Identities and Properties

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Pre-Algebra › Identities and Properties

Questions 1 - 10

1

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

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

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

demonstrates this property, so it is the correct choice.

2

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

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

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

demonstrates this property, so it is the correct choice.

3

Which of the following displays the commutative property of multiplication?

$a \cdot b = b \cdot a$

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

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

$a \cdot 1 = a$

$a \cdot 0 = 0$

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.

4

Simplify the expression.

Explanation

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

Simplify.

5

Simplify the expression.

Explanation

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

6

Simplify the expression.

Explanation

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

7

Which of the following displays the commutative property of multiplication?

$a \cdot b = b \cdot a$

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

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

$a \cdot 1 = a$

$a \cdot 0 = 0$

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.

8

Simplify the expression.

Explanation

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

Simplify.

9

What digit is in the tenths place?

Explanation

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

10

What digit is in the thousandths place?

$9\textup,834.172$

Explanation

The thousandths place will always be the third digit to the right of the decimal point.

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