1. Warm Up Evaluate. 1. 42 16 2. |5 – 16| 11 3. –23 –8 4. |3 – 7| 4
Translate each word phrase into a numerical or algebraic expression.
5. The product of 8 and 6
8  6
6. The difference of 10y and 4
10y – 4
Simplify each fraction. 7. 8 8.

2. Simplifying Expressions
Lesson 1.7
Simplifying Expressions

3. California
Standards
1.0 Students use properties of numbers to demonstrate whether assertions are true or false Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

4. Order of Operations
When an expression contains more than one operation, the order of operations tells you which operation to perform first.
Order of Operations
First:
Perform operations inside grouping symbols.
Second:
Evaluate powers.
Third:
Perform multiplication and division from left to right.
Fourth:
Perform addition and subtraction from left to right.

5. Good To Know
Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, begin with the innermost set. Follow the order of operations within that set of grouping symbols and then work outward.
Helpful Hint
Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.

6. Examples Simplify each expression. A. 15 – 2  3 + 1 15 – 2  3 + 1
There are no grouping symbols.
15 – 6 + 1
Multiply.
9 + 1
Subtract. 10
Add.
B ÷ 2
÷ 2
There are no grouping symbols.
÷ 2
Evaluate powers. The exponent applies only to the 3.
Divide. 26
Add.

7. Simplify each expression.
The fraction bar is a grouping symbol.
Evaluate powers. The exponent applies only to the 4.
Multiply above the bar and subtract below the bar.
Add above the bar and then divide.

8. Simplify the expression.
The square root sign
acts as a grouping symbol.
Subtract.
Take the square root.
3  7
Multiply. 21 21
Multiply.

9. Parts of an Expression 4x – 3x + 2
The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.
Like terms
Constant
4x – 3x + 2

10. Parts of an Expression 1x2 + 3x
A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.
Coefficients
1x2 + 3x

11. Combining Like Terms Like Terms Unlike Terms 7x 3x 7x 4y 5a 4a 4 9a
4ab 7ab
x2y 10x2y
3a2b 4ba2
Unlike Terms
7x 4y
4 9a
3x 3x2
2a2b 3ab
6m2n mn2

12. Simplify by Combining Like Terms
1. 3x x
2. 6a + 12 – 5a – 3
x – 3 + 2y – x + 6y 9x
+ 7 a
+ 9 4
+ x
+ 8y

13. Add or subtract only the coefficients. 6.8y² – y² ≠ 6.8
Caution!
Add or subtract only the coefficients. 6.8y² – y² ≠ 6.8

14. Examples 72p and 25p are like terms. 1) 72p – 25p 72p – 25p
Subtract the coefficients.
47p
2) 0.5m + 2.5n
0.5m + 2.5n
0.5m + 2.5n
Do not combine the terms.

15. Simplify by combining like terms.
a. 16p + 84p
16p + 84p
16p + 84p are like terms.
100p
Add the coefficients.
b. –20t – 8.5t
–20t – 8.5t
20t and 8.5t are like terms.
–28.5t
Subtract the coefficients.
c. 3m2 + m3 – m2
3m2 – m2 + m3
3m2 and – m2 are like terms.
2m2 + m3
Subtract coefficients.

16. Now You Try Simplify the following by combing like terms
1) 7x + y + 3x
2) y x + 3y
3) 5 + 2(x + 8)
4) 5(a + b) + a(2 + b)
5) a + 2(4 + a)
6) 2r2 + 3rs – 5 – r2
= 10x + y
= 4y + 2x + 4
= 2x + 21
= 7a + 5b + ab
= 3a + 8
= r2 + 3rs – 5

17. Simplifying Algebraic Expressions
Use properties and operations to show that 14x + 4(2 + x) simplifies to 18x + 8.
Statements
Reasons 1.
14x + 4(2 + x) 2.
14x + 4(2) + 4(x)
Distributive Property 3.
14x x
Multiply. 4.
14x + 4x + 8
Commutative Property of Addition 5.
(14x + 4x) + 8
Associative Property of Addition 6.
18x + 8
Combine like terms.

18. Use properties and operations to show that
Check It Out!
Use properties and operations to show that
6(x – 4) + 9 simplifies to 6x – 15.
Statements
Reasons 1.
6(x – 4) + 9 2.
6x – 6(4) + 9
Distributive Property 3.
6x –
Multiply. 4.
6x – 15
Combine like terms.

19. Lesson Quiz
Simplify each expression. 2.
200 8
3. The volume of a storage box can be found using the expression lw(w + 2). Find the volume of the box if l = 3 feet and w = 2 feet.
24 ft3
Simplify each expression by combining like terms. 4.
5. 14c2 – 9c
14c2 – 9c
6. Use properties and operations to show that
24a + b² + 3a + 2b² simplifies to 27a + 3b².
Check students’ work.

20. Four suits in a deck of cards
Hearts
spades
Clubs
Diamonds