This lesson introduces students to basic arithmetic operations like identity, commutative, and associative properties. It provides examples of applying these properties to multiplication and addition. Students are asked to simplify expressions using the different properties and solve systems of equations to find the values of variables.

1. LESSON 2
OB J : S T U D E N T S WI L L I D E N T I F Y T H E OP E R A T ION S OF
A R I T HME T I C.

2. NOTES
• Inverse = the opposite ex. Inverse of 7 is -7
• Property of 0 for multiplication a x 0 = 0
• Identity property of multiplication (IPM) a x 1 = a
• Identity property of addition (IPA) a + 0 = a
• Commutative property of multiplication (CPM) ab=ba
• Commutative property of addition (CPA) a+b = b+a
• Associative property of multiplication (APM) (a x b)x c = a x(b x c)
• Associative property of addition (APA) (a + b)+c = a+(b + c)

3. IDENTITY PROPERTY
(IPM) 5 x 1 = 5
100 x 1 = 100
m x 1 = m
(IPA) 10 + 0 = 10
6457 + 0 = 6457
y + 0 = y

4. COMMUTATIVE PROPERTY
• (CPM) 5x7 = 7x5
400 x 20 = 20 x 400
xy = yx
• (CPA) 3+4 = 4+3
756 + 2 = 2 + 756
r + z = z + r

5. ASSOCIATIVE PROPERTY
• (APM) (5 x 3) x 7 = 5 x (3 x 7)
24 x (12 x 10) = (24 x 12) x 10
(w x g) x v = w x (g x v)
• (APA) (5 + 3) + 7 = 5 +(3 + 7)
24 + (12 + 10) = (24 + 12) + 10
(w + g) + v = w + (g + v)

6. MORE PRACTICE
Show two ways to simplify the expression.
(25 * 15) * 4
100 - 365

7. FIND THE VALUE OF X AND Y
6 + x = 30 4 + y = 10 x + 3 = 7
Y + 10 = 20 15 = x + 5 22 = 2 + y
3x = 30 2y = 10 20 = 5x 66 = 6y
10w = 100 4y = 12 35 = 7y 4 = 2x