1.2 Add whole numbers

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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 $\text{base-10}$ 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 .

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.

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 .

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

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

Model addition of whole numbers

Addition is really just counting. We will model addition with $\text{base-10}$ 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. Then we model the second number with 4 blocks. Count the total number of blocks.

There are $7$ blocks in all. We use an equal sign $\text{(=)}$ 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. Model the second number with 6 blocks. Count the total number of blocks There are $8$ blocks in all, so $2+6=8.$

Model: $3+6.$

Model: $5+1.$

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. Model the second number with 8 blocks. Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod. 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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