1. California
Standards
Preview of Grade AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used.
Also covered: 6AF1.2, 6AF3.1, 6AF3.2

2. Vocabulary
term
coefficient

3. In the expression 7x + 9y, 7x and 9y are called terms
In the expression 7x + 9y, 7x and 9y are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by plus or minus signs.
In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression.
Coefficient
Variable 7 x

4. Like terms are terms with the same variable raised to the same power
Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 w 7
Like Terms
Unlike Terms
3x and 2x
w and
5 and 1.8
5x2 and 2x
6a and 6b
3.2 and n
Only one term
contains a
variable
The exponents
are different
The variables
are different

5. Teacher Example 1: Identifying Like Terms
Identify like terms in the list.
3t 5w2 7t 9v w2 8v
Look for like variables with like powers.
3t 5w2 7t 9v w2 8v
Like terms: 3t and 7t 5w2 and 4w2 9v and 8v
Use different shapes or colors to indicate sets of like terms.
Helpful Hint

6. Student Practice 1:
Identify like terms in the list.
2x 4y3 8x 5z y3 8z
Look for like variables with like powers.
2x 4y3 8x 5z y3 8z
Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

7. To simplify an algebraic expression that contains like terms, combine like terms. Combining like terms is like grouping similar objects. x x x x x x x x + = x x x x x x x x x x = 9x 4x + 5x
To combine like terms that have variables, use the Distributive Property.
4x + 5x = (4 + 5)x = 9x

8. Teacher Example 2A & 2B: Simplifying Algebraic Expressions
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
A. 6t – 4t
6t – 4t
6t and 4t are like terms. 2t
Subtract the coefficients.
B. 45x – 37y + 87
In this expression, there are no like terms
to combine.

9. Teacher Example 2C: Simplifying Algebraic Expressions
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6
Identify like
terms.
3a2 + 5b + 11b2 – 4b + 2a2 – 6
Commutative Property.
3a2 + 2a2 + 5b – 4b + 11b2 – 6
(3 + 2)a2 + (5 – 4)b + 11b2 – 6
Distributive Property.
5a2 + b + 11b2 – 6

10. Distributive Property.
Student Practice 2A & 2B:
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
A. 5y + 3y
5y + 3y
5y and 3y are like terms. 8y
Add the coefficients.
B. 2(x2 – 13x) + 6
2x – 26x + 6 2
Distributive Property.
There are no like terms to combine.

11. Student Practice 2C:
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
C. 4x2 + 5y + 3x2 – 4y + 2x2 + 5
4x2 + 5y + 3x2 – 4y + 2x2 + 5
Identify like
terms.
4x2 + 3x2 + 2x2 + 5y – 4y + 5
Commutative Property.
Distributive Property.
( )x2 + (5 – 4)y + 5
9x2 + y + 5

12. Teacher Example 3: Geometry Application
Write an expression for the perimeter of the triangle. Then simplify the expression.
2x + 3
3x + 2 x
Write an expression using
the side lengths.
2x x x
(2x + 3x + x) + (3 + 2)
Identify and group like terms.
( )x + (3 + 2)
Distributive Property.
6x + 5

13. Write an expression using the side lengths. x + 2x + 1 + 2x + 1
Student Practice 3:
Write an expression for the perimeter of the triangle. Then simplify the expression.
2x + 1
2x + 1 x
Write an expression using
the side lengths.
x + 2x x + 1
x + 2x + 2x
Identify and group like terms.
( )x + (1 + 1)
Distributive Property.
5x + 2

14. Lesson Quiz: Part I
Identify like terms in the list.
1. a5 2a2 a3 3a 4a2
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
2. 4a + 3b + 2a
5n, 8n
2a2, 4a2
6a + 3b
9x2 + 2y

15. Lesson Quiz: Part II
3. Write an expression for the perimeter of the given figure.
2x + 3y
x + y
x + y
2x + 3y
6x + 8y

16. Lesson Quiz: Part I
Identify like terms in the list.
1. 3n2 5n 2n3 8n
2. a5 2a2 a3 3a 4a2
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
3. 4a + 3b + 2a
4. x2 + 2y + 8x2
5n, 8n
2a2, 4a2
6a + 3b
9x2 + 2y