Notation and Modeling Subtraction of Integers
Learning Outcomes
- Model integer subtraction with color counters
- [latex]5 - 3[/latex]
- [latex]- 5-\left(-3\right)[/latex]
- [latex]-5 - 3[/latex]
- [latex]5-\left(-3\right)[/latex]
example
Model: [latex]5 - 3[/latex]. Solution:Interpret the expression. | [latex]5 - 3[/latex] means [latex]5[/latex] take away [latex]3[/latex] . |
Model the first number. Start with [latex]5[/latex] positives. | |
Take away the second number. So take away [latex]3[/latex] positives. | |
Find the counters that are left. | |
[latex]5 - 3=2[/latex] . The difference between [latex]5[/latex] and [latex]3[/latex] is [latex]2[/latex] . |
try it
Model the expression: [latex-display]6 - 4[/latex-display]Answer: [latex-display]2[/latex-display]
Model the expression: [latex-display]7 - 4[/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 [latex]-5[/latex] take away [latex]-3[/latex] . |
Model the first number. Start with [latex]5[/latex] negatives. | |
Take away the second number. So take away [latex]3[/latex] negatives. | |
Find the number of counters that are left. | |
[latex]-5-\left(-3\right)=-2[/latex] . The difference between [latex]-5[/latex] and [latex]-3[/latex] is [latex]-2[/latex] . |
try it
Model the expression: [latex-display]-6-\left(-4\right)[/latex-display]Answer: [latex-display]−2[/latex-display]
Model the expression: [latex-display]-7-\left(-4\right)[/latex-display]Answer: [latex-display]−3[/latex-display]
- First, we subtracted [latex]3[/latex] positives from [latex]5[/latex] positives to get [latex]2[/latex] positives.
- Then we subtracted [latex]3[/latex] negatives from [latex]5[/latex] negatives to get [latex]2[/latex] negatives.
example
Model: [latex]-5 - 3[/latex].Answer: Solution:
Interpret the expression. | [latex]-5 - 3[/latex] means [latex]-5[/latex] take away [latex]3[/latex] . |
Model the first number. Start with [latex]5[/latex] negatives. | |
Take away the second number. So we need to take away [latex]3[/latex] positives. | |
But there are no positives to take away. Add neutral pairs until you have [latex]3[/latex] positives. | |
Now take away [latex]3[/latex] positives. | |
Count the number of counters that are left. | |
[latex]-5 - 3=-8[/latex] . The difference of [latex]-5[/latex] and [latex]3[/latex] is [latex]-8[/latex] . |
try it
Model the expression: [latex-display]-6 - 4[/latex-display]Answer: [latex-display]−10[/latex-display]
Model the expression: [latex-display]-7 - 4[/latex-display]Answer: [latex-display]−11[/latex-display]
example
Model: [latex]5-\left(-3\right)[/latex].Answer: Solution:
Interpret the expression. | [latex]5-\left(-3\right)[/latex] means [latex]5[/latex] take away [latex]-3[/latex] . |
Model the first number. Start with [latex]5[/latex] positives. | |
Take away the second number, so take away [latex]3[/latex] negatives. | |
But there are no negatives to take away. Add neutral pairs until you have [latex]3[/latex] negatives. | |
Then take away [latex]3[/latex] negatives. | |
Count the number of counters that are left. | |
The difference of [latex]5[/latex] and [latex]-3[/latex] is [latex]8[/latex] . [latex]5-\left(-3\right)=8[/latex] |
try it
Model the expression: [latex-display]6-\left(-4\right)[/latex-display]Answer: [latex-display]10[/latex-display]
Model the expression: [latex-display]7-\left(-4\right)[/latex-display]Answer: [latex-display]11[/latex-display]
- subtracting a positive number from a positive number
- subtracting a positive number from a negative number
- subtracting a negative number from a positive number
- subtracting a negative number from a negative number
example
Model each subtraction. [latex-display]8 − 2[/latex-display] [latex-display]−5 − 4[/latex-display] [latex-display]6 − (−6)[/latex-display] [latex-display]−8 − (−3)[/latex-display]Answer:
1. | |
[latex]8 - 2[/latex] This means [latex]8[/latex] take away [latex]2[/latex] . | |
Start with [latex]8[/latex] positives. | |
Take away [latex]2[/latex] positives. | |
How many are left? | [latex]6[/latex] |
[latex]8 - 2=6[/latex] |
2. | |
[latex]-5 - 4[/latex] This means [latex]-5[/latex] take away [latex]4[/latex] . | |
Start with [latex]5[/latex] negatives. | |
You need to take away [latex]4[/latex] positives. Add [latex]4[/latex] neutral pairs to get [latex]4[/latex] positives. | |
Take away [latex]4[/latex] positives. | |
How many are left? | |
[latex]-9[/latex] | |
[latex]-5 - 4=-9[/latex] |
3. | |
[latex]6-\left(-6\right)[/latex] This means [latex]6[/latex] take away [latex]-6[/latex] . | |
Start with [latex]6[/latex] positives. | |
Add [latex]6[/latex] neutrals to get [latex]6[/latex] negatives to take away. | |
Remove [latex]6[/latex] negatives. | |
How many are left? | |
[latex]12[/latex] | |
[latex]6-\left(-6\right)=12[/latex] |
4. | |
[latex]-8-\left(-3\right)[/latex] This means [latex]-8[/latex] take away [latex]-3[/latex] . | |
Start with [latex]8[/latex] negatives. | |
Take away [latex]3[/latex] negatives. | |
How many are left? | |
[latex]-5[/latex] | |
[latex]-8-\left(-3\right)=-5[/latex] |
try it
Model each subtraction. 1. [latex]7 - (-8)[/latex] 2. [latex]-2 - (-2)[/latex] 3. [latex]4 - 1[/latex] 4. [latex]-6 - 8[/latex]Answer: 1. 2. 3. 4.
Model each subtraction. 1. [latex]4 - (-6)[/latex] 2. [latex]-8 - (-1)[/latex] 3. [latex]7 - 3[/latex] 4. [latex]-4 - 2[/latex]Answer: 1. 2. 3. 4.
example
Model each subtraction expression:- [latex]2 - 8[/latex]
- [latex]-3-\left(-8\right)[/latex]
Answer: Solution
1. We start with [latex]2[/latex] positives. | |
We need to take away [latex]8[/latex] positives, but we have only [latex]2[/latex]. | |
Add neutral pairs until there are [latex]8[/latex] positives to take away. | |
Then take away [latex]8[/latex] positives. | |
Find the number of counters that are left. There are [latex]6[/latex] negatives. | |
[latex]2 - 8=-6[/latex] |
2. We start with [latex]3[/latex] negatives. | |
We need to take away [latex]8[/latex] negatives, but we have only [latex]3[/latex]. | |
Add neutral pairs until there are [latex]8[/latex] negatives to take away. | |
Then take away the [latex]8[/latex] negatives. | |
Find the number of counters that are left. There are [latex]5[/latex] positives. | |
[latex]-3-\left(-8\right)=5[/latex] |
try it
Model each subtraction expression.- [latex]7 - 9[/latex]
- [latex]-5--9[/latex]
Answer: 1. [latex-display]−2[/latex-display] 2. [latex-display]4[/latex-display]
Model each subtraction expression.- [latex]4 - 7[/latex]
- [latex]-7-\left(-10\right)[/latex]
Answer: 1. [latex-display]−3[/latex-display] 2. [latex-display]3[/latex-display]
Licenses & Attributions
CC licensed content, Shared previously
- Subtracting Integers with Color Counters (No Extra Zeros Needed). 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].