### About Properties of Real Numbers:

Test Objectives
• Demonstrate an understanding of the commutative property
• Demonstrate an understanding of the associative property
• Demonstrate an understanding of the inverse properties
• Demonstrate the ability to rewrite a product as a sum using the distributive property
• Demonstrate the ability to rewrite a sum as a product using the distributive property
Properties of Real Numbers Practice Test:

#1:

Instructions: Rewrite each using the commutative property.

$$a)\hspace{.2em}6 + 5$$

$$b)\hspace{.2em}(-2) \cdot (-8)$$

$$c)\hspace{.2em}x + y$$

$$d)\hspace{.2em}a \cdot b$$

#2:

Instructions: Rewrite each using the associative property.

$$a)\hspace{.2em}(4 + 9) + 3$$

$$b)\hspace{.2em}2(7 \cdot 5)$$

$$c)\hspace{.2em}(x + y) + z$$

$$d)\hspace{.2em}a(b \cdot c)$$

#3:

Instructions: Find the number required to obtain a 0 through addition and a 1 through multiplication.

$$a)\hspace{.2em}{-12}$$

$$b)\hspace{.2em}\frac{1}{5}$$

$$c)\hspace{.2em}x$$

#4:

Instructions: Rewrite each product as a sum.

$$a)\hspace{.2em}{-3}(x - y)$$

$$b)\hspace{.2em}6(x^2 - 2y + z)$$

#5:

Instructions: Rewrite each sum as a product.

$$a)\hspace{.2em}8x - 4xy$$

$$b)\hspace{.2em}2x^2 + 10xz$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}6 + 5=5 + 6$$

$$b)\hspace{.2em}(-2) \cdot (-8)=(-8) \cdot (-2)$$

$$c)\hspace{.2em}x + y=y + x$$

$$d)\hspace{.2em}a \cdot b=b \cdot a$$

#2:

Solutions:

$$a)\hspace{.2em}(4 + 9) + 3=4 + (9 + 3)$$

$$b)\hspace{.2em}2(7 \cdot 5)=(2 \cdot 7) \cdot 5$$

$$c)\hspace{.2em}(x + y) + z=x + (y + z)$$

$$d)\hspace{.2em}a(b \cdot c)=(a \cdot b) \cdot c$$

#3:

Solutions:

$$a)\hspace{.2em}12, -\frac{1}{12}$$

$$b)\hspace{.2em}-\frac{1}{5}, 5$$

$$c)\hspace{.2em}{-x}, \frac{1}{x}, x \ne 0$$

#4:

Solutions:

$$a)\hspace{.2em}{-3}x + 3y$$

$$b)\hspace{.2em}6x^2 - 12y + 6z$$

#5:

Solutions:

$$a)\hspace{.2em}4x(2-y)$$

$$b)\hspace{.2em}2x(x + 5z)$$