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Pre-Algebra : One-Step Equations with Fractions

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Example Questions

Example Question #41 : One Step Equations With Fractions

Solve: $\frac{7}{9}x = 3$

Possible Answers:

$\frac{3}{7}$

$\frac{7}{3}$

$\frac{7}{27}$

$\frac{1}{21}$

$\frac{27}{7}$

Correct answer:

$\frac{27}{7}$

Explanation:

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

$\frac{7}{9}x \times \frac{9}{7}= 3\times \frac{9}{7}$

By multiplying the reciprocal of the coefficient in front of , we can see that that can be left as a single variable.

Multiply the whole number with the numerator.

$x= 3\times \frac{9}{7} = \frac{27}{7}$

The answer is: $\frac{27}{7}$

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Example Question #42 : One Step Equations With Fractions

Solve for the unknown variable: $\frac{4x}{3} = 9$

Possible Answers:

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{4}{27}$

$\frac{3}{2}$

$\frac{27}{4}$

Correct answer:

$\frac{27}{4}$

Explanation:

To isolate the unknown variable, multiply both sides by $\frac{3}{4}$ , which is the reciprocal of the coefficient in front of the variable.

$\frac{4x}{3} \times \frac{3}{4} = 9\times \frac{3}{4}$

The left side of the equation will become . On the right side of the equation, multiply the integer with the numerator of the fraction.

The answer is:

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

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Example Question #43 : One Step Equations With Fractions

Solve: $\frac{5}{8}x = \frac{7}{9}$

Possible Answers:

$\frac{56}{45}$

$\frac{35}{72}$

$\frac{45}{56}$

$\frac{72}{35}$

$\frac{1}{3}$

Correct answer:

$\frac{56}{45}$

Explanation:

In order to isolate the variable, first multiply both sides by the reciprocal of $\frac{5}{8}$ .

$\frac{5}{8}x \times \frac{8}{5}= \frac{7}{9}\times \frac{8}{5}$

Cancel out the fractions on the left side of the equation.

$x= \frac{7}{9}\times \frac{8}{5}$

For these two fractions, multiply the numerator with the numerator, and the denominator with the denominator.

$x= \frac{7}{9}\times \frac{8}{5}=\frac{56}{45}$

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Example Question #42 : One Step Equations With Fractions

Solve: $\frac{3}{8}x = \frac{7}{6}$

Possible Answers:

$\frac{28}{9}$

$\frac{28}{3}$

$\frac{3}{28}$

$\frac{19}{24}$

$\frac{24}{19}$

Correct answer:

$\frac{28}{9}$

Explanation:

In order to isolate the variable, multiply both sides by the reciprocal of the coefficient in front of the .

$\frac{3}{8}x \times \frac{8}{3}= \frac{7}{6}\times \frac{8}{3}$

Simplify the fractions on the left side.

$x= \frac{7}{6}\times \frac{8}{3}$

Reduce the on the denominator with the in the numerator.

$x= \frac{7}{2 \times 3}\times \frac{2\times 4}{3} = \frac{7\times 4}{3 \times 3} = \frac{28}{9}$

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Example Question #44 : One Step Equations With Fractions

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

Possible Answers:

$\frac{21}{2}$

$\frac{7}{6}$

$\frac{2}{21}$

$\frac{6}{7}$

$\frac{23}{7}$

Correct answer:

$\frac{21}{2}$

Explanation:

In order to isolate the variable, multiply the reciprocal of $\frac{2}{7}$ on both sides of the equation.

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

Simplify the fractions on the left side of the equation.

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

Multiply the three with the seven on the right side of the equation.

$x= 3\times \frac{7}{2} = \frac{21}{2}$

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Example Question #45 : One Step Equations With Fractions

Solve for in the following equation.

$\frac{x}{4} = 8$

Possible Answers:

x = 2

x = 12

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

x = 32

x = 4

Correct answer:

x = 32

Explanation:

$\frac{x}{4} = 8$

When solving for x, we need to get x alone. To do that, we need to multiply both sides by 4.

$\frac{x}{4} * 4 = 8 * 4$

Multiply through.

$\frac{4x}{4} = 32$

Simplify.

$\frac{1x}{1} = 32$

Solution.

x = 32

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Example Question #46 : One Step Equations With Fractions

Find the solution for g.

$g - \frac{3}{4} = \frac{3}{4}$

Possible Answers:

$\frac{6}{8}$

$g = \frac{6}{4}=\frac{3}{2}$

g= 0

g= 1

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

Correct answer:

$g = \frac{6}{4}=\frac{3}{2}$

Explanation:

This is a simple one-step equation. The objective is to solve for g and isolate it on the right side.

The steps are as follows:

$g-\frac{3}{4}+\frac{3}{4}=\frac{3}{4}+\frac{3}{4}$

$g = \frac{3}{4}+\frac{3}{4}=\frac{6}{4}=\frac{3}{2}$

You can check your answer by inserting g into the original equation as follows.

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

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

It works!

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Example Question #47 : One Step Equations With Fractions

Solve for in the following equation:

$x + \frac{1}{2} = \frac{3}{4}$

Possible Answers:

$-\frac{1}{4}$ $\frac{4}{6}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{2}{2}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

When solving for x, we want to get x to stand alone. We subtract $\frac{1}{2}$ from both sides. We get

$x + \frac{1}{2} - \frac{1}{2} = \frac{3}{4} - \frac{1}{2}$

We must find a common denominator. In this case, the lowest common denominator is 4. So we get

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

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

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Example Question #47 : One Step Equations With Fractions

Solve for in the following equation:

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

Possible Answers:

$\frac{6}{15}$

$\frac{22}{15}$

$\frac{6}{8}$

$\frac{2}{15}$

$\frac{2}{8}$

Correct answer:

$\frac{22}{15}$

Explanation:

When solving for x, we must get x to stand by itself. Therefore, in the equation

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

we will add $\frac{2}{3}$ to both sides. We get

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

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

To add the fractions, we must find a common denominator.

In this case, it's 15.

So,

$x = \frac{12}{15} + \frac{10}{15}$

$x = \frac{22}{15}$

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Example Question #44 : One Step Equations With Fractions

Solve for a in the following equation:

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

Possible Answers:

$a = \frac{7}{6}$

$a = \frac{-1}{-1}$

$a = -\frac{1}{6}$

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

$a = \frac{1}{6}$

Correct answer:

$a = -\frac{1}{6}$

Explanation:

When solving for a, we want to get a by itself. So in the equation,

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

we must subtract $\frac{2}{3}$ from both sides. We get

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

$a = \frac{1}{2} - \frac{2}{3}$

When subtracting fractions, we need to find a common denominator. In this case, it's 6. So,

$a = \frac{3}{6} - \frac{4}{6}$

Now, we subtract the numerators and get

$a = - \frac{1}{6}$

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Pre-Algebra : One-Step Equations with Fractions

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #41 : One Step Equations With Fractions

Example Question #42 : One Step Equations With Fractions

Example Question #43 : One Step Equations With Fractions

Example Question #42 : One Step Equations With Fractions

Example Question #44 : One Step Equations With Fractions

Example Question #45 : One Step Equations With Fractions

Example Question #46 : One Step Equations With Fractions

Example Question #47 : One Step Equations With Fractions

Example Question #47 : One Step Equations With Fractions

Example Question #44 : One Step Equations With Fractions

All Pre-Algebra Resources

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