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Pre-Algebra : One-Step Equations with Fractions

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Example Questions

Example Question #1 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

Correct answer:

Explanation:

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:

x=4

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Example Question #2 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$3\frac{1}{5}$

$8\frac{2}{5}$

Correct answer:

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:

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

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Example Question #2 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{8}{5}$

$\frac{10}{4}$

$\frac{8}{10}$

$\frac{5}{8}$

$\frac{4}{10}$

Correct answer:

$\frac{8}{5}$

Explanation:

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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Example Question #3 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{21}{18}$

$\frac{18}{7}$

$\frac{18}{6}$

$\frac{7}{2}$

$\frac{18}{21}$

Correct answer:

$\frac{7}{2}$

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:

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

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Example Question #3 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{8}{3}$

$\frac{13}{6}$

$-\frac{6}{13}$

$-\frac{13}{6}$

$\frac{8}{6}$

Correct answer:

$-\frac{13}{6}$

Explanation:

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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Example Question #4 : One Step Equations With Fractions

Solve for :

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

Possible Answers:

$\frac{13}{12}$

$-\frac{5}{4}$

$\frac{10}{12}$

$\frac{5}{4}$

$\frac{7}{12}$

Correct answer:

$\frac{5}{4}$

Explanation:

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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Example Question #1 : One Step Equations With Fractions

Solve for y

6y=15

Possible Answers:

y=90

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

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

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

y=6

Correct answer:

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

Explanation:

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

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

which simplifies to

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

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Example Question #1 : One Step Equations With Fractions

Solve for x

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

Possible Answers:

x=3

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

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

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

x=5

Correct answer:

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

Explanation:

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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Example Question #2 : One Step Equations With Fractions

Solve the equation below for x:

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

Possible Answers:

$\small \small 25$

$\small 45$

$\small 5$

$\small 125$

$\small 50$

Correct answer:

$\small \small 25$

Explanation:

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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Example Question #1 : One Step Equations With Fractions

Solve for n:

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

Possible Answers:

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

n=6

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

n=12

Correct answer:

n=12

Explanation:

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

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

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

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Pre-Algebra : One-Step Equations with Fractions

Study concepts, example questions & explanations for Pre-Algebra

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Example Question #1 : One Step Equations With Fractions

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