In this lesson from OpenStax Prealgebra 2E, Chapter 3, students learn how to subtract integers, including subtracting negative numbers using a counter model. The lesson covers simplifying integer expressions, evaluating variable expressions with integers, and translating word phrases into algebraic expressions. Students also apply integer subtraction to real-world problems, building a concrete foundation for working with signed numbers.
Section 1
📘 Subtract Integers
Subtracting an integer is the same as adding its opposite. This key idea, expressed as , transforms subtraction problems, especially with negatives, into simpler addition problems you already know how to solve.
Now, let's put this rule into practice. You'll master this concept through interactive examples with counters and a series of challenging practice problems.
Section 2
Model subtraction of integers
We can use counters to model subtraction. Blue counters represent positive numbers and red counters represent negative numbers. When we read as 'five take away three', we can model this by starting with a number of counters and then taking some away.
When there would be enough counters of the color to take away, subtract.
Section 3
Modeling with neutral pairs
When there would not be enough of the counters to take away, add neutral pairs.
A neutral pair consists of one positive counter and one negative counter. The value of a neutral pair is zero. Adding neutral pairs to the workspace does not change the overall value of the number.
Section 4
Subtraction property
Subtraction of signed numbers can be done by adding the opposite. This is known as the Subtraction Property and is written as:
Knowing this property helps when we are subtracting negative numbers.
Section 5
Solve application problems
To solve application problems involving integer subtraction, follow these steps:
Step 1. Identify what you are asked to find.
Step 2. Write a phrase that gives the information to find it.
Step 3. Translate the phrase to an expression.
Step 4. Simplify the expression.
Step 5. Answer the question with a complete sentence.
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Section 1
📘 Subtract Integers
Subtracting an integer is the same as adding its opposite. This key idea, expressed as , transforms subtraction problems, especially with negatives, into simpler addition problems you already know how to solve.
Now, let's put this rule into practice. You'll master this concept through interactive examples with counters and a series of challenging practice problems.
Section 2
Model subtraction of integers
We can use counters to model subtraction. Blue counters represent positive numbers and red counters represent negative numbers. When we read as 'five take away three', we can model this by starting with a number of counters and then taking some away.
When there would be enough counters of the color to take away, subtract.
Section 3
Modeling with neutral pairs
When there would not be enough of the counters to take away, add neutral pairs.
A neutral pair consists of one positive counter and one negative counter. The value of a neutral pair is zero. Adding neutral pairs to the workspace does not change the overall value of the number.
Section 4
Subtraction property
Subtraction of signed numbers can be done by adding the opposite. This is known as the Subtraction Property and is written as:
Knowing this property helps when we are subtracting negative numbers.
Section 5
Solve application problems
To solve application problems involving integer subtraction, follow these steps:
Step 1. Identify what you are asked to find.
Step 2. Write a phrase that gives the information to find it.
Step 3. Translate the phrase to an expression.
Step 4. Simplify the expression.
Step 5. Answer the question with a complete sentence.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter