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Pre-Algebra : Operations and Properties

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Associative Property Of Multiplication

Which of the following displays the associative property of multiplication?

Possible Answers:

$a \cdot 1 = a$

$a \cdot 0 = 0$

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

$a(b \cdot c) = ab \cdot ac$

$a \cdot b = ab$

Correct answer:

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

Explanation:

The associative property of multiplication states that you can multiply numbers together in any order, and the answer will not change. Therefore,

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

displays the associative property of multiplication since the two sides are equal no matter which set of parentheses you solve first.

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Example Question #1 : Distributive Property

Simplify the expression.

(-2)(x^2+x-8)

Possible Answers:

2x^2+2x+16

2x^2+2x-16

-2x^2-2x-16

-2x^2-2x+16

Correct answer:

-2x^2-2x+16

Explanation:

Use the distributive property to multiply each term of the polynomial by $\small -2$ . Be careful to distribute the negative as well.

(-2)(x^2)+(-2)(x)-(-2)(8)

(-2x^2)+(-2x)-(-16)

-2x^2-2x+16

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Example Question #2 : Distributive Property

Find the value of 2(3-2) -4(2+5-7) .

Possible Answers:

-6

-2

Correct answer:

Explanation:

We can seperate the problem into two steps:

2(3-2) = 2(1)=2

-4(2+5-7) = -4(0)=0

We then combine the two parts:

2+0=2

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Example Question #2 : Distributive Property

Distribute -4(5x+15y-9) .

Possible Answers:

-20x-60y-36

-20x-60y+36

20x-60y+36

20x+60y-36

Correct answer:

-20x-60y+36

Explanation:

When distributing with negative numbers we must remember to distribute the negative to all of the variables in the parentheses.

Distribute the through the parentheses by multiplying it with each object in the parentheses to get ((-4)5x+(-4)15y-(-4)9) .

Perform the multiplication remembering the positive/negative rules to get -20x-60y+36 , our answer.

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Example Question #3 : Distributive Property

Simplify the expression.

(-x+2)(-xy)

Possible Answers:

-x^2y-2xy

-2x^3y^2

2x^3y^2

x^2y-2xy

Correct answer:

x^2y-2xy

Explanation:

Multiply the mononomial by each term in the binomial, using the distributive property.

(-x+2)(-xy)

(-xy)(-x)+(-xy)(2)

x^2y+(-2xy)

x^2y-2xy

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Example Question #5 : Distributive Property

Simplify the expression.

2x(5+4x+y)

Possible Answers:

5+6x+y

10x+6x^2+2xy

10x+8x^2+y

10x+8x^2+2xy

10+8x+2y

Correct answer:

10x+8x^2+2xy

Explanation:

2x(5+4x+y)

Use the distributive property to multiply each term by $\small 2x$ .

2x(5)+2x(4x)+2x(y)

Simplify.

10x+8x^2+2xy

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Example Question #2 : Distributive Property

Distribute:

-3(-4x+5y-8)

Possible Answers:

-12x+15y-24

12x+15y+24

12x+15y-24

12x-15y+24

x-7y+24

Correct answer:

12x-15y+24

Explanation:

When distributing with negative numbers we must remember to distribute the negative to all of the terms in the parentheses.

Remember, a negative multiplied by a negative is positive, and a negative multiplied by a positive number is negative.

Distribute the through the parentheses:

-4x(-3)+5y(-3)-8(-3)

Perform the multiplication, remembering the positive/negative rules:

12x-15y+24

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Example Question #1 : Distributive Property

Which of the following is equivalent to -3(2d - 4) ?

Possible Answers:

-6d + 4

-6d - 4

-6d + 12

6d - 12

-6d - 12

Correct answer:

-6d + 12

Explanation:

We need to distribute -3 by multiplying both terms inside the parentheses by -3.:

-3(2d - 4) = -3(2d) + (-3)(-4) .

Now we can multiply and simplify. Remember that multiplying two negative numbers results in a positive number:

-3(2d)+(-3)(-4)= -6d + 12

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Example Question #2 : Distributive Property

Expand:

-4x(3x^2-7x+2)

Possible Answers:

12x^3-28x+8x

$-12x^3+28x^{2}-8x$

12x^3+28x-8

12x^3+28x-8x

-12x^3-28x-8x

Correct answer:

$-12x^3+28x^{2}-8x$

Explanation:

$\small -4x(3x^2-7x+2)$

Use the distributive property. Do not forget that the negative sign needs to be distributed as well!

$\small \small (-4x)(3x^2)=-12x^3$

$\small (-4x)(-7x)=28x^2$

$\small (-4x)(2)=-8x$

Add the terms together:

$\small -12x^3+28x^2+(-8x)=-12x^3+28x^2-8x$

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Example Question #6 : Distributive Property

Distribute:

-5(x+15)

Possible Answers:

-5x-15

-5x+75

5x+75

-5x-75

-5x+15

Correct answer:

-5x-75

Explanation:

Remember that a negative multiplied by a negative is positive, and a negative multiplied by a positive is negative.

Distribute the through the parentheses by multiplying it by each of the two terms:

-5x-75

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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #2 : Associative Property Of Multiplication

Example Question #1 : Distributive Property

Example Question #2 : Distributive Property

Example Question #2 : Distributive Property

Example Question #3 : Distributive Property

Example Question #5 : Distributive Property

Example Question #2 : Distributive Property

Example Question #1 : Distributive Property

Example Question #2 : Distributive Property

Example Question #6 : Distributive Property

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