Bell Work What is the difference between isosceles, scalene and equilateral?

Answer: Isosceles: 2 sides equal Scalene: No sides equal Equilateral: All sides equal

Lesson 21: Distributive Property, Order of Operations

These two formulas can be used to find the perimeter of a rectangle. P = 2(l + w) P = 2l + 2w Using the first formula we add the length and width then double the sum. Using the second formula we double the length and width and then add the products.

Both formulas produce the same result because the formulas are equivalent. 2(l + w) = 2l + 2w

Distributive Property*: a(b + c) = ab + ac Multiplication is distributive over addition.

The distributive property works in two ways. We can expand and we can factor. We expand 2(a + b) and get 2a + 2b We factor 2a + 2b and get 2(a + b)

We factor an expression by writing the expression as a product of two or more numbers or expressions.

Example: How can we factor the expression ? Explain and rewrite the expression.

Answer: Five is a factor of both 15 and 10. when it is factored out, the expression can be written as: 5(3 + 2)

Example: Expand: 3(w + m)

Answer: 3w + 3m

Example: Factor: ax + ay

Answer: a(x + y)

Example: Expand: 3(x + 2)

Answer: 3x + 6

Order of Operations: If there is more than one operation in an expression we follow this order. 1. Simplify within parentheses 2. Simplify exponent expressions 3. Multiply and divide in order from left to right 4. Add and subtract in order from left to right

The first letters in all of the underlined words are also the first letters of the words in the following sentence, which can help us remember this order. Please Excuse My Dear Aunt Sally

Example: Simplify: 20 – 2  3 + (7 + 8) ÷5 2

Answer: 20 – 2  3 + (7 + 8) ÷ 5 20 – 2  ÷ 5 20 – 2  ÷ 5 20 –

Brackets [ ] and braces { } are used as grouping symbols like parentheses. We use brackets to enclose parentheses and braces to enclose brackets. To simplify expressions with multiple grouping symbols, we begin from the inner most symbols

Example: Simplify: 10 – {8 – [6 – (5 – 3)]}

Answer: 10 – {8 – [6 – (5 – 3)]} 10 – {8 – [6 – 2]} 10 – {8 – 4} 10 – 4 6

Absolute value symbols, division bars, and radicals sometimes group multiple terms as well.

Example: Simplify: 2 – 7

Answer: = 5

Example: √(9 + 16)

Answer: 5

Example: 12 

Answer: = 24

HW: Lesson 21 #1-30 Due Tomorrow