5 and 1 1/10 into improper fractions. An improper fraction is when the numerator is larger than the denominator. For 6 3/5, the improper fraction will be \( \frac{6*5+3}{5}= \frac{33}{5}\). For 1 1/10, the improper fraction will be \( \frac{1*10+1}{10}= \frac{11}{10}\).

Step 2: Perform the division

According to the law of fractions, division is performed by multiplying the dividend by the reciprocal of the divisor. This means \( \frac{33}{5} ÷ \frac{11}{10} = \frac{33}{5} * \frac{10}{11}\). When you multiply these fractions you get \( \frac{330}{55}\).

Step 3: Reduce the result to lowest terms

The obtained fraction is not in the lowest term, so reduce it. The greatest common divisor (GCD) of 330 and 55 is 55. So, \( \frac{330}{55} = \frac{330 ÷ 55}{55 ÷ 55} = \frac{6}{1}\). Hence, the solution in lowest terms is 6.