One-Step Equations with Fractions - Pre-Algebra

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Question

Solve for n:

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

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Answer

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

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

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

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Question

Solve for .

$p-\frac{2}{5}=3$

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Answer

Perform the same operation on both sides of the equation.

$p-\frac{2}{5}=3$

It will be easier to write the right side of the equation as a fraction.

$3=\frac{15}{5}$

$p-\frac{2}{5}=\frac{15}{5}$

Now, we add two-fifths to both sides of the equation.

$p-\frac{2}{5}+\frac{2}{5}=\frac{15}{5}+\frac{2}{5}$

$p=\frac{17}{5}$

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Question

Solve for :

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

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Answer

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:

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

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Question

Solve for :

$\frac{x}{\frac{2}{3}}=6$

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Answer

Isolate the variable to one side.

Multiply each side by $\frac{2}{3}$ :

$\frac{x}{\frac{2}{3}}=6$

$\frac{x\frac{2}{3}}{\frac{2}{3}}=\frac{6}{1}*\frac{2}{3}$

Simplify and reduce:

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Question

Solve for :

$\frac{3}{4}x=\frac{6}{3}$

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Answer

$\frac{3}{4}x=\frac{6}{3}$

Divide both sides by $\frac{3}{4}$ :

$\frac{\frac{3}{4}x}{\frac{3}{4}}=\frac{\frac{6}{3}}{\frac{3}{4}}$

$x=\frac{\frac{6}{3}}{\frac{3}{4}}$

Simplify:

$\frac{\frac{6}{3}}{\frac{3}{4}}=\frac{6}{3}\times \frac{4}{3}=\frac{24}{9}=\frac{8}{3}=x$

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Question

Solve for :

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

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Answer

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:

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Question

Solve for :

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

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Answer

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

$\frac{3}{4}x4=\frac{4}{3}\4$

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:

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

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Question

Solve:

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

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Answer

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:

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

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Question

Solve for :

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

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Answer

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.

$\small x=20$

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Question

Solve for :

$\frac{x}{\frac{4}{5}} = 2$

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Answer

The goal is to isolate the variable on one side.

$\frac{x}{\frac{4}{5}} = 2$

The opposite operation of division is multiplication, therefore , multiply each side by $\frac{4}{5}$ :

$\frac{\frac{4}{5}x}{\frac{4}{5}} = \frac{4}{5}\times 2$

The left hand side can be reduced by recalling that anything divided by itself is equal to 1:

$1\times x = \frac{4}{5} \times 2$

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

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

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Question

Solve for :

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

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Answer

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:

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

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Question

Solve for :

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

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Answer

The goal is to isolate the variable on one side.

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

The opposite operation of addition is subtraction so subtract $\frac{1}{2}$ from each side:

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

Simplifying, we get the solution:

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

Finally, reducing to simplest terms:

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Question

Solve for :

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

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Answer

The goal is to isolate the variable on one side.

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

The opposite operation of addition is subtraction so subtract $\frac{7}{3}$ from each side:

$x + \frac{7}{3} - \frac{7}{3} = \frac{1}{6} - \frac{7}{3}$

In order to complete the subtraction on the right hand side, we must first determine the common denominator, or common multiples of 3 and 6. The least common multiple of 3 and 6 is 6 itself.

$x = \frac{1}{6} - \frac{14}{6}$

Simplifying, we get the final solution:

$x = -\frac{13}{6}$

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Question

Solve for :

$x - \frac{3}{4} = \frac{7}{4}$

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Answer

The goal is to isolate the variable on one side.

$x - \frac{7}{4} = \frac{3}{4}$

The opposite operation of subtraction is addition so add $\frac{7}{4}$ to each side:

$x - \frac{7}{4} + \frac{7}{4} = \frac{3}{4} + \frac{7}{4}$

Simplifying, we get the final solution:

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

Reducing the fraction we obtain the final solution:

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

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Question

Solve for :

$x - \frac{5}{6} = \frac{5}{12}$

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Answer

The goal is to isolate the variable on one side.

$x - \frac{5}{6} = \frac{5}{12}$

The opposite operation of subtraction is addition so add $\frac{5}{6}$ to each side:

$x - \frac{5}{6} + \frac{5}{6} = \frac{5}{12} + \frac{5}{6}$

In order to complete the addition on the right hand side, we must first determine the common denominator, or common multiples of 6 and 12. The least common multiple of 6 and 12 is 12 itself.

$x = \frac{5}{12} + \frac{10}{12}$

Simplifying, we obtain the solution:

$x = \frac{15}{12}$

Reducing the fraction to its simplest terms we get the final solution:

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

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Question

Solve for :

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

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Answer

Explanation:

Isolate the variable to one side.

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

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

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

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Question

Solve for .

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Answer

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

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

which simplifies to

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

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Question

Solve for y

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Answer

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

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

which simplifies to

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

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Question

Solve for x

$\frac{x}{5}=\frac{1}{3}$

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Answer

To get x by itself, you must multiply both sides of the equation by 5

$\frac{x}{5}\times5=\frac{1}{3}\times5$

which simplifies to

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

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Question

Solve the equation below for x:

$\small \small \frac{1}{5}x=5$

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Answer

For this equation, isolate the variable $\small x$ by preforming equivalent operations on both sides of the equation.

To isolate a variable multiplied by a fraction, any fraction multiplied by it's reciprocal equals one.

$\small \left(\frac{5}{1}\right)\small \frac{1}{5}x=5\left(\frac{5}{1}\right)$

Because $\small \frac{5}{5} = 1$ , we isolate $\small x$ , and the equation becomes $\small x=5\cdot \left(\frac{5}{1}\right)$

multiplying the values on the right side gives us

$\small x=\frac{25}{1}= 25$

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