# Real numbers properties of addition and multiplication relationship

### A study of number properties | nzmaths

What are the associative, commutative, distributive, and equality properties? What is Real numbers are also closed under addition and subtraction. They are. The associative property in math is when you re-group items and come to the same It refers to grouping of numbers or variables in algebra. This concept reviews the properties of addition that apply to real numbers.

Commutativity and Associativity together imply that it doesn't matter what order we add things up in. This property says using a formula that it doesn't matter which way you do it. What about those people who add a and c together first? Well, that is where commutativity comes in. It tells us that we don't have add things up in exactly the order people write things down.

You can switch things around and still get the same answer. Let's do one more example of using these properties to "juggle parentheses" to see that commutativity says you really can add a and c first and get the same answer.

You will get the same answer regardless of order. The rule holds even if there are more than three terms: There may be 4, 12, or several thousand. These properties would still tell us that it doesn't matter how we add things up. The same properties for multiplication tell us it doesn't matter in what order we multiply things together.

We are free to change the order to anything that we find easier. Does it ever really make things easier?

## Algebra/Real Numbers

You can often simplify expressions using the Distributive Property. This is one of the reasons it is so important. What happens if we use the distributive property on the first term in this expression?

Require students to reference their observations to specific Room numbers. These are number properties. Highlight the fact that all of the examples involve zero. Write a large zero on the class chart and add the title, What we know about zero. Brainstorm together and record the students ideas about zero.

These are likely to include the ideas above, and others such as: Use this as a class poster. Return to the classroom equations. Highlight Rooms 1, 2, 4, and 5. Have a student describe again what is happening. Any letter could be used here. Explain that, because this is a really important idea in mathematics, it has a special name.

Return to the other equations, which have not been highlighted and together record similar equations, using variables. Discuss this with a partner. Provide student pairs with a number line and some counters. Write again on the class chart: Have some students model this again for the class.

These are simple to model, but doing so is helpful. Write on the class chart: Write the equations in place on the class chart.

### Associative & Commutative Property of Addition & Multiplication (With Examples) | Sciencing

Have students buddy mark their equations then conclude the lesson by having them share their summary comments. Describe in words the commutative property of addition and the commutative property of multiplication, and name these properties. Describe in words the associative property of addition and the associative property of multiplication, and name these properties.

Describe in words the distributive property of multiplication over addition, and name this property. Activity 1 Refer to Session 1. Focus on the sustainability work that is happening in Kiwi School. Display Attachment 3 Kiwi School planting plan and pose this scenario: Kiwi School students planned and have planted green, red and yellow flaxes and grasses in an area near their adventure playground.

Here is their plan.

**Commutative property for addition - Arithmetic properties - Pre-Algebra - Khan Academy**

Look at the plan Attachment 3. In pairs, have them discuss what they see and write the many ways they know for working out how many of each kind of plant there are. Have students pair-share their equations, discussing and recording any different calculations. Have students record their equations on the class chart.

Ensure that the equations below are included in their recording and explained with reference to the planting plan. Emphasise that they are to look at what is happening with the numbers and the number operations in each example, and write a description of this in words in the space provided.

They should write other equations to which this description applies. These may be from the planting plan, or may be unrelated equations. They should leave the final column blank, unless they know or have their own ideas. Have students pair-share their work. Discuss student ideas as a class.

## A study of number properties

We accept number properties as true and we do not have to prove them. Explain that mathematicians have given names to these behaviours and properties.

Ask if anyone knows the names of these properties, recording ideas. The associative property of addition. The associative property of multiplication. The commutative property of addition.

The commutative property of multiplication.

The distributive property of multiplication over addition. Discuss the root words of associate, commute and distribute. How are the definitions of the properties related to the meanings of the root words? Have students discuss in pairs which property name might go with which set of equations and why.