45 - week 4 - Algebra 1 pg. 33- 45

solve - (-2/3)²

(-2/3)² (-2/3)(-2/3) = 4/9

Use the commutative property to solve - 2xy² +3x³y⁵

(2)(3)(x)(x³)(y²)(y⁵) 6x⁴y⁷

Solve - (8.67)(4.8)(1/4)=

(8.67(4.8)(1/4)= 41.616 (1/4)= 41.616(.25)= 10.404

solve - -3/5 + (-2/3) =

-3/5 + (-2/3) = -9/15 + (-10/15) = -19/15 -1 4/15

solve - -7[3(6-8)]

-7[3(6-8)] = -7[3(-2)] -7[-6] 42

Simplify after removing the parentheses -[-(2-3)]

-[-(2-3)] -[-2+3] 2+-3 -1

The way in which numbers are grouped does not change their sum or product -

Associative Property

Write a formula for this situation - The circumference C of a circle equals 2 times pi,π, times the radius r.

C = 2πr

Translate into a formula - The cost C in cents for n bars of candy at 75⊄ per bar.

C = 75n

The property that says that two or more numbers can be added or multiplied n any order without changing the result.

Commutative Property

Identify the property used to manipulate this expression - 4 +0 =4

Identity ( addition)

Identify the property used to manipulate this expression - 1/2 + 1/3 = 3/6 + 3/6

Identity (multiplication)

Jason has x dollars, and Ryan has 5 more dollars than Jason. How many dollars does Ryan have? How many dollars do both boys have?

Ryan has x+5 They both have x +x + 5 or 2x +5

Identity Property

a) the sum of a number and 0 is the number; 5+0=5 b) the product of a number and 1 is the number 6x1=6

Identify the property used to manipulate this expression - 2(x+4) = (x + 4)2

communicative (multiplication)

consecutive

following in order like 1,2,3,4..

Identify the property used to manipulate this expression - 4 + (-4) =0

inverse (addition)

If the first of three consecutive numbers is x, what are the other two?

x+1 x+2

solve for z z +2/3 =6 1/6

z + 2/3 = 6 1/6 z +2/3 - 2/3 = 37/6 -2/3 z = 37/6 - 4/6 z = 33/6 z = 11/2

Find the simple interest- p = $2500 r = 12% t = 6 mo.

2500(12%)(1/2 yr.) 2500(.12)(.5) 300(.5) i = $150

Determine whether the number in parentheses is a solution to the equation. 2c + 3 = 13 (10)

2c + 3 =13 (10) 2(10) + 3 =13 20 +3 =13 23 ≠13

Use the commutative Property to solve - 2x +4y -x +5y +3x -6y

2x + 4y + (-x) + 5y +3x + (-6y) 2x + (-x) + 3x + 4y +5y +(-6y) = 4x +3y

solve 3(-2)(4)(-3)(6) / 6-8

3(-2)(4)(-3)(6) / 6-8 = -6(4)(-3)(6) / -2 -24(-3)(6) / -2 72(6) / -2 432 / -2 -216

solve 3(-4)(2)(-5)(6) / -2

3(-4)(2)(-5)(6) / -2 = -12(2)(-5)(6) / -2 -24(-5)(6) / -2 120(6) / -2 720 / -2 -360

Solve using the distributive property 3(4+5) = 3(4+5)

3(4+5) = 3(4+5) 3 x 4 + 3 x 5 =3(9) 12 + 15 = 3(9) 27 = 27

Solve using the associative property - 3(4x5) =(3x4)5

3(4x5) =(3x4)5 3(20) =12(5) 60 = 60

Write a formula for this story problem - The product of two numbers equals 36. If one number is x, what is the other number?

36/x

Determine whether the number in parentheses is a solution to the equation. 5 + r = 9 (4)

5+r =9 (4) 5+4 = 9 9 = 9

Translate into a formula - The cost D in dollars for n bars of candy at $.75 per bar

D = 0.75n

Identify the property used to manipulate this expression - 2(x + 4) = 2x +8

Distributive

A property indicating a special way in which multiplication is applied to addition or two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b+c) = ab +ac

Distributive Property