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Properties of Addition & Multiplication. Why do we need rules or properties in math? Lets see what can happen if we didn’t have rules. What is a VARIABLE ? A variable is an unknown amount in a number sentence represented as a letter: 5 + n 8 x 6( g ) t + d = s.
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Why do we need rules or properties in math? Lets see what can happen if we didn’t have rules.
What is a VARIABLE? • A variable is an unknown amount in a number sentence represented as a letter: • 5 + n 8x 6(g) t + d = s Before We Begin…
What do these symbols mean? • ( ) = multiply: 6(a)or group: (6 + a) • * = multiply • · = multiply • ÷ = divide • / = divide Before We Begin…
To COMMUTE something is to change it • The COMMUTATIVEproperty says that the orderof numbers in a number sentence can be changed • Addition & multiplication have COMMUTATIVE properties Commutative Property
Commutative Property Examples: (a + b = b + a) 7 + 5 = 5 + 7 9 x 3 = 3 x 9 Note: subtraction & division DO NOT have commutative properties!
a b As you can see, when you have two lengths a and b, you get the same length whether you put a first or b first. a b
b a a b The commutative property of multiplication says that you may multiply quantities in any order and you will get the same result. When computing the area of a rectangle it doesn’t matter which side you consider the width, you will get the same area either way.
Practice: Show the commutative property of each number sentence. • 13 + 18 = • 42 x 77 = • 5 + y = • 7(b) = Commutative Property
Practice: Show the commutative property of each number sentence. • 13 + 18 = 18 + 13 • 42 x 77 = 77 x 42 • 5 + y = y + 5 • 7(b) = b(7) or (b)7 Commutative Property
You can change You can change + to to + And the result will not change Keep in mind the and do not have to be numbers. They can be expressions that evaluate to a number.
Example: (2 * 7) + (8 – 5) (8 - 5) + (2 * 7) + + _ _ * * 2 7 8 5 8 5 2 7 14 + 3 3 + 14 17 17
The commutative property: a + b = b + a and a * b = b * a 7 + 3 = 3 + 7 and 7 * 3 = 3 * 7 10 = 10 21 = 21 Try this subtraction: 8 – 4 = 4 – 8 8 ÷ 4 = 4 ÷ 8 and division 4 ≠ -4 2 ≠ 0.5
Practice: Show the associative property of each number sentence. • (7 + 2) + 5 = 7 + (2 + 5) • 4 x (8 x 3) = (4 x 8) x 3 • 5 + (y + 2) = (5 + y) + 2 • 7(b x 4) = (7b) x 4 or (7 x b)4 Associative Property
To DISTRIBUTE something is give it out or share it. • The DISTRIBUTIVEproperty says that we can distribute a multiplier out to each number in a group to make it easier to solve • The DISTRIBUTIVE property uses MULTIPLICATION and ADDITION! Distributive Property
Examples: a(b + c) = a(b) + a(c) 2 x (3 + 4) = (2 x 3) + (2 x 4) 5(3 + 7) = 5(3) + 5(7) Note: Do you see that the 2 and the 5 were shared (distributed) with the other numbers in the group? Distributive Property
Practice: Show the distributive property of each number sentence. • 8 x (5 + 6) = • 4(8 + 3) = • 5 x (y + 2) = • 7(4 + b) = Distributive Property (8x 5) + (8x 6) 4(8) + 4(3) (5y) + (5x 2) 7(4) + 7b
Ella sold 37 necklaces for $20.00 each at the craft fair. She is going to donate half the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Use the Associative Property to write two equivalent expressions for the perimeter of the triangle
Six Friends are going to the state fair. The cost of one admission is $9.50, and the cost for one ride on the Ferris wheel is $1.50. Write two equivalent expressions and then find the total cost.
