Easy Algebra Step-by-Step

Numbers of Algebra 11

Examples

66 =− 666 = 0

74 .. 4373743 =− 74 .. 4373777. 4343 = 0

10. Multiplicative Inverse Property. For every nonzero real
    number a, there is a real number called its multiplicative
    inverse, denoted a−^1 or^1
    a

, such that

aa a

a

a−^1 ==aa⋅

1

1 and a−^1 ⋅ ==⋅

a^11

a

a.

This property guarantees that every real

number, except zero, has a multiplicative

inverse (its reciprocal) whose product with

the number is 1.

11. Distributive Property. a(b + c) = a · b + a · c and (b + c) a = b · a + c · a.
    This property says that when you have a number times a sum (or a sum
    times a number), you can either add fi rst and then multiply, or multiply fi rst
    and then add. Either way, the fi nal answer is the same.
    Examples

(^3) () (^105) can be computed two ways:
add fi rst to obtain 3 () 105 = 313 545 or
multiply fi rst to obtain 3(10 + 5) = 311030 ⋅ 535 0115545
Either way, the answer is 45.
1
4

3

4

⎛ + 8

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ can be computed two ways:

add fi rst to obtain^1

4

3

4

⎛ + 8188

⎝

⎛⎛⎛⎛

⎝⎝

⎛⎛⎛⎛ ⎞

⎠

⎞⎞⎞⎞

⎠⎠

⎞⎞⎞⎞ 1 ⋅ or

multiply fi rst to obtain

1

4

3

4

⎝⎝⎛⎛⎛⎝⎛⎛⎛⎛⎛⎛ + ⎠⎞⎞⎞⎞⎞⎠⎠⎞⎞⎞⎞^8 =

1

4

8

3

4

⋅+ ⋅=+= 8268

Either way, the answer is 8.

Problem State the fi eld property that is illustrated in each of the

following.

a. 0 11252525 = 11. 25

b. ())∈ real numbers

Notice that when you add the additive

inverse to a number, you get the additive

identity as an answer, and when you

multiply a number by its multiplicative

inverse, you get the multiplicative identity

as an answer.

The distributive property is the only fi eld

property that involves both addition and

multiplication at the same time. Another

way to express the distributive property is

to say that multiplication distributes over

addition.

The symbol ∈ is read “is an

element of.”