Algebraic Fractions

Help Questions

ACT Math › Algebraic Fractions

Questions 1 - 10

Solve the following equation for :

$\frac{36}{5x} = 4$ .

Reduce any fractions in your final answer.

$x = \frac{9}{5}$

$x = \frac{36}{20}$

$x = \frac{5}{9}$

Explanation

To solve an equation with a variable in a fraciton, treat the denominator as a constant value and multiply both sides of the equation by the denominator in order to eliminate it.
$\5x * \left(\frac{36}{5x}\right) = 4 * 5x\ \newline 36 = 20x \newline \newline \frac{36}{20} = x \ \newline \frac{9}{5}= x$

Evaluate the following equation when and round your answer to the nearest hundredth.

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

Explanation

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

1. Plug in wherever there is an in the above equation.

$\frac{5^{3}-(2)(5^{2})-(3)(5)+5}{(5)(5)+3}$

2. Perform the above operations.

$\frac{5^{3}-(2)(25)-(3)(5)+5}{(5)(5)+3}$

$\frac{125-50-15+5}{25+3}$

$\frac{65}{28}=2.32$

Maria owns an art studio and spent $\$1850$ in supplies. She sells her paintings for $\$150$ each. How many paintings does Maria need to sell until she makes a profit?

Explanation

Divide the total money spent by the cost of each painting.

$\frac{$1850}{$150}=12.33333$

Therefore, to make a profit, she needs to sell more than this amount. Since she can't sell a portion of a painting, the answer has to be the next nearest whole number ().