Skip to ContentGo to accessibility page Prealgebra

# Key Concepts

PrealgebraKey Concepts

### 3.1Introduction to Integers

• Opposite Notation
• $−a−a$ means the opposite of the number $aa$
• The notation $−a−a$ is read the opposite of $a.a.$
• Absolute Value Notation
• The absolute value of a number $nn$ is written as $|n||n|$.
• $|n|≥0|n|≥0$ for all numbers.

### 3.2Add Integers

• Addition of Positive and Negative Integers
 $5+35+3$ $−5+(−3)−5+(−3)$ both positive, sum positive both negative, sum negative When the signs are the same, the counters would be all the same color, so add them. $−5+3−5+3$ $5+(−3)5+(−3)$ different signs, more negatives different signs, more positives Sum negative sum positive When the signs are different, some counters would make neutral pairs; subtract to see how many are left.

### 3.3Subtract Integers

• Subtraction of Integers
 $5–35–3$ $–5–(–3)–5–(–3)$ $22$ $–2–2$ 2 positives 2 negatives When there would be enough counters of the color to take away, subtract. $–5–3–5–3$ $5–(–3)5–(–3)$ $–8–8$ $88$ 5 negatives, want to subtract 3 positives 5 positives, want to subtract 3 negatives need neutral pairs need neutral pairs When there would not be enough of the counters to take away, add neutral pairs.
Table 3.13
• Subtraction Property
• $a−b=a+(−b)a−b=a+(−b)$
• $a−(−b)=a+ba−(−b)=a+b$
• Solve Application Problems
• 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.

### 3.4Multiply and Divide Integers

• Multiplication of Signed Numbers
• To determine the sign of the product of two signed numbers:
Same Signs Product
Two positives
Two negatives
Positive
Positive

Different Signs Product
Positive • negative
Negative • positive
Negative
Negative
• Division of Signed Numbers
• To determine the sign of the quotient of two signed numbers:
Same Signs Quotient
Two positives
Two negatives
Positive
Positive

Different Signs Quotient
Positive • negative
Negative • Positive
Negative
Negative
• Multiplication by $−1−1$
• Multiplying a number by $−1−1$ gives its opposite: $−1a=−a−1a=−a$
• Division by $−1−1$
• Dividing a number by $−1−1$ gives its opposite: $a÷(−1)=−aa÷(−1)=−a$

### 3.5Solve Equations Using Integers; The Division Property of Equality

• How to determine whether a number is a solution to an equation.
• Step 1. Substitute the number for the variable in the equation.
• Step 2. Simplify the expressions on both sides of the equation.
• Step 3. Determine whether the resulting equation is true.
• If it is true, the number is a solution.
• If it is not true, the number is not a solution.
• Properties of Equalities
Subtraction Property of Equality Addition Property of Equality
$For any numbersa,b,c,For any numbersa,b,c,$
$ifa=bthena−c=b−c.ifa=bthena−c=b−c.$
$For any numbersa,b,c,For any numbersa,b,c,$
$ifa=bthena+c=b+c.ifa=bthena+c=b+c.$
• Division Property of Equality
• For any numbers $a,b,c,a,b,c,$ and $c≠0c≠0$
If $a=ba=b$, then $ac=bcac=bc$.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

Attribution information
• If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
• If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
Citation information

© Sep 16, 2020 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.