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High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #371 : High School Math

$x=13*\frac{1}{2}$

What is ?

Possible Answers:

$6\tfrac{1}{2}$

$7\tfrac{1}{2}$

Correct answer:

$6\tfrac{1}{2}$

Explanation:

To solve this problem, multiply across: $x=13*\frac{1}{2}=\frac{13}{1}*\frac{1}{2}=\frac{13}{2}$ .

is a prime number, so we cannot reduce further. From here, covert $\frac{13}{2}$ into a mixed fraction: $x=6\tfrac{1}{2}$

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Example Question #221 : Pre Algebra

$x=14*\frac{3}{2}$

What is ?

Possible Answers:

$3\tfrac{1}{2}$

$17\tfrac{1}{2}$

Correct answer:

Explanation:

To solve this problem, multiply across:

$x=14*\frac{3}{2}=\frac{14}{1}*\frac{3}{2}=\frac{42}{2}= 21$

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Example Question #122 : Algebraic Equations

$x=9*\frac{2}{3}$

Solve for .

Possible Answers:

$9\tfrac{2}{3}$

$\frac{27}{2}$

Correct answer:

Explanation:

$x=9*\frac{2}{3}$

$x=\frac{9}{1}*\frac{2}{3}$

$x=\frac{9*2}{1*3}$

$x=\frac{18}{3}$

x=6

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Example Question #373 : High School Math

$x*\frac{2}{3}=12$

Solve for .

Possible Answers:

$11\tfrac{1}{3}$

Correct answer:

Explanation:

To solve for , we need to isolate our variable. That means that we want ONLY the on the left side of the equation.

$x*\frac{2}{3}=12$

We want to divide by $\frac{2}{3}$ . The way you divide by a fraction is to multiply by the reciprocal. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ .

Therefore:

$x*\frac{2}{3}*\frac{3}{2}=12*\frac{3}{2}$

Since $\frac{2}{3}*\frac{3}{2}=\frac{6}{6}=1$ , we can ignore it.

$x=12*\frac{3}{2}$

$x=\frac{12}{1}*\frac{3}{2}$

$x=\frac{36}{2}$

x=18

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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 #373 : High School Math

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

Possible Answers:

$\frac{3}{5}$

$\frac{5}{3}$

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

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

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

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

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 #374 : High School Math

Solve for if

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

Possible Answers:

x=108

x=3

x=36

x=5

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 #21 : 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 #22 : 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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High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #371 : High School Math

Example Question #221 : Pre Algebra

Example Question #122 : Algebraic Equations

Example Question #373 : High School Math

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

Example Question #373 : High School Math

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

Example Question #374 : High School Math

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

All High School Math Resources

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