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Algebra II : Real Numbers

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Example Question #11 : Number Theory

Using the properties of negative numbers, determine which answer is equivalent to

-(1-2)

Possible Answers:

-1+2

2-1

All of the other answers

Correct answer:

All of the other answers

Explanation:

Recall the following property of negative numbers:

-(a-b)=-a+b=b-a

It follows that:

-(1-2)=-1+2=2-1=1

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Example Question #12 : Number Theory

Using the properties of negative numbers, determine which answer is equivalent to

(-9)(-2)

Possible Answers:

All of the other answers

(-9)(2)

Correct answer:

Explanation:

Recall the following property of negative numbers:

(-a)(-b)=ab

It follows that:

$(-9)(-2)=9\times 2=18$

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Example Question #13 : Number Theory

Solve the following using properties of fractions:

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

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

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

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Example Question #14 : Number Theory

Solve the following using properties of fractions:

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

Possible Answers:

$\frac{1}{3}$

$\frac{4}{5}$

$\frac{1}{2}$

$\frac{7}{6}$

$\frac{11}{6}$

Correct answer:

$\frac{11}{6}$

Explanation:

$\frac{3}{2}+\frac{1}{3}=\frac{3\times3}{2\times3}+\frac{1\times2}{3\times2}=\frac{9}{6}+\frac{2}{6}=\frac{11}{6}$

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Example Question #15 : Number Theory

Solve the following using properties of fractions:

$\frac{4}{3}\times\frac{3}{5}=$

Possible Answers:

$\frac{3}{2}$

$\frac{20}{9}$

$\frac{9}{6}$

$\frac{4}{5}$

$\frac{7}{8}$

Correct answer:

$\frac{4}{5}$

Explanation:

$\frac{4}{3}\times\frac{3}{5}=\frac{4\times3}{3\times5}=\frac{12}{15}=\frac{4}{5}$

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Example Question #16 : Number Theory

Solve the following using properties of fractions:

$\frac{3\times2}{2\times2}=$

Possible Answers:

All answers are correct.

$\frac{3}{2}$

$\frac{6}{4}$

$1\tfrac{1}{2}$

Correct answer:

All answers are correct.

Explanation:

$\frac{3\times2}{2\times2}=\frac{6}{4}=\frac{3}{2}$

Every answer choice is equivalent to this, so they are all correct.

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Example Question #17 : Number Theory

Solve the following using properties of fractions:

$\frac{7}{9}\div \frac{1}{2}=$

Possible Answers:

$\frac{14}{9}$

$\frac{7}{18}$

$\frac{9}{10}$

$\frac{8}{11}$

Correct answer:

$\frac{14}{9}$

Explanation:

When dividing fractions, remember to multiply the first fraction by the reciprocal of the second, as illustrated by the following identity:

$\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$

$\frac{7}{9}\div \frac{1}{2}=\frac{7}{9}\times\frac{2}{1}=\frac{7\times2}{9\times1}=\frac{14}{9}$

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Example Question #18 : Number Theory

Find the equivalent of the following:

$\frac{x}{y}=\frac{m}{n}$

Possible Answers:

xn=ym

x+m=y+n

x+n=y+m

xm=yn

Correct answer:

xn=ym

Explanation:

One of the properties of fractions states that if $\frac{a}{b}=\frac{c}{d}$ , then ad=bc .

It follows that if $\frac{x}{y}=\frac{m}{n}$ , then xn=ym .

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Example Question #19 : Real Numbers

Which of the following is a NOT a real number?

Possible Answers:

$\frac{1}{8}$

$\sqrt{-4}$

$\sqrt{2}$

3.2

$\sqrt{4}$

Correct answer:

$\sqrt{-4}$

Explanation:

By definition, a real number is one that is NOT imaginary. Imaginary numbers are numbers that, when squared, give a negative result.

So, the correct answer choice for the above question must be one that is, in fact, an imaginary number.

Using the above defintion, we are able to identify only one of the answer choices as a number that, when squared, gives a negative result. This is $\sqrt{-4}$ . When we take the square of $\sqrt{-4}$ , we get , ultimately, satisfying our definition of an imaginary number, and giving us the correct answer choice.

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Example Question #20 : Real Numbers

Which is NOT a real number?

$\sqrt{36}, \, \sqrt{49}, \, \sqrt{81}, \, \sqrt{-4}$

Possible Answers:

$\sqrt{36}$

$\sqrt{-4}$

$\sqrt{81}$

$\sqrt{49}$

Correct answer:

$\sqrt{-4}$

Explanation:

The mathematics a real number is any integer, irrational, or rational number. The set of real numbers does not include imaginary numbers.

If we look at the possible answers we see that three out of the four are real numbers because they are integers.

$\sqrt{49} = 7$

$\sqrt{36} = 6$

$\sqrt{81} = 9$

7, 6, and 9 are all Real Numbers.

The answer is $\sqrt{-4}$ because when a negative number is under a radical sign it creates an imaginary number which is not included in the set of real numbers.

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Algebra II : Real Numbers

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Number Theory

Example Question #12 : Number Theory

Example Question #13 : Number Theory

Example Question #14 : Number Theory

Example Question #15 : Number Theory

Example Question #16 : Number Theory

Example Question #17 : Number Theory

Example Question #18 : Number Theory

Example Question #19 : Real Numbers

Example Question #20 : Real Numbers

All Algebra II Resources

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