warm up add. 1. 427 + 35
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Warm Up Add. 1. 427 + 35. 1.80. 2. 1.06 + 0.74. 462. 3. 10. Multiply. 4. 25(8). 5. 1.3(22). 28.6. 200. 6. The Distributive Property is used with Addition to Simplify Expressions. - PowerPoint PPT PresentationTRANSCRIPT
Holt Algebra 1
1-7 Simplifying Expressions
Warm UpAdd.
1. 427 + 35 2. 1.06 + 0.74
3.
Multiply.
4. 25(8)
6.
5. 1.3(22) 28.6200
10
462 1.80
Holt Algebra 1
1-7 Simplifying Expressions
The Distributive Property is used with Addition to Simplify Expressions.
The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.
Holt Algebra 1
1-7 Simplifying Expressions
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.
4x – 3x + 2
Like terms Constant
Holt Algebra 1
1-7 Simplifying Expressions
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.
1x2 + 3x
Coefficients
Holt Algebra 1
1-7 Simplifying Expressions
Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression.
7x2 – 4x2 = (7 – 4)x2
= (3)x2
= 3x2
Factor out x2 from both terms.
Perform operations in parenthesis.
Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.
Holt Algebra 1
1-7 Simplifying Expressions
Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
72p – 25p
72p – 25p
47p
72p and 25p are like terms.
Subtract the coefficients.
Holt Algebra 1
1-7 Simplifying Expressions
Example 3B: Combining Like Terms
Simplify the expression by combining like terms.
A variable without a coefficient has a coefficient of 1.
Write 1 as .
Add the coefficients.
and are like terms.
Holt Algebra 1
1-7 Simplifying Expressions
Example 3C: Combining Like Terms
Simplify the expression by combining like terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
Do not combine the terms.
Holt Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p
100p
16p + 84p are like terms.
Add the coefficients.
3b. –20t – 8.5t2
–20t – 8.5t2 20t and 8.5t2 are not like terms.
–20t – 8.5t2 Do not combine the terms.
3m2 + m3 3m2 and m3 are not like terms.
3c. 3m2 + m3
Do not combine the terms.3m2 + m3
Holt Algebra 1
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 14x + 4(2 + x). Justify each step.
14x + 4(2) + 4(x) Distributive Property
Multiply.
Commutative Property
Associative Property
Combine like terms.
14x + 8 + 4x
(14x + 4x) + 8
14x + 4x + 8
18x + 8
14x + 4(2 + x)1. 2. 3. 4. 5. 6.
Procedure Justification
Holt Algebra 1
1-7 Simplifying Expressions
6(x) – 6(4) + 9 Distributive Property
Multiply.Combine like terms.
6x – 24 + 9
6x – 15
6(x – 4) + 91. 2. 3. 4.
Procedure Justification
Check It Out! Example 4a
Simplify 6(x – 4) + 9. Justify each step.
Holt Algebra 1
1-7 Simplifying Expressions
–12x – 5x + x + 3a Commutative Property
Combine like terms.–16x + 3a
–12x – 5x + 3a + x1. 2. 3.
Procedure Justification
Check It Out! Example 4b
Simplify −12x – 5x + 3a + x. Justify each step.
Holt Algebra 1
1-7 Simplifying Expressions
Lesson Quiz: Part II
Simplify each expression by combining like terms. Justify each step with an operation or property.
7. 301x – x
8. 24a + b2 + 3a + 2b2
5.
300x
27a + 3b2
6. 14c2 – 9c 14c2 – 9c