Notation and Modeling Addition of Integers
Learning Outcomes
- Model addition of integers with color counters
example
Model: [latex]5+3[/latex]. Solution:Interpret the expression. | [latex]5+3[/latex] means the sum of [latex]5[/latex] and [latex]3[/latex] . |
Model the first number. Start with [latex]5[/latex] positives. | |
Model the second number. Add [latex]3[/latex] positives. | |
Count the total number of counters. | |
The sum of [latex]5[/latex] and [latex]3[/latex] is [latex]8[/latex]. | [latex]5+3=8[/latex] |
try it
Model the expression. [latex-display]2+4[/latex-display]Answer: [latex-display]6[/latex-display]
Model the expression. [latex-display]2+5[/latex-display]Answer: [latex-display]7[/latex-display]
example
Model: [latex]-5+\left(-3\right)[/latex].Answer: Solution:
Interpret the expression. | [latex]-5+\left(-3\right)[/latex] means the sum of [latex]-5[/latex] and [latex]-3[/latex] . |
Model the first number. Start with [latex]5[/latex] negatives. | |
Model the second number. Add [latex]3[/latex] negatives. | |
Count the total number of counters. | |
The sum of [latex]−5[/latex] and [latex]−3[/latex] is [latex]−8[/latex]. | [latex]-5+-3=-8[/latex] |
try it
Model the expression. [latex-display]-2+\left(-4\right)[/latex-display]Answer: [latex-display]−6[/latex-display]
Model the expression. [latex-display]-2+\left(-5\right)[/latex-display]Answer: [latex-display]−7[/latex-display]
example
Model: [latex]-5+3[/latex].Answer: Solution:
Interpret the expression. | [latex]-5+3[/latex] means the sum of [latex]-5[/latex] and [latex]3[/latex] . |
Model the first number. Start with [latex]5[/latex] negatives. | |
Model the second number. Add [latex]3[/latex] positives. | |
Remove any neutral pairs. | |
Count the result. | |
The sum of [latex]−5[/latex] and [latex]3[/latex] is [latex]−2[/latex]. | [latex]-5+3=-2[/latex] |
try it
Model the expression, and then simplify: [latex-display]2+\left(-4\right)[/latex-display]Answer: [latex-display]−2[/latex-display]
Model the expression, and then simplify: [latex-display]2+\left(-5\right)[/latex-display]Answer: [latex-display]−3[/latex-display]
example
Model: [latex]5+\left(-3\right)[/latex].Answer: Solution:
Interpret the expression. | [latex]5+\left(-3\right)[/latex] means the sum of [latex]5[/latex] and [latex]-3[/latex] . |
Model the first number. Start with [latex]5[/latex] positives. | |
Model the second number. Add [latex]3[/latex] negatives. | |
Remove any neutral pairs. | |
Count the result. | |
The sum of [latex]5[/latex] and [latex]−3[/latex] is [latex]2[/latex]. | [latex]5+\left(-3\right)=2[/latex] |
try it
Model the expression, and then simplify: [latex-display]\left(-2\right)+4[/latex-display]Answer: [latex-display]−2[/latex-display]
Model the expression: [latex-display]\left(-2\right)+5[/latex-display]Answer: [latex-display]3[/latex-display]
example
Model each addition.- [latex]4 + 2[/latex]
- [latex]−3 + 6[/latex]
- [latex]4 + (−5)[/latex]
- [latex]-2 + (−3)[/latex]
Answer: Solution
1. | |
[latex]4+2[/latex] | |
Start with [latex]4[/latex] positives. | |
Add two positives. | |
How many do you have? | [latex]6[/latex]. [latex]4+2=6[/latex] |
2. | |
[latex]-3+6[/latex] | |
Start with [latex]3[/latex] negatives. | |
Add [latex]6[/latex] positives. | |
Remove neutral pairs. | |
How many are left? | |
[latex]3[/latex]. [latex]-3+6=3[/latex] |
3. | |
[latex]4+\left(-5\right)[/latex] | |
Start with [latex]4[/latex] positives. | |
Add [latex]5[/latex] negatives. | |
Remove neutral pairs. | |
How many are left? | |
[latex]-1[/latex]. [latex]4+\left(-5\right)=-1[/latex] |
4. | |
[latex]-2+\left(-3\right)[/latex] | |
Start with [latex]2[/latex] negatives. | |
Add [latex]3[/latex] negatives. | |
How many do you have? | [latex]-5[/latex]. [latex]-2+\left(-3\right)=-5[/latex] |
try it
Model each addition. 1. [latex]3 + 4[/latex] 2. [latex]−1 + 4[/latex] 3. [latex]4 + (−6)[/latex] 4. [latex]−2 + (−2)[/latex]Answer: 1. 2. 3. 4.
1. [latex]5 + 1[/latex] 2. [latex]−3 + 7[/latex] 3. [latex]2 + (−8)[/latex] 4. [latex]−3 + (−4)[/latex]Answer: 1. 2. 3. 4.
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- Adding Integers with the Same Sign Using Color Counters. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].