The document summarizes key rules and properties for operations on real numbers including addition, subtraction, multiplication, and division. Some key points are: 1) The additive inverse of a number a is -a. -(-a) = a. Absolute value is the distance from 0 on the number line. 2) To add numbers with the same sign, add their absolute values and use the common sign. To add numbers with opposite signs, subtract their absolute values and use + if the positive number has a larger absolute value, and - if the negative number has a larger absolute value. 3) Subtraction can be written as addition of an additive inverse, for example a - b = a + (-

1. Operation/Property Rule Note
Additive Inverse The additive inverse of a is -a
Double Negative -(-a) = a
Absolute Value Absolute value is distance
from 0 on the number line.
Adding two numbers Add their absolute values and
with the same sign put the common sign in front.
Adding two numbers Subtract their absolute values. Sum of 2 positive numbers is
with opposite signs positive.
Answer "+" if positive number
Sum of 2 negative numbers is
has larger absolute value. negative.
Answer "-" if negative number In a + b = c, a, b, and c
has larger absolute value. areterms.
Subtraction a - b = a + (-b)
Multiplication Product of two numbers with Product is the result from
like signs is positive. multiplying.
In a x b = c, a and b
Product of two numbers with are factorsand c is
opposite signs is negative. the product.
Multiplicative ax0=0
property of zero 0xa=0
Division Quotient of two numbers with Quotient is the result from
like signs is positive. dividing.
Quotient of two numbers with
opposite signs is negative.
For real numbers a, b, and c:
Property Addition Multiplication
Commutative a+b=b+a ab = ba
Associative (a + b) + c = a + (b + c) (ab)c = a(bc)
Identity a+0=a ax1=a

2. 0+a=0 1xa=a
0 is the additive 1 is the multiplicative
identity element identity element
Inverse a + (-a) = 0
(-a) + a = 0
0 is the additive inverse
or opposite of a
1 is the multiplicative inverse
or reciprocal of a, a nonzero
Distributive a(b + c) = ab + ac
(of multiplication over addition) a(b + c + d + ... + n) = ab + ac + ad + ... + an
Some Useful Rules
For real numbers a, b, c, and d:
Note
Invert
and
Multiply