Want to create interactive content? It’s easy in Genially!

Reuse this genially

Module 3 Lesson 5: Algebraic Properties

Simon Ainsworth

Created on July 11, 2024

Start designing with a free template

Discover more than 1500 professional designs like these:

Math Lesson Plan

Primary Unit Plan 2

Animated Chalkboard Learning Unit

Business Learning Unit

Corporate Signature Learning Unit

Code Training Unit

History Unit plan

Explore all templates

Transcript

Module 3

Algebraic Properties

Lesson 5

Start

Goals

Objective:

  • Generate equivalent expressions using the algebraic properties.

Algebraic Properties

  • Using algebraic properties will help you create
  • Using properties can save you time.
  • Makes solving problems easier.

equivalent expressions

Distributive Property

Associative Property

Commutative Property

Identity Property

Let's take a deeper look into each property!

Three Properties of Addition

Associative Property of Addition

Commutative Property of Addition

Identity Property of Addition

The grouping of the addends does not change the sum.

Allows you to switch the order of addends, without changing the sum.

Adding 0 to a number does not change the identify (or value).

a + 0 = a

a + b = b + a

(a + b) + c = a + (b + c)

Numerical Example

Numerical Example

Numerical Example

Three Properties of Multiplication

Associative Property of Multiplication

Commutative Property of Multiplication

Identity Property of Multiplication

The grouping of the factors does not change the product.

Allows you to switch the order of factors, without changing the product.

Multiplying a number by 1 does not change the identify (or value).

a • 1 = a

ab = ba

(a • b) • c = a • (b • c)

Numerical Example

Numerical Example

Numerical Example

Distributive Property ( + and -)

Distributive Property (with a difference)

Distributive Property (with a sum)

Any number multiplied to a difference of two or more numbers is equal to the difference of the products.

Any number multiplied to a sum of two or more numbers is equal to the sum of the products.

a (b - c) = a • b - a • c

a (b +c) = a • b + a • c

Numerical Example

Numerical Example

Practice

Please complete to check your understanding.

Practice

Please complete to check your understanding.
Complete the other side of the expression following the property characteristics.

Associative

Commutative

(2+4n) + 12 =
2+(4n+12)
3y + 4x
4x + 3y =
3•(5•b) =
(3•5)•b
m • 5
5 • m =

Distributive

Identity

1,234
4(x + 5) =
1,234 + 0 =
4x + 20
1,234
1,234 • 1 =
35 - 7m
7(5 - m) =

Summary

4 Algebraic Properities

Extra, Extra!

Use the word ACID to recall the 4 properties

This property does NOT work for division or subtraction.
This property does NOT work if the expression contains more than one operation.

A C I D

Associative Property of Addition/Multiplication Commutative Property of Addition/Multiplication Identity Property of Addition or Multiplication Distributive Property of Addition or Subtraction
This property does NOT work for division or subtraction.
This property does NOT work on expressions that contain only one operation or on division problems.

(2 + 3) + 4 = 2 + (3 + 4) 9 = 9

  • Same addends 2, 3, and 4
  • Order changed with parenthesis of what addends to add first, but the sum on each side of the equal sign is still the same value.

Do First!

Do First!

= 2 + 7

5 + 4

4(7 - 5) = 4(7) - 4(5) 4(2) = 28 - 20 8 = 8

  • One factor: 4
  • Terms: 7 and 5
  • The factor 4 multiplied to the term of 7 and the difference of (-) the factor 4 multiplied to the term of 5.

4(7 + 5) = 4(7) + 4(5) 4(12) = 28 + 20 48 = 48

  • One factor: 4
  • Terms: 7 and 5
  • The factor 4 multiplied to the term of 7 and (+) the factor 4 multiplied to the term of 5.

3.9 • 1 = 3.9 3.9 = 3.9

  • Multipliying a factor by 1 maintains the same product.

4.5 + 0 = 4.5 4.5 = 4.5

  • Adding 0
  • Adding zero to an addend, maintains the same sum.

(2 • 3) • 4 = 2 • (3 • 4) 24 = 24

Do First!

Do First!

6 • 4

= 2 • 12

  • Same factors 2, 3, and 4
  • Order changed with parenthesis of what factors need to be multiplied first, but the product on each side of the equal sign is still the same value.

Expressions that represent the same value but are written differently.

Example: 3x + 7y = 7y + 3x

4.5 + 7.3 = 7.3 + 4.5 11.8 = 11.8

  • Same addends: 4.5 and 7.3
  • Order changed, but the sum on each side of the equal sign is still the same.

4 • 7 = 7 • 4 28 = 28

  • Same factors: 4 and 7
  • Order changed, but the product on each side of the equal sign is still the same.