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GED Math : Basic Operations

Study concepts, example questions & explanations for GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : Division

Solve for $\small x$ : $\small \frac{2}{x}=y$

Possible Answers:

$\small x=\frac{2}{y}$

$\small x=2y$

$\small x=\frac{y}{2}$

$\small x=y^2$

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

Correct answer:

$\small x=\frac{2}{y}$

Explanation:

In order to solve for $\small x$ , we'll need to move all of the variables on its side to the other side of the equation.

We can see that $\small x$ is currently the denominator to $\small 2$ , so we need to move the $\small 2$ in order to solve for $\small x$ .

To move the $\small 2$ , we'll have to divide it on the other side. Keep in mind though that the $\small 2$ is in the numerator, so it will stay in the numerator when it divides over.

$\small \frac{2}{x}=y$

$\small x=\frac{2}{y}$

We cannot proceed with the question as there is nothing left to do. Our variables are different and the $\small 2$ can stay where it is.

Our answer is $\small x=\frac{2}{y}$

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Example Question #7 : Division

Solve for $\small x$ : $\small 2x=6y+4z$

Possible Answers:

$\small x=\frac{3y+2z}{2}$

$\small x=12y+8z$

$\small x=\frac{6y+4z}{2}$

$\small x=3y+2z$

$\small x=\frac{2}{6y+4z}$

Correct answer:

$\small x=3y+2z$

Explanation:

In order to solve for $\small x$ , we need to move all the numbers and variables to the other side of the equation.

We can see that $\small x$ is currently being multiplied by $\small 2$ . In order to move the $\small 2$ , we need to divide it on the other side of the equation.

$\small 2x=6y+4z$

$\small x=\frac{6y+4z}{2}$

Both $\small 6$ and $\small 4$ can be divided by $\small 2$ , which in turn gets rid of the $\small 2$ in the denominator.

$\small x=3y+2z$

We cannot proceed any farther since there is nothing left to do in the equation.

Our answer is $\small x=3y+2z$

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Example Question #7 : Division

Solve for $\small n$ : $\small nm=p+r$

Possible Answers:

$\small n=p+r+m$

$\small n=\frac{p+r}{m}$

$\small n=p+\frac{r}{m}$

$\small n=pm+rm$

$\small n=\frac{p}{m}+r$

Correct answer:

$\small n=\frac{p+r}{m}$

Explanation:

In order to solve for $\small n$ , we'll need to move all the other variables to the other side of the equation. Currently $\small n$ is stuck to $\small m$ , so we need to move the $\small m$ to the other side.

In order to move $\small m$ , we'll have to divide it to the other side of the equation.

$\small nm=p+r$

$\small n=\frac{p+r}{m}$

Since all the variables are different, we cannot do anything else to simplify this equation.

Our answer is $\small n=\frac{p+r}{m}$

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Example Question #272 : Numbers And Operations

Solve the equation: $\frac{8}{2}$

Possible Answers:

Correct answer:

Explanation:

Division is another way of seeing how many of the number we are dividing with is in the number we are dividing.

Let's take a look at . This is the number we are dividing, and is the number we are dividing with as told by their placement. We want to see how many 's there are in .

To figure this out, we'll add a each time until we get to .

2+2=4

2+2+2=6

2+2+2+2=8

We have now reached , so how many 's did it take us to get there? It took us 's to get to , and if you check with a calculator you will see that this is the answer as well.

Our answer is .

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Example Question #1 : Operations With Negative Numbers

Solve:

$\small -4\times 12=$

Possible Answers:

Correct answer:

Explanation:

When a negative number is multipied by a positive number, the result is negative.

$\small 4\times 12=48$

Therefore,

$\small -4\times12=-48$ .

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Example Question #2 : Operations With Negative Numbers

Evaluate:

3.7 - 9.17

Do not use a calculator.

Possible Answers:

-6.53

-5.47

-8.8

-6.67

Correct answer:

-5.47

Explanation:

To subtract a larger positive number from a smaller positive number, do the reverse, then affix a negative symbol, as demonstrated here:

$3.7 - 9.17 = 3.7 +\left ( - 9.17 \right ) = - (9.17-3.7)$

So subtract 3.7 from 9.17:

$\begin{matrix} \; \; 9.17\\ \underline{-3.70}\\ \; \; 5.47 \end{matrix}$

Since the answer must be negative, it is -5.47 .

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Example Question #2 : Operations With Negative Numbers

Evaluate:

$-13 \left ( - 24 \right )$

Do not use a calculator.

Possible Answers:

312

Correct answer:

312

Explanation:

To obtain the product of two numbers of unlike sign, multiply their absolute values:

$-13 \left ( - 24 \right ) = 13 \times 24 = 312$

The product will remain positive.

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Example Question #1 : Operations With Negative Numbers

Evaluate 4x + 11 for x = -7 . Do NOT use a calculator.

Possible Answers:

Correct answer:

Explanation:

Substitute for in the expression.

4x + 11

$= 4 \cdot (-7 )+ 11$

$= (-4 \cdot 7) + 11$

=-28 + 11

= -(28 - 11)

= -17

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Example Question #2 : Operations With Negative Numbers

Evaluate:

-17 - (-62)

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

To subtract with negative numbers, change to an addition and make the second number its opposite:

-17 - (-62)

= -17 +62

To add two numbers of unlike sign, if the positive has the greater absolute value, simply subtract the absolute values.

-17 +62

=62-17 = 45

The answer is 45.

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Example Question #5 : Operations With Negative Numbers

Evaluate:

$- 6 \cdot 16$

Do NOT use a calculator.

Possible Answers:

Correct answer:

Explanation:

To obtain the product of two numbers of unlike sign, multiply their absolute values and affix a negative symbol.

$- 6 \cdot 16 = -(6\cdot 16) = -96$

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All GED Math Resources

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GED Math : Basic Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #6 : Division

Example Question #7 : Division

Example Question #7 : Division

Example Question #272 : Numbers And Operations

Example Question #1 : Operations With Negative Numbers

Example Question #2 : Operations With Negative Numbers

Example Question #2 : Operations With Negative Numbers

Example Question #1 : Operations With Negative Numbers

Example Question #2 : Operations With Negative Numbers

Example Question #5 : Operations With Negative Numbers

All GED Math Resources

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