Order of Operations
7 + 10 × 5 + 4 =
7 + 10 × 5 + 4 =
7 + 50 + 4 =
61
Expand 34 (Write it as a product.)
34
= 3 • 3 • 3• 3
x cubed times y squared
x cubed times y squared
x3y2
Which property is illustrated by:
a + b = b + a
a + b = b + a
The Commutative Property of Addition
In the expression, 3X + 2Y + 5X , 3X and 5X are called __________ terms.
In the expression, 3X + 2Y + 5X , 3X and 5X are called __________ terms.
In the expression, 3X + 2Y + 5X , 3X and 5X are called LIKE terms.
17 – 8 ÷ 2 x 4 + 1 =
17 – 8 ÷ 2 x 4 + 1 =
17 –4 x 4 + 1 =
17 –16 + 1 =
1+1 =
2
Expand W5 (Write it as a product.)
W5
= W • W • W • W • W
x less than 2 cubed
x less than 2 cubed
23 - x
Which property is illustrated by:
(a • b) • c = a • (b • c)
(a • b) • c = a • (b • c)
The Associative Property of Multiplication
Evaluate X + Y – Z if X = 7; Y = 4; and Z = 3
Evaluate X + Y – Z if X = 7; Y = 4; and Z = 3
X + Y – Z
= 7 + 4 - 4
= 11 - 4
= 7
4 • 10/5 – 6 + 2
4 • 10/5 – 6 + 2
4 • 2 – 6 + 2
8 – 6 + 2
2 + 2
4
Simplify 2•2•2•d•d•x•x•x•y•y•y•y
2•2•2•d•d•x•x•x•y•y•y•y
= 23 • d2 • x3 •y4
= 8d2 x3 y4
The quantity 2x plus 1 to the fourth power
The quantity 2x plus 1 to the fourth power
(2x + 1)4
Is division commutative? Explain your answer.
Is division commutative? Explain your answer.
Division is NOT commutative because if you change the order of the division, you will change the answer. For example: 10 / 2 = 5 , but 2 / 10 = 1/5.
Explain the difference between an expression and an equation.
Explain the difference between an expression and an equation.
An expression is a number sentence like 2x - 4, but an equation is a number sentence with an equal sign like 2x - 4 = 10.
(10-(5-2))2
(10-(5-2))2
(10-(3))2
(7)2
49
Simplify f•2•2•d•f•x•x•f•y•f•y•y
f•2•2•d•f•x•x•f•y•f•y•y
= 22 • d • f4 • x2 • y3
=4 d f4 x2y3
A pair of shoes that costs x dollars is discounted by 3/10 of its price. Write an expression for the discounted price.
A pair of shoes that costs x dollars is discounted by 3/10 of its price. Write an expression for the discounted price.
x - 3/10x
1x - 3/10 x
10/10 x - 3/10 x
7/10 x
Using the properties, simplify 2A + 11B - 5B + 7A
2A + 11B - 5B + 7A
= 9A + 11B - 5B
= 9A + 6B
Add 2/3 + 5/6
Add 2/3 + 5/6
2/3 + 5/6
= (2/3)(2/2) + 5/6
= 4/6 + 5/6
= 9/6
= 9/6 (divide the num. and denom. by 3)
= 3/2 or 1 and 1/2.
What are the 4 steps of the order of operations?
1. Parentheses
2. Exponents
3. Multiply & Divide from left to right
4. Add & Subtract from left to right
Expand (R2X)3
(R2X)3
= (R2X) • (R2X) • (R2X)
= R6X3
Write an expression with three terms. The coefficient of the first term is -3 and of the second term is 1.
The last term is the constant -4. The variable part of the first term is x squared, and the variable of the second term, x.
Write an expression with three terms. The coefficient of the first term is -3 and of the second term is 1. The last term is the constant -4. The variable part of the first term is x squared, and the variable of the second term, x.
-3x2 + x - 4
Using the Distributive Property, fill in the blanks:
4a + 20 = ____ (a + ____ )
Using the Distributive Property, fill in the blanks:
4a + 20 = ____ (a + ____ )
4a + 20 = 4 (a + 5 )
Draw a rectangle to model:
3 (x + y )
Find the perimeter and the area.
Draw a rectangle to model:
3 (x + y )
Find the perimeter and the area.
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