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1-2 Properties of Real Numbers

Name the sets of numbers to which each number belongs.

2.

SOLUTION:

The number

is a real number. Since

can be expressed as a ratio

where a and b are integers and b is not 0 it

is also a rational number. It is not a part of the set {…–2, –1, 0, 1, 2, …} so it is not an integer. Since it is not a part

of the set {…0, 1, 2, 3, …} it is not a whole number or a natural number.

Q, R

4. –12

SOLUTION:

The number -12 is a real number. Since -12 can be expressed as a ratio where a and b are integers and b is not 0

it is also a rational number. It is part of the set {…–2, –1, 0, 1, 2, …} so it is an integer. It is not part of the set {…0,

1, 2, 3, …} so it is not a whole number and since it is not a whole number it is not a natural number either.

Z, Q, R

Name the property illustrated by each equation.

6.

SOLUTION:

Distributive Property; the Distributive Property states that there is no difference between a term multiplied by each

term in a group and the term multiplied by the group.

8.

SOLUTION:

Distributive Property; the Distributive Property states that there is no difference between a term multiplied by each

term in a group and the term multiplied by the group.

Find the additive inverse and multiplicative inverse for each number.

10.

SOLUTION:

Since

, the additive inverse of

is

.

is .

Since

, the multiplicative inverse of

12.

SOLUTION:

Since

, the additive inverse of

is

.

Since

, the multiplicative inverse of

is

.

Simplify each expression.

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