One-Step Equations with Fractions - Pre-Algebra

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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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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 ""

$\frac{1}{6}x=10$

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Answer

Because of the fraction, you must mulitply each side by 6, removing the $\frac{1}{6}$ .

$6\left(\frac{1}{6} \right )x=10\cdot6$

The problem then reads .

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Question

Solve this equation: $x-\frac{5}{2}=\frac{3}{4}$

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Answer

$x-\frac{5}{2}=\frac{3}{4}$

Isolate x:

$x=\frac{3}{4}+\frac{5}{2}$

Find a common denominator:

$x=\frac{3}{4}+\frac{5}{2}*\frac{2}{2}\rightarrow x=\frac{3}{4}+\frac{10}{4}=\frac{13}{4}$

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Question

Solve for :

$\frac{18}{2}x=81$

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Answer

Normally when we have a fraction we multiply by the reciprocal to get the fractions to equate to 1. Consider this fraction and its reciprocal $\frac{5}{2}*\frac{2}{5}=1$ . But since our fraction can be reduced to a whole number we can just divide both sides by that number.

$\frac{18}{2}x=81$

Reduce the fraction:

Isolate x by dividing both sides by nine:

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Question

Solve: $\frac{2}{3}x=2$

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Answer

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 in order to isolate the variable.

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

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Question

Solve: $9x = \frac{1}{9}$

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Answer

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.

Divide by nine on both sides to isolate the variable.

$\frac{9x }{9}= \frac{\frac{1}{9}}{9}$

$x=\frac{1}{9}\times\frac{1}{9}=\frac{1}{81}$

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Question

Solve:

$\frac{6}{10}+x = \frac{1}{10}$

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Answer

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 unknown variable, subtract $\frac{6}{10}$ from both sides.

$\frac{6}{10}+x -\left(\frac{6}{10}\right)= \frac{1}{10}-\left(\frac{6}{10}\right)$

$x=-\frac{5}{10} =-\frac{1}{2}$

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Question

Solve: $\frac{1}{500}x = \frac{1}{5}$

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Answer

In order to solve for x, multiply both sides of the equation by the reciprocal of the coefficient in front of the unknown variable.

When multiplying fractions, multiply the numerators together and multiply the denominators together. After multiplication is done, find common factors in the numerator and denominator to cancel out and completely simplify the fraction.

$\\frac{1}{500}x \times 500\\= \frac{1}{5}\times 500\\=\frac{500}{5}\\=\frac{5\cdot 100}{5}$

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Question

Solve for :

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

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Answer

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 solve for the unknown variable in this particular case, isolate by multiplying both sides by the reciprocal of the fraction coefficient in front of the .

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

$x=\frac{9}{4}$

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Question

Evaluate: $\frac{x}{3} = 27$

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Answer

In order to isolate the variable, multiply three on both sides of the equation.

$\frac{x}{3} \times3 = 27 \times 3$

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Question

Solve: $\frac{3}{4} +x = \frac{5}{4}$

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Answer

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.

Subtract $\frac{3}{4}$ from both sides of the equation.

$x = \frac{5}{4}-\frac{3}{4} = \frac{2}{4}$

Reduce the fraction.

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

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Question

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

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Answer

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,

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

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Question

Solve:

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

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Answer

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 solve for , simply add $\frac{2}{7}$ on both sides to isolate the unknown variable.

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

Since the denominators are same, the numerators can be added. The denominators do not change.

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

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Question

Solve the equation:

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

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Answer

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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Question

Solve: $\frac{4}{9} = 9x$

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Answer

In order to solve for , isolate the variable by dividing nine on both sides. This is also the same as multiplying both sides by $\frac{1}{9}$ .

$\frac{4}{9} \times \frac{1}{9}= 9x\times \frac{1}{9}$

$x=\frac{4}{81}$

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