# Whole Numbers

## Add Whole Numbers


### Use Addition Notation

A college student has a part-time job. Last week he worked  hours on Monday and  hours on Friday. To find the total number of hours he worked last week, he added  and 
The operation of addition combines numbers to get a sum. The notation we use to find the sum of  and  is:
We read this as three plus four and the result is the sum of three and four. The numbers  and  are called the addends. A math statement that includes numbers and operations is called an expression.

### Model Addition of Whole Numbers

Addition is really just counting. We will model addition with  blocks. Remember, a block represents  and a rod represents  Let’s start by modeling the addition expression we just considered, 
Each addend is less than  so we can use ones blocks.
There are  blocks in all. We use an equal sign  to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that. 
When the result is  or more ones blocks, we will exchange the  blocks for one rod.
Next we will model adding two digit numbers.


### Add Whole Numbers Without Models

Now that we have used models to add numbers, we can move on to adding without models. Before we do that, make sure you know all the one digit addition facts. You will need to use these number facts when you add larger numbers.
Imagine filling in  by adding each row number along the left side to each column number across the top. Make sure that you get each sum shown. If you have trouble, model it. It is important that you memorize any number facts you do not already know so that you can quickly and reliably use the number facts when you add larger numbers.
Did you notice what happens when you add zero to a number? The sum of any number and zero is the number itself. We call this the Identity Property of Addition. Zero is called the additive identity.
Look at the pairs of sums.

Notice that when the order of the addends is reversed, the sum does not change. This property is called the Commutative Property of Addition, which states that changing the order of the addends does not change their sum.
In the previous example, the sum of the ones and the sum of the tens were both less than  But what happens if the sum is  or more? Let’s use our  model to find out.  shows the addition of  and  again.
When we add the ones,  we get  ones. Because we have more than  ones, we can exchange  of the ones for  ten. Now we have  tens and  ones. Without using the model, we show this as a small red  above the digits in the tens place.
When the sum in a place value column is greater than  we carry over to the next column to the left. Carrying is the same as regrouping by exchanging. For example,  ones for  ten or  tens for  hundred.

### Translate Word Phrases to Math Notation

Earlier in this section, we translated math notation into words. Now we’ll reverse the process. We’ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in .

### Add Whole Numbers in Applications

Now that we have practiced adding whole numbers, let’s use what we’ve learned to solve real-world problems. We’ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.
Some application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.

### Key Concepts

1. Addition Notation To describe addition, we can use symbols and words. 
 
2. Identity Property of Addition


3. Commutative Property of Addition

4. Add whole numbers.


### Practice Makes Perfect

Use Addition Notation 
In the following exercises, translate the following from math expressions to words.
Model Addition of Whole Numbers 
In the following exercises, model the addition.
Add Whole Numbers 
In the following exercises, fill in the missing values in each chart.
In the following exercises, add.
Translate Word Phrases to Math Notation 
In the following exercises, translate each phrase into math notation and then simplify.
Add Whole Numbers in Applications 
In the following exercises, solve the problem.
In the following exercises, find the perimeter of each figure.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
