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GED Math : GED Math

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

Example Questions

Example Question #2 : Operations With Negative Numbers

Evaluate:

$\displaystyle 3.7 - 9.17$

Do not use a calculator.

Possible Answers:

-8.8 $\displaystyle -8.8$

-6.67 $\displaystyle -6.67$

-5.47 $\displaystyle -5.47$

-6.53 $\displaystyle -6.53$

Correct answer:

-5.47 $\displaystyle -5.47$

Explanation:

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

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

So subtract 3.7 from 9.17:

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

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

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Example Question #2 : Operations With Negative Numbers

Evaluate:

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

Do not use a calculator.

Possible Answers:

$\displaystyle -11$

$\displaystyle -312$

312 $\displaystyle 312$

$\displaystyle 11$

Correct answer:

312 $\displaystyle 312$

Explanation:

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

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

The product will remain positive.

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Example Question #3 : Operations With Negative Numbers

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

Possible Answers:

$\displaystyle -17$

$\displaystyle -39$

$\displaystyle 16$

$\displaystyle 8$

Correct answer:

$\displaystyle -17$

Explanation:

Substitute $\displaystyle - 7$ for $\displaystyle x$ in the expression.

4x + 11 $\displaystyle 4x + 11$

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

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

$\displaystyle =-28 + 11$

$\displaystyle = -(28 - 11)$

= -17 $\displaystyle = -17$

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Example Question #4 : Operations With Negative Numbers

Evaluate:

$\displaystyle -17 - (-62)$

Do not use a calculator.

Possible Answers:

$\displaystyle 45$

$\displaystyle 79$

$\displaystyle -45$

$\displaystyle -79$

Correct answer:

$\displaystyle 45$

Explanation:

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

$\displaystyle -17 - (-62)$

$\displaystyle = -17 +62$

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

-17 +62 $\displaystyle -17 +62$

$\displaystyle =62-17 = 45$

The answer is 45.

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Example Question #5 : Operations With Negative Numbers

Evaluate:

$- 6 \cdot 16$ $\displaystyle - 6 \cdot 16$

Do NOT use a calculator.

Possible Answers:

$\displaystyle -10$

$\displaystyle -22$

$\displaystyle -96$

$\displaystyle 10$

Correct answer:

$\displaystyle -96$

Explanation:

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

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

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Example Question #6 : Operations With Negative Numbers

Which of these is not equal to $\displaystyle -9$ ?

Do not use a calculator.

Possible Answers:

$\frac{-27}{-3}$ $\displaystyle \frac{-27}{-3}$

The reciprocal of $- \frac{1}{9}$ $\displaystyle - \frac{1}{9}$

$\frac{-45}{5}$ $\displaystyle \frac{-45}{5}$

$\frac{36}{-4}$ $\displaystyle \frac{36}{-4}$

Correct answer:

$\frac{-27}{-3}$ $\displaystyle \frac{-27}{-3}$

Explanation:

Only one of the choices is positive - $\frac{-27}{-3}$ $\displaystyle \frac{-27}{-3}$, which is the quotient of two negative numbers. This must be the correct response.

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Example Question #7 : Operations With Negative Numbers

Evaluate:

$\displaystyle | 24 + (-34) | - 6$

Possible Answers:

$\displaystyle 52$

$\displaystyle 64$

$\displaystyle 4$

$\displaystyle 16$

Correct answer:

$\displaystyle 4$

Explanation:

$\displaystyle | 24 + (-34) | - 6$

$\displaystyle = | -( 34-24) | - 6$

$\displaystyle = | -10| - 6$

$\displaystyle = 10 - 6$

$\displaystyle =4$

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Example Question #8 : Operations With Negative Numbers

How many of these statements are correct?

I) $0.5 \leq |- 0.5 |$ $\displaystyle 0.5 \leq |- 0.5 |$

II) $0 \leq |- 0.5 |$ $\displaystyle 0 \leq |- 0.5 |$

III) $-0.5 \leq |- 0.5 |$ $\displaystyle -0.5 \leq |- 0.5 |$

Possible Answers:

One

None

Two

Three

Correct answer:

Three

Explanation:

The absolute value of a negative number can be determined by removing the negative symbol, so $\displaystyle |-0.5 | = 0.5$. Of the three numbers $\left \{ -0.5, 0, 0.5 \right \}$ $\displaystyle \left \{ -0.5, 0, 0.5 \right \}$, all are less than or equal to 0.5.

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Example Question #9 : Operations With Negative Numbers

Raise $\displaystyle -11$ to the third power.

Do not use a calculator.

Possible Answers:

$\displaystyle -33$

$\displaystyle 33$

1,331 $\displaystyle 1,331$

-1,331 $\displaystyle -1,331$

Correct answer:

-1,331 $\displaystyle -1,331$

Explanation:

An odd power of a negative number is negative, so take 11 to the third power, then affix a negaitve symbol.

$11^{3} = 11 \times 11 \times 11 = 121 \times 11 = 1,331$ $\displaystyle 11^{3} = 11 \times 11 \times 11 = 121 \times 11 = 1,331$

The result must be negative, so the correct response is -1,331 $\displaystyle -1,331$.

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Example Question #11 : Operations With Negative Numbers

Order from least to greatest:

$\displaystyle | -10 |, |-5| , | 4| , |9|$

Possible Answers:

$\displaystyle | -10 | ,|9| ,|-5| ,| 4|$

$\displaystyle | -10 |, |-5| , | 4| , |9|$

$\displaystyle |9| , | 4| ,|-5| ,| -10 |$

$\displaystyle | 4| ,|-5| ,|9| ,| -10 |$

Correct answer:

$\displaystyle | 4| ,|-5| ,|9| ,| -10 |$

Explanation:

The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is obtained by removing the negative symbol. Therefore:

$\displaystyle | 4| = 4$

$\displaystyle |-5| = 5$

|9| = 9 $\displaystyle |9| = 9$

$\displaystyle | -10 | = 10$

In ascening order, the numbers are $\displaystyle | 4| ,|-5| ,|9| ,| -10 |$.

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All GED Math Resources

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #2 : Operations With Negative Numbers

Example Question #2 : Operations With Negative Numbers

Example Question #3 : Operations With Negative Numbers

Example Question #4 : Operations With Negative Numbers

Example Question #5 : Operations With Negative Numbers

Example Question #6 : Operations With Negative Numbers

Example Question #7 : Operations With Negative Numbers

Example Question #8 : Operations With Negative Numbers

Example Question #9 : Operations With Negative Numbers

Example Question #11 : Operations With Negative Numbers

All GED Math Resources

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