Transcript Properties of Real Numbers

The properties of real numbers help us
simplify math expressions and help us better
understand the concepts of algebra.
Some of these properties are as ancient as your teacher.
a+b=b+a
Example:
7+3=3+7
Two real numbers can be added in either
order to achieve the same sum.
Does this work with subtraction? Why or
why not?
axb=bxa
Example:
3x7=7x3
Two real numbers can be multiplied in
either order to achieve the same product.
Does this work with division? Why or why
not?
(a + b) + c = a + (b + c)
Example: (29 + 13) + 7 = 29 + (13 + 7)
When three real numbers are added, it
makes no difference which are added
first.
Notice how adding the 13 + 7 first makes
completing the problem easier mentally.
(a x b) x c = a x (b x c)
Example: (6 x 4) x 5 = 6 x (4 x 5)
When three real numbers are multiplied,
it makes no difference which are
multiplied first.
Notice how multiplying the 4 and 5 first
makes completing the problem easier.
a+0=a
Example:
9+0=9
The sum of zero and a real number equals
the number itself.
Memory note: When you add zero to a
number, that number will always keep its
identity.
a x1 =a
Example:
8 x1=8
The product of one and a number equals the
number itself.
Memory note: When you multiply any
number by one, that number will keep its
identity.
a(b + c) = ab + ac
or
a(b – c) = ab – ac
Example: 2(3 + 4) = (2 x 3) + (2 x 4)
or
2(3 - 4) = (2 x 3) - (2 x 4)
Distributive Property is the sum or
difference of two expanded products.
a + (-a) = 0
Example:
3 + (-3) = 0
The sum of a real number and its opposite
is zero.
1
𝑎 · =𝟏
𝑎
Example:
𝟒
𝟏
however,
·
a≠0
𝟏
=𝟏
𝟒
The product of a nonzero real number
and its reciprocal is one.
Go forth and use them wisely.
Use them confidently.
And use them well, my friends!