It is important to be familiar with the properties in this tutorial. They lay the foundation that you need to work with equations, functions, and formulas all of which are covered in later tutorials, as well as, your algebra class. In some cases, it isn't very helpful to rewrite an expression, but in other cases it helps to write an equivalent expression to be able to continue with a problem and solve it. An equivalent expression is one that is written differently, but has the same value. The properties on this page will get you up to speed as to how you can write expressions in equivalent forms.
a + b = b + a and
ab = ba
The two sides are called equivalent expressions because they look different
but have the same value.
2.5x + 3y = 3y + 2.5x.
The Associative Properties of
Addition and Multiplication
a + (b + c) = (a + b) + c and
a(bc) = (ab)c
At this point it is good to remind you that
both the commutative and associative properties do NOT work for subtraction
3: Use the associative property to write an equivalent
expression to (a + 5b) + 2c.
(a + 5b) + 2c = a + (5b + 2c).
(1.5x)y = 1.5(xy)
a(b + c) = ab + ac
(b + c)a = ba + ca
Remember terms are separated by + and -.
This idea can be extended to more than two terms in the ( ).
5: Use the distributive property to write 2(x - y) without parenthesis.
The additive identity is 0
a + 0 = 0 + a = a
Multiplication identity is 1
a(1) = 1(a) = a
For each real number a, there is a unique real number,
denoted -a, such that
a + (-a) = 0.
For each real number a, except 0, there is a unique real number such that
These two inverses will come in big time handy
when you go to solve equations later on. Keep them in your memory
bank until that time.
8: Write the opposite (or additive inverse) and
reciprocal (or multiplicative inverse) of -3.
When you take the reciprocal, the sign of the original number stays
intact. Remember that you need a number that when you multiply times
the given number you get 1. If you change the sign when you take
the reciprocal, you would get a -1, instead of 1, and that is a no no.
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1b: Use a commutative property to write an equivalent expression.
Practice Problems 2a - 2b: Use an associative property to write an equivalent expression.
2a. (a + b)
(answer/discussion to 2a)
(answer/discussion to 2b)
Practice Problems 3a - 3b: Use the distributive property to find the product.
Practice Problems 4a - 4b: Write the opposite (additive inverse) and the reciprocal (multiplicative inverse) of each number.
(answer/discussion to 4a)
(answer/discussion to 4b)
Need Extra Help on these Topics?
This webpage helps with the commutative property.
This webpage helps with the associative property.
This webpage helps with the distributive property.
This webpage goes over the commutative, associative, and distributive properties.
Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.
Last revised on July 24, 2011 by Kim Seward.
All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.