Problem 24 - College Algebra Essentials

Question

Multiply or divide as indicated. $$\frac{x+5}{7} \div \frac{4 x+20}{9}$$

Step-by-Step Solution

Answer

\(\frac{9}{28}\)

Step 1: Rewrite the problem

First, rewrite the problem by converting the division into multiplication by the reciprocal. The reciprocal of a fraction is simply switching the numerator and denominator. So, \(\frac{4x+20}{9}\) becomes \(\frac{9}{4x+20}\). Therefore, our equation to solve turns into \(\frac{x+5}{7} * \(\frac{9}{4x+20}\)

Step 2: Simplify

Now, simplify wherever possible before proceeding further to eliminate any complex fractions. Notice that \(4x+20\) is equal to \(4(x+5)\), so it can be reduced with \(x+5\). As a result, we have to solve for \(\frac{1}{7} * \(\frac{9}{4}\)

Step 3: Multiply

Finally, simplify the product by multiplying straight across. Multiply the numerators together to find the numerator of the answer and multiply the denominators to find the denominator of the answer. So, \(\frac{1*9}{7*4} = \frac{9}{28}\)