One-Step Equations with Fractions

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Pre-Algebra › One-Step Equations with Fractions

Questions 1 - 10

1

Solve for :

$\frac{2}{5}x=8$

$3\frac{1}{5}$

$8\frac{2}{5}$

Explanation

Step 1: Multiply both sides of the equation by the fraction's reciprocal to get alone on one side:

$\frac{5}{2}*\frac{2}{5}x=8*\frac{5}{2}$

$1x=8*\frac{5}{2}$

$x=8*\frac{5}{2}$

Step 2: Multiply:

$x=8*\frac{5}{2}=\frac{40}{2}=20$

2

Solve for :

$\frac{3}{4}x=36$

$\small 48$

$\small 27$

$\small 18$

$\small 16$

$\small 0$

Explanation

To get x by itself multiply both sides by 4 to get

, then divide both sides by 3 to get

$x=\left(\frac{4*36}{3}\right)$

When you simplify, you can cancel the three on bottom with the 3 in the numerator because it is a factor of 36 leaving you with:

3

Solve for :

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

$\frac{16}{9}$

$\frac{4}{3}$

$\frac{3}{4}$

Explanation

The goal is to isolate x so to solve this you will first multiple both sides by 4

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

This gives you:

$3x=\frac{16}{3}$

You must then divide both sides by 3

$\frac{3x}{3}=\frac{16}{3}*\frac{1}{3}$

you then get your answer:

$x=\frac{16}{9}$

4

Solve for n:

$\frac{3}{4}n=9$

$n=\frac{33}{4}$

$n=\frac{27}{4}$

Explanation

$\frac{3}{4}n=9$

$\frac{4}{3}\left(\frac{3}{4}\cdot n\right)=\left(\frac{4}{3}\right)\left(9 \right )$

$n=\frac{36}{3}=12$

5

Solve:

$\frac{6x}{5}= 4$

$\frac{10}{3}$

$\frac{24}{5}$

$\frac{30}{4}$

$\frac{20}{6}$

Explanation

Eliminate the denominator by multiplying both sides by 5:

$6x=5\cdot 4$

Isolate the variable by dividing both sides by 6:

$\frac{6x}{6}=\frac{20}{6}$

$1x=\frac{20}{6}$

Reduce the fraction to it lowest terms by dividing 20 and 6 by 2:

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

6

Solve for :

$\small \frac{3}{5}x=12$

$\small 20$

$\small \frac{36}{5}$

$\small 12$

$\small \frac{3}{5}$

$\small 16$

Explanation

To solve this equation, isolate on one side.

First, move the fraction to the other side by multiplying by its reciprocal.

$\small \frac{5}{3}*\frac{3}{5}x = \frac{12}{1}*\frac{5}{3}$

$\small x = \frac{60}{3}$

Next, simplify the complex fraction.

$\small x=20$

7

Solve for y

$y=\frac{5}{2}$

$y=\frac{5}{6}$

$y=\frac{6}{15}$

Explanation

To get y by itself, you must divide by 6 on both sides

$\frac{6y}{6}=\frac{15}{6}$

which simplifies to

$y=\frac{15}{6}=\frac{5}{2}$

8

Solve for .

$z=\frac{5}{2}$

$z=\frac{10}{2}$

$z=\frac{5}{4}$

Explanation

To get z by itself, you must divide both sides of the equation by 4

$\frac{4z}{4}=\frac{10}{4}$

which simplifies to

$z=\frac{10}{4}=\frac{5}{2}$

9

Solve for :

$\frac{x}{\frac{3}{4}}=12$

Explanation

Explanation:

Isolate the variable to one side.

Multiply each side by $\frac{3}{4}$ :

$\frac{x}{\frac{3}{4}}=12$

$\frac{x\frac{3}{4}}{\frac{3}{4}}=\frac{12}{1}*\frac{3}{4}$

10

Solve for a in the following equation:

$\frac{2}{3} + a = \frac{1}{2}$

$a = -\frac{1}{6}$

$a = \frac{3}{5}$

$a = \frac{-1}{-1}$

$a = \frac{7}{6}$

$a = \frac{1}{6}$

Explanation

When solving for a, we want to get a by itself. So in the equation,

$\frac{2}{3} + a = \frac{1}{2}$

we must subtract $\frac{2}{3}$ from both sides. We get

$\frac{2}{3} + a - \frac{2}{3} = \frac{1}{2} - \frac{2}{3}$

$a = \frac{1}{2} - \frac{2}{3}$

When subtracting fractions, we need to find a common denominator. In this case, it's 6. So,

$a = \frac{3}{6} - \frac{4}{6}$

Now, we subtract the numerators and get

$a = - \frac{1}{6}$

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