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High School Math : How to solve one-step equations with fractions in pre-algebra

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Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

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

Solve for .

Possible Answers:

$\frac{3}{5}$

$1\tfrac{2}{3}$

Correct answer:

Explanation:

To solve for , the first thing we need to do is isolate the variable. That means we want ONLY on the left side of the equation.

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

To divide by a fraction, we need to multiply by the reciprocal. The reciprocal of $\frac{1}{3}=\frac{3}{1}=3$ .

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

x=5*3

x=15

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Example Question #22 : How To Solve One Step Equations With Fractions In Pre Algebra

Solve for if, $\frac{2x}{5}=\frac{2}{3}$

Possible Answers:

$\frac{5}{3}$

$\frac{3}{5}$

Correct answer:

$\frac{5}{3}$

Explanation:

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being divided by a number, we must multiply both sides of the equation by the number.

Since it is a fraction we must multiply each side by the reciprocal like this

$\left(\frac{5}{2}\right)\frac{2x}{5}=\frac{2}{3}\left(\frac{5}{2}\right)$

The numbers on the left cancel and we have

$x=\frac{2}{3}\left(\frac{5}{2}\right)$

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

We do this and find the answer is

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

Reduce the fraction to get

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

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Example Question #23 : How To Solve One Step Equations With Fractions In Pre Algebra

Solve for if, $\frac{5x}{3}=\frac{8}{15}$

Possible Answers:

x=3

$x=\frac{8}{25}$

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

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

Correct answer:

$x=\frac{8}{25}$

Explanation:

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being divided by a number, we must multiply both sides of the equation by the number.

Since it is a fraction we must multiply each side by the reciprocal like this

$\left(\frac{3}{5}\right)\cdot \frac{5x}{3}=\frac{8}{15}\cdot \left(\frac{3}{5}\right)$

The numbers on the left cancel and we have

$x=\left(\frac{8}{15}\right)\cdot \left(\frac{3}{5}\right)$

We do this and find the answer is

$x=\frac{24}{75}$

Reduce the fraction to get

$x=\frac{8}{25}$ .

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Example Question #24 : How To Solve One Step Equations With Fractions In Pre Algebra

Solve for if

$\frac{x}{6}=18$

Possible Answers:

x=108

x=36

x=5

x=3

Correct answer:

x=108

Explanation:

To solve for we must get all of the numbers on the other side of the equation of .

To do this in a problem where is being divided by a number, we must multiply both sides of the equation by the number.

In this case the number is so we multiply each side of the equation by to make it look like this

$6\cdot \left(\frac{x}{6}\right)=(18)\cdot 6$

The 6's on the left side cancel and then we multiply $x=6\cdot 18$

The answer is x=108 .

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Example Question #25 : How To Solve One Step Equations With Fractions In Pre Algebra

$7=\frac{1}{2}x$

Solve for .

Possible Answers:

3.5

Correct answer:

Explanation:

To solve $7=\frac{1}{2}x$ , we need to isolate . That means we want all the numbers on one side and the on the other side.

For this problem, that means we need to get rid of $\frac{1}2{}$ on the right side. To divide by a fraction, we multiply by the reciprocal.

$\frac{2}{1}*7=\frac{1}{2}x*\frac{2}{1}$

$\frac{2*7}{1}=\frac{2}{2}x$

$\frac{14}{1}=1*x$

14=x

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Example Question #26 : How To Solve One Step Equations With Fractions In Pre Algebra

$10=\frac{1}{4}x$

Solve for .

Possible Answers:

$2\tfrac{1}{2}$

$10\tfrac{1}{4}$

$\frac{1}{40}$

Correct answer:

Explanation:

To solve $10=\frac{1}{4}x$ , we need to isolate . Therefore, we want all the numbers on one side and the on the other side.

For this problem, we need to get rid of $\frac{1}4{}$ on the right side. To divide by a fraction, we multiply by the reciprocal.

$\frac{4}{1}*10=\frac{1}{4}x*\frac{4}{1}$

$\frac{4*10}{1}*=\frac{4}{4}x$

40=x

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Example Question #27 : How To Solve One Step Equations With Fractions In Pre Algebra

Solve for if $x-\frac{7}{5}=\frac{5}{8}$ .

Possible Answers:

$x=\frac{38}{9}$

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

$x=\frac{7}{8}$

$x=\frac{81}{40}$

Correct answer:

$x=\frac{81}{40}$

Explanation:

To solve for we must get all of the constants on the other side of the equation as .

To do this in a problem where is being subtracted by a number, we must add the number to both sides of the equation.

In this case the number is $\frac{7}{5}$ so we add $\frac{7}{5}$ to each side of the equation: $x-\frac{7}{5}+\frac{7}{5}=\frac{5}{8}+\frac{7}{5}$

To add fractions we must first ensure that we have the same denominator.

To do this we must find the least common multiple of the denominators.

In this case the LCM is .

We then multiply $\frac{5}{8}*\frac{5}{5}$ and $\frac{7}{5}*\frac{8}{8}$ to get the same denominator for both fractions.

To multiply a fraction, multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

$x=\frac{25}{40}+\frac{56}{40}$

We then add the numerators together and place the result over the new denominator.

$x=\frac{81}{40}$

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Example Question #28 : How To Solve One Step Equations With Fractions In Pre Algebra

$\frac{2}{7}x=18$

Solve for .

Possible Answers:

126

5.14

Correct answer:

Explanation:

Our goal here is to isolate . That means we want just on the left side.

For our problem, $\frac{2}{7}x=18$ , we need to get rid of the fraction. Dividing by a fraction is the same as multiplying by the reciprocal.

$\frac{2}{7}x=18$

$\frac{7}{2}*\frac{2}{7}x=18*\frac{7}{2}$

$\frac{14}{14}x=\frac{18*7}{2}$

$x=\frac{126}{2}$

x=63

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Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

$32=\frac{1}2{}x$

Solve for .

Possible Answers:

Correct answer:

Explanation:

When solving for , we want to isolate it. That means we want only on the right side of the equation.

For our given equation, $32=\frac{1}2{}x$ , we need to divide both sides by $\frac{1}{2}$ .

Dividing by a fraction is the same as multiplying by the reciprocal so this will look like:

$\frac{2}{1}*32=\frac{1}2{}x*\frac{2}{1}$

$\frac{2}{1}*\frac{32}{1}=\frac{1}2{}x*\frac{2}{1}$

$\frac{2*32}{1}=\frac{1*2}{2*1}x$

$\frac{64}{1}=\frac{2}{2}x$

64=x

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Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

$x=4*\frac{1}{2}$

Solve for .

Possible Answers:

$4\tfrac{1}{2}$

4.2

Correct answer:

Explanation:

$x=4*\frac{1}{2}$

$x=\frac{4}{1}*\frac{1}{2}$

$x=\frac{4*1}{1*2}$

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

x=2

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High School Math : How to solve one-step equations with fractions in pre-algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #22 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #23 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #24 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #25 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #26 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #27 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #28 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

Example Question #21 : How To Solve One Step Equations With Fractions In Pre Algebra

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