One-Step Equations with Fractions

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Pre-Algebra › One-Step Equations with Fractions

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Solve for :

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

CORRECT

$3\frac{1}{5}$

$8\frac{2}{5}$

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:

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

Solve for :

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

$\small 48$

CORRECT

$\small 27$

$\small 18$

$\small 16$

$\small 0$

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:

Solve for :

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

$\frac{16}{9}$

CORRECT

$\frac{4}{3}$

$\frac{3}{4}$

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:

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

Solve for n:

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

CORRECT

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

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

Explanation

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

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

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

Solve:

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

$\frac{10}{3}$

CORRECT

$\frac{24}{5}$

$\frac{30}{4}$

$\frac{20}{6}$

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:

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

Solve for :

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

$\small 20$

CORRECT

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

$\small 12$

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

$\small 16$

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.

$\small x=20$

Solve:

$\frac{7x}{2} = 14$

CORRECT

$\frac{1}{4}$

$\frac{1}{2}$

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

To isolate the variable, multiply $\frac{2}{7}$ on both sides.

$\frac{7x}{2} \times \frac{2}{7}= 14\times \frac{2}{7}$

$x= \frac{14}{1}\times \frac{2}{7}$

When multiplying fractions, multiply the numerators together and multiply the denominators together.

$x= \frac{28}{7}$

From here factor the numerator to find values that will cancel and reduce.

$x=\frac{28}{7}=\frac{4\cdot 7}{7}=4$

Solve for :

$\frac{6}{7} x = 3$

$\frac{7}{2}$

CORRECT

$\frac{18}{6}$

$\frac{18}{7}$

$\frac{18}{21}$

$\frac{21}{18}$

Explanation

The goal is to isolate the variable on one side.

$\frac{6}{7} x = 3$

The opposite operation of multiplication is division, therefore, we can either divide each side by $\frac{6}{7}$ or multiply each side by its reciprocal $\frac{7}{6}$ :

$\frac{7}{6}\times \frac{6}{7}x = \frac{7}{6}\times 3$

The left hand side can be reduced by recalling that anything multiplying a fraction by its reciprocal is equal to 1:

$1\times x = \frac{7}{6} \times 3$

The identity law of multiplication takes effect and we get the solution as:

$x = \frac{21}{6}$

However, this solution can be reduced by dividing both the numerator and denominator by 3:

$x = \frac{7}{2}$

Solve: $\frac{3}{5}x = \frac{3}{7}$

$\frac{5}{7}$

CORRECT

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{7}{5}$

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Multiply both sides by the reciprocal of the coefficient in front of the unknown variable.

$\frac{3}{5}x \times \frac{5}{3}= \frac{3}{7}\times \frac{5}{3}$

The three in the numerator and in the denominator cancel out and you are left with,

$x = \frac{5}{7}$ .

Solve the equation:

$\frac{7}{3}x= \frac{2}{7}$

$\frac{6}{49}$

CORRECT

$\frac{3}{19}$

$\frac{3}{13}$

$\frac{2}{3}$

$\frac{3}{2}$

Explanation

In order to solve the equation, we have to isolate the variable. We do this by performing the same operation to either side of the equation.

Multiply by the reciprocal of the coefficient in front of .

$\frac{7}{3}x\times \frac{3}{7}= \frac{2}{7}\times \frac{3}{7}$

$x=\frac{6}{49}$

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