po d basicadvanced 4b + 6 b= 5, c= 3, d=7 (10c ÷b) 2 + d 4(5) + 6 20 + 6 26 (10(3) ÷5) 2 + 7 (30...
TRANSCRIPT
POD
basic advanced
4b + 6
b= 5, c= 3, d=7
(10c ÷b)2 + d
4(5) + 620 + 6
26
(10(3) ÷5)2 + 7(30 ÷5)2 + 7(6)2 + 736 + 7
43
PODb= 5, c= 3, d=7
basic advanced
b + 4c × d (b2 × 4 + 44) ÷ (4c)
5 + 4(3) × 75 + 12 × 7
5 + 84 89
(52 × 4 + 44) ÷ (4 × 3)(25 × 4 + 44) ÷ (4 × 3)
(100 + 44) ÷ (4 × 3)
(144) ÷ (4 × 3)(144) ÷ (12)
12
POD
State whether the conjecture is true or false. If false, provide a counterexample.
Subtraction of whole numbers is associative
False
(8−5) − 3 ≠ 8 − (5−3)
Properties of OperationsThe Commutative Property states that the order in which numbers are added or multiplied does not change the sum or product.
a + b = b + a a × b = b × a
The Associative Property states that the way in which numbers are grouped when they are added or multiplied does not change the sum or product.
a + (b+c) = (a+ b) + c a × (b×c) = (a × b) × c
The Additive Identity Property states that when 0 is added to any number, the sum is the number.
a + 0 = a 0 + a = a
The Multiplicative Identity Property states that when any number is multiplied by 1, the product is the number.
a × 1 = a 1 × a = a
The Multiplicative Property of Zero states that when any number is multiplied by 0, the product is 0.
a × 0 = 0 0 × a = 0
The Distributive Property states that to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.
a( b + c ) = ab + ac a( b – c ) = ab − ac
2 ( y + 2) = 2(y) +2(2)
= 2y + 4
The expressions 2(y+2) and 2y+4 are equivalent expressions. No matter what y is, these expressions have the same value.
Whiteboard time
Name the property shown by the statement:
2 × (5 × n) = (2 × 5) × n
Associative Property
Whiteboard time
Name the property shown by the statement:
42 + b + y = 42 + y + b
Commutative Property
Whiteboard time
Name the property shown by the statement:
3m × 0 × 5m = 0
Multiplicative Property of Zero
Whiteboard time
Name the property shown by the statement:
(3 × m) × 2 = 2 × (3 × m)
Commutative Property
Whiteboard time
Name the property shown by the statement:
8(-9 + 4) = 8(-9) + 8(4)
Distributive Property
Simplify each expression
(7 + g) + 5(7 + g) + 5 = (g + 7) + 5
= g + (7 + 5) = g + 12
Commutative Property of Multiplication
Associative Property of Multiplication
Simplify each expression
(m × 11) × m(m × 11) × m = (11 × m) × m
= 11 × (m × m)
= 11 × m2
Commutative Property of Multiplication
Associative Property of Multiplication
= 11m2
Simplify each expression
a (9 b) a (9 b) = (a 9) b (9 a) b
9 (a b)
Associative Property of Multiplication
commutative Property of Multiplication
= 9ab
Associative Property of Multiplication
Simplify each expression
9c + (8+3c)9c + (8+3c) = 9c + (3c +8)
(9c + 3c) +8
12c +8
Associative Property of Multiplication
commutative Property of Multiplication
Simplify each expression
6 + (d + 8)6 + (d + 8)= 6 + (8 + d)
(6 + 8) +d
14 + d
Associative Property of Multiplication
commutative Property of Multiplication