SOL 4.22 Demonstrating the Meaning of Equality

Now Lets Review What We Just Learned

= Means Equal = = Balanced means = Balanced means = This is NOT EQUAL This is NOT EQUAL = = 10

These Are Examples of Equations 2 = 2 2 = 2 17 = = x = 7 x = 7 7 = x 7 = x t + 3 = 8 what does t =? t + 3 = 8 what does t =? 5 x 3= x 3= = = 5 Remember- Both sides Remember- Both sides of an equation have to be equal! of an equation have to be equal!

Commutative Property of Addition Definition – The addends can exchange places and still equal the same sum. Definition – The addends can exchange places and still equal the same sum. Example – 7+2=2+7 Example – 7+2=2+7

Commutative Property of Multiplication Definition – The factors can exchange places and still equal the same product. Definition – The factors can exchange places and still equal the same product. Example – 3 x 2 = 2 x 3 Example – 3 x 2 = 2 x 3

Associative Property of Addition Definition – The addends can be grouped differently and still equal the same sum. Definition – The addends can be grouped differently and still equal the same sum. Example – 2+(3+4)=(2+3)+4 Example – 2+(3+4)=(2+3)+4

Associative Property of Multiplication Definition – The factors can be grouped differently and still equal the same product. Definition – The factors can be grouped differently and still equal the same product. Example – 5x(3x2)=(5x3)x2 Example – 5x(3x2)=(5x3)x2

Let’s Practice a Few Problems

Question 1 What property is shown here? What property is shown here? = A. Commutative Property of Addition B. Commutative Property of Multiplication C. Associative Property of Addition D. Associative Property of Multiplication

Answer 1 What property is shown here? What property is shown here? = Answer: A. Commutative Property of Addition

Question 2 What property is shown here? What property is shown here? 48 + ( ) = ( ) + 16 A. Commutative Property of Addition B. Commutative Property of Multiplication C. Associative Property of Addition D. Associative Property of Multiplication

Answer 2 What property is shown here? What property is shown here? 48 + ( ) = ( ) + 16 Answer: C. Associative Property of Addition

Question 3 What property is shown here? What property is shown here? 18 x (22 x 49) = (18 x 22) x 49 A. Commutative Property of Addition B. Commutative Property of Multiplication C. Associative Property of Addition D. Associative Property of Multiplication

Answer 3 What property is shown here? What property is shown here? 18 x (22 x 49) = (18 x 22) x 49 Answer: D. Associative Property of Multiplication

Question 4 What property is shown here? What property is shown here? 66 x 37 = 37 x 66 A. Commutative Property of Addition B. Commutative Property of Multiplication C. Associative Property of Addition D. Associative Property of Multiplication

Answer 4 What property is shown here? What property is shown here? 66 x 37 = 37 x 66 Answer: B. Commutative Property of Multiplication

Question 5 Which shows the Commutative Property of Addition? Which shows the Commutative Property of Addition? A =3+7+8 B. 7+(2+3)=(2+2)+7 C =2+3+7 D =5+7+2

Answer 5 Which shows the Commutative Property of Addition? Which shows the Commutative Property of Addition?Answer: C =2+3+7

Question 6 Which shows the Associative Property of Multiplication? Which shows the Associative Property of Multiplication? A. (6 x 5) x 2 = 6 x (5 x 2) B. 6 x 5 x 2 = 5 x 6 x 2 C. 5 x (6 x 2) = 5 x (6 x 2) D. 5 x 6 x 2 = 6 x 10

Answer 6 Which shows the Associative Property of Multiplication? Which shows the Associative Property of Multiplication?Answer: A. (6 x 5) x 2 = 6 x (5 x 2)

Question 7 Which shows the Commutative Property of Multiplication? Which shows the Commutative Property of Multiplication? A. 7 x 8 x 4 = 7 x 16 x 2 B. (7 x 8) x 4 = 7 x (2 x 16) C. 7 x 8 x 4 = 8 x 4 x 7 D. 7 x (8 x 4) = (7 x 8) x 4

Answer 7 Which shows the Commutative Property of Multiplication? Which shows the Commutative Property of Multiplication?Answer: C. 7 x 8 x 4 = 8 x 4 x 7

Question 8 Which shows the Associative Property of Addition? Which shows the Associative Property of Addition? A = B. 6 + (9 + 12) = (6 + 9) + 12 C = D. 6 + (9 + 12) = (9 + 12) + 6

Answer 8 Which shows the Associative Property of Addition? Which shows the Associative Property of Addition?Answer: B. 6 + (9 + 12) = (6 + 9) + 12

Answer 9 Which of the following goes in the blank to make this statement true: Which of the following goes in the blank to make this statement true: 62 + (13 + 4) = ______ Answer: A. 62 x 17 B ( ) C. ( ) + 4 D

Question 10 Which will be true if an equal sign (=) is placed in the empty box? Which will be true if an equal sign (=) is placed in the empty box? A. 5 x4 ___ 4 x 5 B. 5 x 4___ 4 ÷ 5 C. 5 x 4 ___ D. 5 x 4 ___ 5 - 4

Answer 10 Which is the best answer for: Which is the best answer for: = _____ Answer: A. 22 – 14 B. 22 x 14 C. 22 ÷ 14 D

These properties also work using symbols If = 5 and = 4 and = 2, which statement would be true? If = 5 and = 4 and = 2, which statement would be true? A + = + A + = + B + = + B + = + C + = + C + = + D + = + D + = +

How Should we solve this problem? First, lets substitute each shape with its numerical value. First, lets substitute each shape with its numerical value. Remember, = 5 and = 4 and = 2, which statement would then be true? Remember, = 5 and = 4 and = 2, which statement would then be true? A = A = B = B = C = C = D = D = 4 + 5

The Answer is…… D = D = ( + = + )