This chapter covers the laws used for solving algebraic equations.
Given an equation, DETERMINE the governing
algebraic law from the following:
Most of the work in basic mathematics completed by DOE facility personnel involves real
numbers, as mentioned in the last section. As a result, one should be very familiar with the basic
laws that govern the use of real numbers. Most of these laws are covered under the general area
Many operations on real numbers are based on the commutative, associative, and distributive
laws. The effective use of these laws is important. These laws will be stated in written form as
well as algebraic form, where letters or symbols are used to represent an unknown number.
The commutative laws indicate that numbers can be added or multiplied in any order.
Commutative Law of Addition: a + b = b + a
Commutative Law of Multiplication: a(b) = b(a)
The associative laws state that in addition or multiplication, numbers can be grouped in any
Associative Law of Addition: a+(b+c) = (a+b)+c
Associative Law of Multiplication: a(bc) = (ab)c
The distributive laws involve both addition and multiplication and state the following.
Distributive law: a(b + c) = ab + ac
Distributive law: (a + b)c = ac + bc