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Pre-Algebra : Identities and Properties

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Example Questions

Example Question #11 : Identities And Properties

Which of the following displays the commutative property of multiplication?

Possible Answers:

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

$a \cdot 1 = a$

$a \cdot 0 = 0$

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

$a \cdot b = b \cdot a$

Correct answer:

$a \cdot b = b \cdot a$

Explanation:

The commutative property of multiplication states that 2 numbers can be multiplied in any order. Therefore,

$a \cdot b = b \cdot a$

displays the commutative property of multiplication.

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Example Question #11 : Identities And Properties

Which property is illustrated by the example?

(3+2)+4=3+(2+4)

Possible Answers:

Commutative property of addition

Inverse property of addition

Zero property

Associative property of addition

Correct answer:

Associative property of addition

Explanation:

The associative property of addition states:
(a+b)+c=a+(b+c)

When considering only addition and subtraction, the order of operations does not matter.

(3+2)+4=3+(2+4)

(3+2)+4=5+4=9

3+(2+4)=3+6=9

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Example Question #2 : Associative Property Of Addition

Simplify.

4(a+2) -3a+5

Possible Answers:

15a

a+5

6a+9

a+13

-a+7

Correct answer:

a+13

Explanation:

Working left to right use the distributive property by multiplying the 4 to each term in parentheses.

4(a+2)-3a+5

$(4a)+(4\times 2)-3a+5$

4a+8-3a+5

Now, use the associative property to group like terms. Note that -3a+5 cannot be combined because they are not like terms.

(4a-3a)+(8+5)

Like terms can be combined with addition or subtraction.

a+13

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Example Question #12 : Identities And Properties

What property can be applied to the following expression?

$\left ( 8 + 4\right ) + 11 = 8 + \left ( 4 + 11\right )$

Possible Answers:

Commutative of Addition

Associative of Multiplication

Additive Inverse

Additive Identity

Associative of Addition

Correct answer:

Associative of Addition

Explanation:

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

Expression given in the question is: $\left ( 8 + 4\right ) + 11 = 8 + \left ( 4 + 11\right )$

Hence the property is Associative of Addition.

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Example Question #13 : Identities And Properties

Use the "Associative of Addition" property to write the below expression in a different way.

$\left ( x + 2\right ) + y$

Possible Answers:

$\left ( 2 + x\right ) + y$

$y + \left ( x + 2\right )$

$x + \left ( 2 + y\right )$

$2 + \left ( x + y\right )$

$\left ( x + y\right ) + 2$

Correct answer:

$x + \left ( 2 + y\right )$

Explanation:

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

Using this rule, the expression $\left ( x + 2\right ) + y$ can be written as $x + \left ( 2 + y\right )$

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Example Question #13 : Identities And Properties

What property is being demonstrated?

3+(5+2)=(3+5)+2

Possible Answers:

PEMDAS

Distribution Property

Communitive Property of Addition

Associative Property of Addition

Correct answer:

Associative Property of Addition

Explanation:

The Associative Property of Addition says that when we add more than two numbers the grouping of the addends does not change the sum.

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Example Question #7 : How To Add Fractions

Which of the following statements demonstrates the associative property of addition?

Possible Answers:

2.5+5= 5+2.5

2.5 + 0 = 2.5

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

None of the examples in the other responses demonstrates the associative property of addition.

2.5+ (-2.5) = 0

Correct answer:

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

Explanation:

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

demonstrates this property, so it is the correct choice.

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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 #14 : Identities And Properties

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:

$p=11,\ q=8$

$p=8,\ q=13$

$p=13,\ q=11$

$p=11,\ q=13$

$p=13,\ q=8$

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:

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

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

The answer is not present.

a*1=a

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

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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Pre-Algebra : Identities and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Identities And Properties

Example Question #11 : Identities And Properties

Example Question #2 : Associative Property Of Addition

Example Question #12 : Identities And Properties

Example Question #13 : Identities And Properties

Example Question #13 : Identities And Properties

Example Question #7 : How To Add Fractions

Example Question #5 : Associative Property Of Addition

Example Question #14 : Identities And Properties

Example Question #2 : Associative Property Of Multiplication

All Pre-Algebra Resources

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