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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

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

Example Questions

Example Question #5 : Associative Property Of Addition

Which of the following displays the associative property of addition?

Possible Answers:

(a +b) + c = a + (b + c)

a + 0 = a

$2(a + b) = 2a +2b$

ab = a+b

(a + b) = a + b

Correct answer:

(a +b) + c = a + (b + c)

Explanation:

The associative property of addition states that you can group, or "associate," additive terms in any order and still get the same answer. Here (a +b) + c = a + (b + c) does just that: whether you add $a+b$ first and then add $c$ , or add $b+c$ first and then $a$ , as long as you add those three terms you'll get the same answer.

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Example Question #1 : Associative Property Of Multiplication

If the below expression is written using the Associative Property of Multiplication, what are the values of and ?

$\left ( p \times 11\right ) \times 8 = 13 \times \left ( 11 \times q\right )$

Possible Answers:

$p=11,\ q=13$

$p=8,\ q=13$

$p=13,\ q=11$

$p=11,\ q=8$

$p=13,\ q=8$

Correct answer:

$p=13,\ q=8$

Explanation:

The rule for Associative Property of Multiplication is $\left ( a \times b\right )\times c = a \times \left ( b \times c\right )$

Using this rule, we can determine that for the given expression $\left ( p \times 11\right )\times 8 = 13 \times \left ( 11 \times q\right )$ ,

$p=13\ and\ q=8$

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Example Question #2 : Associative Property Of Multiplication

Which set of equations illustrates the Associative property of Multiplication?

Possible Answers:

8(x+3)=8*x+8*3

a*1=a

The answer is not present.

(6x^2*8)4x=6x^2(8*4x)

8x*7x^2=7x^2*8x

Correct answer:

(6x^2*8)4x=6x^2(8*4x)

Explanation:

8(x+3)=8*x+8*3 is the distributive property. Multiply each term in the parenthesis by the outside term.

8x*7x^2=7x^2*8x is the Commutative property of Multiplication. The order of two like terms being multiplied does not change the product.

a*1=a is the Multiplicative Identity property. Anything multiplied by 1 does not change.

${\color{Green} (6x^2*8)4x=6x^2(8*4x)}$ is Associative property of Multiplication. The grouping of terms does not change their product as long as all terms remain in the equation. Try the green equation without the variables to see for yourself.

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Example Question #3 : Associative Property Of Multiplication

Which of the following best represents the associative property of multiplication?

Possible Answers:

$(A\times B)\times C = A\times (B\times C)$

$(6)+(9\cdot Y) = (9\cdot Y)+(6)$

$3\times 4=12$

2(3x+3y) = 2(3x)+2(3y)

$X^2 = X\cdot X$

Correct answer:

$(A\times B)\times C = A\times (B\times C)$

Explanation:

The property states that changing the order of multiplying any two numbers will not change the final answer.

$X\cdot Y = Y \cdot X$

Looking at the answer choices:

The answer $(A\times B)\times C = A\times (B\times C)$ is the best choice.

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Example Question #3 : Associative Property Of Multiplication

Which of the following displays the associative property of multiplication?

Possible Answers:

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

$a \cdot 1 = a$

$a \cdot b = ab$

$a \cdot 0 = 0$

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

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:

-2

-6

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 #1 : How To Use The Distributive Property In Pre Algebra

Simplify the expression.

(-x+2)(-xy)

Possible Answers:

2x^3y^2

-2x^3y^2

x^2y-2xy

-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:

10x+8x^2+y

10x+6x^2+2xy

10x+8x^2+2xy

5+6x+y

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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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #5 : Associative Property Of Addition

Example Question #1 : Associative Property Of Multiplication

Example Question #2 : Associative Property Of Multiplication

Example Question #3 : Associative Property Of Multiplication

Example Question #3 : Associative Property Of Multiplication

Example Question #1 : Distributive Property

Example Question #2 : Distributive Property

Example Question #2 : Distributive Property

Example Question #1 : How To Use The Distributive Property In Pre Algebra

Example Question #5 : Distributive Property

All Pre-Algebra Resources

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