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Pre-Algebra : Other Pre-Algebra Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #431 : Operations And Properties

Simplify.

$x^{3}+y^{2}$

Possible Answers:

$x^{3}+y^{2}$

$x^{6}$

$x^{^{5}}$

Correct answer:

$x^{3}+y^{2}$

Explanation:

Since the two powers are not of the same base, we cannot combine the exponents.

We cannot simplify the equation further.

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Example Question #432 : Operations And Properties

Simplify.

(a+b)(a-b) +b(b+1)

Possible Answers:

a^2+b^2+1

a^2+b^2+b

a^2+b

a^2-b^2+2b

a^2+2b

Correct answer:

a^2+b

Explanation:

(a+b)(a-b) +b(b+1)

The first part is (a+b)(a-b) .

One way to simplify this portion is to apply the distributive property twice to get:

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

a^2-ab+ba-b^2

By the commutative property of multiplication ab=ba , so the two middle terms cancel out (one is positive and the other negative, resulting in zero).

This leaves a^2-b^2 .

Note: the identity (a+b)(a-b)=a^2-b^2 is worth memorizing, because it is very useful in higher math. The same result can be achieved by using FOIL.

Returning to our original expression, we can substitute:

(a+b)(a-b) +b(b+1)=(a^2-b^2)+b(b+1)

Now, apply the distributive property to the second part of the expression:

$b(b+1)=(b\times b)+(b\times1)=b^2+b$

Combining everything together:

(a^2-b^2)+(b^2+b)

Use the associative property of addition to group like terms and simplify.

a^2+(-b^2+b^2)+b

a^2+0+b

a^2+b

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Example Question #432 : Operations And Properties

What property is applied to the following expression?

$3x\left ( a^{2} + ab + \sqrt{7}\right) = 3xa^{2} + 3xab + 3x\sqrt{7}$

Possible Answers:

Multiplicative Inverse Property

Associative Property of Addition

Commutative Property of Multiplication

Distributive Property

Associative Property of Multiplication

Correct answer:

Distributive Property

Explanation:

The rule for Distributive Property is $a\left( b + c + d\right ) = ab + ac + ad$

Expression given in the question is:

$3x\left ( a^{2} + ab + \sqrt{7}\right) = 3xa^{2} + 3xab + 3x\sqrt{7}$

Hence it is Distributive Property.

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Example Question #433 : Operations And Properties

What digit is in the ones place?

497.123

Possible Answers:

Correct answer:

Explanation:

The ones place will always be the first digit to the left of the decimal point.

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Example Question #1 : Other Pre Algebra Properties

What digit is in the hundredths place?

564.391

Possible Answers:

Correct answer:

Explanation:

The hundredths place will always be the second digit to the right of the decimal point.

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Example Question #435 : Operations And Properties

What digit is in the thousands place?

93,748.195

Possible Answers:

Correct answer:

Explanation:

The thousands place will always be the forth digit to the left of the decimal point.

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Example Question #2 : Other Pre Algebra Properties

What digit is in the tens place?

197.82

Possible Answers:

Correct answer:

Explanation:

The tens place will always be the second digit to the left of the decimal point.

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Example Question #442 : Operations And Properties

What digit is in the tenths place?

45.298

Possible Answers:

Correct answer:

Explanation:

The tenths place will always be the first digit to the right of the decimal point.

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Example Question #3 : Other Pre Algebra Properties

What digit is in the hundredths place?

324.769

Possible Answers:

Correct answer:

Explanation:

The hundreths place will always be the second digit to the right of the decimal point.

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Example Question #4 : Other Pre Algebra Properties

What digit is in the thousands place?

3,928.145

Possible Answers:

Correct answer:

Explanation:

The thousands place will always be the forth digit to the left of the decimal point.

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Pre-Algebra : Other Pre-Algebra Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #431 : Operations And Properties

Example Question #432 : Operations And Properties

Example Question #432 : Operations And Properties

Example Question #433 : Operations And Properties

Example Question #1 : Other Pre Algebra Properties

Example Question #435 : Operations And Properties

Example Question #2 : Other Pre Algebra Properties

Example Question #442 : Operations And Properties

Example Question #3 : Other Pre Algebra Properties

Example Question #4 : Other Pre Algebra Properties

All Pre-Algebra Resources

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