Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

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Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6

Transcript of Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

Page 1: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

Addition, Subtraction, and Multiplication

Chapter 4 Sections 1-6

Page 2: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

Simplify the expression within the grouping symbols.

Then simplify powers.Then simplify products and quotients in order

from left to right.Then simplify sums and differences in order from

left to right.

In other words, follow the Acronym PEMDAS:Please Excuse My Dear Aunt Sally

Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction

Page 3: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

Monomial - an expression that is either a number, a variable, or the product of a number and one or more variables

Polynomial - the sum of one or more monomials Binomial - a polynomial with two terms Trinomial - a polynomial with three terms

Coefficient - the numerical value being multiplied in front of the variable

Degree Monomial - the sum of the exponents of each variable Polynomial - the greatest of the degrees of a

polynomial’s terms after it has been simplified.

Page 4: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

Line up the like terms of each polynomial, keeping the sign with each term.Like Terms – monomials with the same variables

raised to the same exponents

Add or subtract the coefficients of like terms, based on the sign of the term

2 35 4 3x x y 3 2 5 13x y

2 35 6 8 13x x y

2 411 2 4a b 2 4 (2 5 1)a b 2 49 7 5a b

Notice we subtract each term of the second polynomial.

Page 5: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

“Popcorn rule” # 1: The Product of Powers

Same base means you add the exponents.

Examples:

m n m na a a

3 5x x 8x 2 45 3y y 615y

2 10 15 42 4a b a b 17 148a b

Page 6: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

3x

Find the total surface area of this object.Remember: total surface area is the sum of the area of each face of the figure

x

xx

x

Page 7: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

3x

Total Surface Area = 12•3x2 + 10•x2 = 46x2

Find the total surface area of this object.Remember: total surface area is the sum of the area of each face of the figure

The surface area of each “panel” or side face of the figure is 3x•x, or 3x2. There are 12 of these.

The area for 1 square of the top and bottom of the figure is x•x, or x2. There are 10 of these.

x

xx

x

x

3x

xx

Page 8: Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.

“Popcorn rule” # 2: The Power of Powers

Two exponents next to each other means you multiply them.

Example:

“Popcorn rule” # 3: The Power of a Product

Raise each factor of the product to the power.

Example:

( )m n m na a

3 5( )x 15x

( )m m nab a b

2 3(5 )xy 3 6125x y