One-Step Equations with Fractions - Pre-Algebra

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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 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 :

$$\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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