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By the end of this section, you will be able to:
  • Use addition notation
  • Model addition of whole numbers
  • Add whole numbers without models
  • Translate word phrases to math notation
  • Add whole numbers in applications

Before you get started, take this readiness quiz.

  1. What is the number modeled by the base-10 blocks?
    An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.
    If you missed this problem, review Introduction to Whole Numbers .
  2. Write the number three hundred forty-two thousand six using digits?
    If you missed this problem, review Introduction to Whole Numbers .

Use addition notation

A college student has a part-time job. Last week he worked 3 hours on Monday and 4 hours on Friday. To find the total number of hours he worked last week, he added 3 and 4 .

The operation of addition combines numbers to get a sum    . The notation we use to find the sum of 3 and 4 is:

3 + 4

We read this as three plus four and the result is the sum of three and four. The numbers 3 and 4 are called the addends. A math statement that includes numbers and operations is called an expression.

Addition notation

To describe addition, we can use symbols and words.

Operation Notation Expression Read as Result
Addition + 3 + 4 three plus four the sum of 3 and 4

Translate from math notation to words:

  1. 7 + 1
  2. 12 + 14

Solution

  • The expression consists of a plus symbol connecting the addends 7 and 1 . We read this as seven plus one or the sum of seven and one .
  • The expression consists of a plus symbol connecting the addends 12 and 14 . We read this as twelve plus fourteen , or the sum of twelve and fourteen .
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Translate from math notation to words:

  1. 8 + 4
  2. 18 + 11
  • eight plus four; the sum of eight and four
  • eighteen plus eleven; the sum of eighteen and eleven
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Translate from math notation to words:

  1. 21 + 16
  2. 100 + 200
  1. twenty-one plus sixteen; the sum of twenty-one and sixteen
  2. one hundred plus two hundred; the sum of one hundred and two hundred
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Model addition of whole numbers

Addition is really just counting. We will model addition with base-10 blocks. Remember, a block represents 1 and a rod represents 10 . Let’s start by modeling the addition expression we just considered, 3 + 4 .

Each addend is less than 10 , so we can use ones blocks.

We start by modeling the first number with 3 blocks. CNX_BMath_Figure_01_02_019_img-02.png
Then we model the second number with 4 blocks. CNX_BMath_Figure_01_02_019_img-03.png
Count the total number of blocks. CNX_BMath_Figure_01_02_019_img-04.png

There are 7 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. 3 + 4 = 7 .

Doing the Manipulative Mathematics activity “Model Addition of Whole Numbers” will help you develop a better understanding of adding whole numbers.

Model the addition 2 + 6 .

Solution

2 + 6 means the sum of 2 and 6

Each addend is less than 10, so we can use ones blocks.

Model the first number with 2 blocks. CNX_BMath_Figure_01_02_016_img-02.png
Model the second number with 6 blocks. CNX_BMath_Figure_01_02_016_img-03.png
Count the total number of blocks CNX_BMath_Figure_01_02_016_img-04.png
There are 8 blocks in all, so 2 + 6 = 8 .
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When the result is 10 or more ones blocks, we will exchange the 10 blocks for one rod.

Model the addition 5 + 8 .

Solution

5 + 8 means the sum of 5 and 8 .

Each addend is less than 10, se we can use ones blocks.
Model the first number with 5 blocks. CNX_BMath_Figure_01_02_017_img-02.png
Model the second number with 8 blocks. CNX_BMath_Figure_01_02_017_img-03.png
Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod. CNX_BMath_Figure_01_02_017_img-04.png
Now we have 1 ten and 3 ones, which is 13. 5 + 8 = 13

Notice that we can describe the models as ones blocks and tens rods, or we can simply say ones and tens . From now on, we will use the shorter version but keep in mind that they mean the same thing.

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Questions & Answers

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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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