Adding Whole Numbers
Learning Outcomes
- Identify and use the identity property of addition
- Identify and use the commutative property of addition
- Add multiple-digit numbers using columns for place value
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 the table below by adding each row number along the left side to each column number across the top. You can use this table for reference, but it will make your work faster and easier if you have the sums memorized.+ | [latex]0[/latex] | [latex]1[/latex] | [latex]2[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] |
---|---|---|---|---|---|---|---|---|---|---|
[latex]0[/latex] | [latex]0[/latex] | [latex]1[/latex] | [latex]2[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] |
[latex]1[/latex] | [latex]1[/latex] | [latex]2[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] |
[latex]2[/latex] | [latex]2[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] |
[latex]3[/latex] | [latex]3[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] |
[latex]4[/latex] | [latex]4[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] |
[latex]5[/latex] | [latex]5[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] | [latex]14[/latex] |
[latex]6[/latex] | [latex]6[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] | [latex]14[/latex] | [latex]15[/latex] |
[latex]7[/latex] | [latex]7[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] | [latex]14[/latex] | [latex]15[/latex] | [latex]16[/latex] |
[latex]8[/latex] | [latex]8[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] | [latex]14[/latex] | [latex]15[/latex] | [latex]16[/latex] | [latex]17[/latex] |
[latex]9[/latex] | [latex]9[/latex] | [latex]10[/latex] | [latex]11[/latex] | [latex]12[/latex] | [latex]13[/latex] | [latex]14[/latex] | [latex]15[/latex] | [latex]16[/latex] | [latex]17[/latex] | [latex]18[/latex] |
Identity Property of Addition
The sum of any number [latex]a[/latex] and [latex]0[/latex] is the number. [latex-display]\begin{array}{}\\ a+0=a\\ 0+a=a\end{array}[/latex-display]example
Find each sum:- [latex]0+11[/latex]
- [latex]42+0[/latex]
1. The first addend is zero. The sum of any number and zero is the number. | [latex]0+11=11[/latex] |
2. The second addend is zero. The sum of any number and zero is the number. | [latex]42+0=42[/latex] |
[latex]2+3=5[/latex] | [latex]3+2=5[/latex] |
[latex]4+7=11[/latex] | [latex]7+4=11[/latex] |
[latex]8+9=17[/latex] | [latex]9+8=17[/latex] |
Commutative Property of Addition
Changing the order of the addends [latex]a[/latex] and [latex]b[/latex] does not change their sum. [latex-display]a+b=b+a[/latex-display]example
Add:- [latex]8+7[/latex]
- [latex]7+8[/latex]
Answer: Solution
1. | |
Add. | [latex]8+7[/latex] |
[latex]15[/latex] |
2. | |
Add. | [latex]7+8[/latex] |
[latex]15[/latex] |
example
Add: [latex]28+61[/latex].Answer: Solution To add numbers with more than one digit, it is often easier to write the numbers vertically in columns.
Write the numbers so the ones and tens digits line up vertically. | [latex]\begin{array}{c}\hfill 28\\ \\ \hfill \underset{\text{____}}{+61}\end{array}[/latex] |
Then add the digits in each place value. Add the ones: [latex]8+1=9[/latex] Add the tens: [latex]2+6=8[/latex] | [latex]\begin{array}{c}\hfill 28\\ \\ \hfill \underset{\text{____}}{+61}\\ \hfill 89\end{array}[/latex] |
Add whole numbers
- Write the numbers so each place value lines up vertically.
- Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than [latex]9[/latex], carry to the next place value.
- Continue adding each place value from right to left, adding each place value and carrying if needed.
example
Add: [latex]43+69[/latex].Answer: Solution
Write the numbers so the digits line up vertically. | [latex]\begin{array}{c}\hfill 43\\ \\ \hfill \underset{\text{____}}{+69}\end{array}[/latex] |
Add the digits in each place. Add the ones: [latex]3+9=12[/latex] | |
Write the [latex]2[/latex] in the ones place in the sum. Add the [latex]1[/latex] ten to the tens place. | [latex]\begin{array}{c}\hfill \stackrel{1}{4}3\\ \hfill \underset{\text{____}}{+69}\\ \hfill 2\end{array}[/latex] |
Now add the tens: [latex]1+4+6=11[/latex] Write the 11 in the sum. | [latex]\begin{array}{c}\hfill \stackrel{1}{4}3\\ \hfill \underset{\text{____}}{+69}\\ \hfill 112\end{array}[/latex] |
try it
Add: [latex]35+98[/latex].Answer: [latex]35+98=133[/latex]
Add: [latex]72+89[/latex].Answer: [latex]72+89=161[/latex]
example
Add: [latex]324+586[/latex].Answer: Solution
Write the numbers so the digits line up vertically. | |
Add the digits in each place value. Add the ones: [latex]4+6=10[/latex] Write the [latex]0[/latex] in the ones place in the sum and carry the [latex]1[/latex] ten to the tens place. | |
Add the tens: [latex]1+2+8=11[/latex] Write the [latex]1[/latex] in the tens place in the sum and carry the [latex]1[/latex] hundred to the hundreds | |
Add the hundreds: [latex]1+3+5=9[/latex] Write the [latex]9[/latex] in the hundreds place. |
try it
Add: [latex]456+376[/latex].Answer: [latex]456+376=832[/latex]
Add: [latex]269+578[/latex].Answer: [latex]269+578=847[/latex]
example
Add: [latex]1,683+479[/latex].Answer: Solution
Write the numbers so the digits line up vertically. | [latex]\begin{array}{c}\hfill 1,683\\ \\ \hfill \underset{\text{______}}{+479}\end{array}[/latex] |
Add the digits in each place value. | |
Add the ones: [latex]3+9=12[/latex]. Write the [latex]2[/latex] in the ones place of the sum and carry the [latex]1[/latex] ten to the tens place. | [latex]\begin{array}{c}\hfill 1,6\stackrel{1}{8}3\\ \\ \hfill \underset{\text{______}}{+479}\\ \hfill 2\end{array}[/latex] |
Add the tens: [latex]1+7+8=16[/latex] Write the [latex]6[/latex] in the tens place and carry the [latex]1[/latex] hundred to the hundreds place. | [latex]\begin{array}{c}\hfill 1,\stackrel{1}{6}\stackrel{1}{8}3\\ \\ \hfill \underset{\text{______}}{+479}\\ \hfill 62\end{array}[/latex] |
Add the hundreds: [latex]1+6+4=11[/latex] Write the [latex]1[/latex] in the hundreds place and carry the [latex]1[/latex] thousand to the thousands place. | [latex]\begin{array}{c}\hfill 1,\stackrel{1}{6}\stackrel{1}{8}3\\ \\ \hfill \underset{\text{______}}{+479}\\ \hfill 162\end{array}[/latex] |
Add the thousands [latex]1+1=2[/latex] . Write the [latex]2[/latex] in the thousands place of the sum. | [latex]\begin{array}{c}\hfill 1,\stackrel{1}{6}\stackrel{1}{8}3\\ \\ \hfill \underset{\text{______}}{+479}\\ \hfill 2,162\end{array}[/latex] |
example
Add: [latex]21,357+861+8,596[/latex].Answer: Solution
Write the numbers so the place values line up vertically. | [latex]\begin{array}{c}\hfill 21,357\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\end{array}[/latex] |
Add the digits in each place value. | |
Add the ones: [latex]7+1+6=14[/latex] Write the [latex]4[/latex] in the ones place of the sum and carry the [latex]1[/latex] to the tens place. | [latex]\begin{array}{c}\hfill 21,3\stackrel{1}{5}7\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\\ \hfill 4\end{array}[/latex] |
Add the tens: [latex]1+5+6+9=21[/latex] Write the [latex]1[/latex] in the tens place and carry the [latex]2[/latex] to the hundreds place. | [latex]\begin{array}{c}\hfill 21,\stackrel{2}{3}\stackrel{1}{5}7\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\\ \hfill 14\end{array}[/latex] |
Add the hundreds: [latex]2+3+8+5=18[/latex] Write the [latex]8[/latex] in the hundreds place and carry the [latex]1[/latex] to the thousands place. | [latex]\begin{array}{c}\hfill 2\stackrel{1}{1,}\stackrel{2}{3}\stackrel{1}{5}7\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\\ \hfill 814\end{array}[/latex] |
Add the thousands [latex]1+1+8=10[/latex] . Write the [latex]0[/latex] in the thousands place and carry the [latex]1[/latex] to the ten thousands place. | [latex]\begin{array}{c}\hfill \stackrel{1}{2}\stackrel{1}{1,}\stackrel{2}{3}\stackrel{1}{5}7\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\\ \hfill 0814\end{array}[/latex] |
Add the ten-thousands [latex]1+2=3[/latex] . Write the [latex]3[/latex] in the ten thousands place in the sum. | [latex]\begin{array}{c}\hfill \stackrel{1}{2}\stackrel{1}{1,}\stackrel{2}{3}\stackrel{1}{5}7\\ \hfill 861\\ \\ \hfill \underset{\text{_______}}{+8,596}\\ \hfill 30,814\end{array}[/latex] |
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- Example: Adding Whole Numbers. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Question ID: 143190, 143191, 143196, 143197, 143204. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.
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