Math - How to solve two-step equations with fractions in pre-algebra

$x=\frac{2}{3}*18$

Solve for .

Explanation

$x=\frac{2}{3}*18$

From here, you can either plug this into your calculator, or take the equation in pieces:

$x=\frac{2*18}{3}$

$x=\frac{36}{3}$

$\frac{2}{3}x=10$

Solve for .

$\frac{20}{3}$

$\frac{3}{20}$

Explanation

To solve $\frac{2}{3}x=10$ , we need to get rid of the fraction. To do that, we multiply both sides by the reciprocal of that fraction.

$\frac{3}{2}*\frac{2}{3}x=10*\frac{3}{2}$

$x=10*\frac{3}{2}$

From here, you can either plug that fraction into your calculator or solve in pieces.

$x=\frac{10*3}{2}$

$x=\frac{30}{2}$

A glass jar is filled to the top with 100 blue marbles, 75 red marbles, and 25 yellow marbles. Each time a marbles is picked from the jar, it must be returned to the jar before another marble is picked again. What is the probability of picking a red marble?

Explanation

First, find the total number of marbles in the glass jar: marbles in total.

It is given that there are 75 red marbles, thus: .

$\frac{2}{3}*(x+5)=12$

Solve for .

$10\tfrac{1}2{}$

Explanation

To solve $\frac{2}{3}*(x+5)=12$ , first we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by a reciprocal, so multiply both sides by $\frac{3}{2}$ .

$\frac{2}{3}*(x+5)=12$

$\frac{3}{2}*\frac{2}{3}*(x+5)=12*\frac{3}{2}$

$x+5=12*\frac{3}{2}$

$x+5=\frac{12*3}{2}$

$x+5=\frac{36}{2}$

Subtract from both sides.

$\frac{3}{4}x=118+2$

Solve for .

$88\tfrac{1}{2}$

$157\tfrac{1}{3}$

Explanation

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

First, combine our like terms on the right side.

$\frac{3}{4}x=118+2$

$\frac{3}{4}x=120$

Now divide both sides by $\frac{3}{4}$ . Remember, dividing by a fraction is the same as multiplying by the reciprocal, so we're going to multiply both sides by $\frac{4}{3}$ .