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!