📚 Practice With Worksheets
Continue practicing integer addition, subtraction, multiplication, division, and real-world applications with the worksheets below.
▶️ Learn With Videos
Review integer rules, zero pairs, movement on a number line, and real-world situations involving positive and negative values.
🛠️ How to Use This Tool
Choose addition, subtraction, multiplication, division, mixed integer operations, or advanced integer expressions.
Select a challenge level, choose numbers only or numbers and word problems, and set a goal of 5, 10, 15, or 20 questions.
Enter one integer and select Check Answer. After making a valid attempt, use Show Solution to review the sign rule, order of operations, and intermediate steps.
🧠 Things to Notice
The rules for addition and subtraction are different from the sign rules used for multiplication and division.
Subtracting a negative integer is equivalent to adding its opposite. For example, \(8-(-3)=8+3\).
In longer expressions, apply the order of operations. Complete grouping symbols first, then multiplication and division from left to right, followed by addition and subtraction from left to right.
📘 Vocabulary
Integer: A positive whole number, a negative whole number, or zero.
Positive integer: An integer greater than zero.
Negative integer: An integer less than zero.
Zero: The integer that is neither positive nor negative.
Opposites: Two numbers that are the same distance from zero on opposite sides of a number line.
Additive inverse: The opposite of a number. A number and its additive inverse have a sum of zero.
Zero pair: A pair consisting of one positive unit and one negative unit whose sum is zero.
Absolute value: A number’s distance from zero on a number line.
Ascending: Moving upward or increasing in value.
Descending: Moving downward or decreasing in value.
Gain: A positive change or increase.
Loss: A negative change or decrease.
Deposit: Money added to an account, usually represented by a positive integer.
Withdrawal: Money removed from an account, usually represented by a negative change.
Elevation: A vertical position compared with sea level or another reference point.
Product: The result of multiplication.
Quotient: The result of division.
Order of operations: The agreed-upon order used to evaluate a mathematical expression.
📐 Integer Operation Rules
Before calculating, identify the operation and examine the signs. Addition and subtraction use different reasoning than multiplication and division.
Adding Integers
Same signs: Add the absolute values and keep the common sign.
Different signs: Subtract the smaller absolute value from the larger absolute value. Use the sign of the number with the greater absolute value.
Subtracting Integers
Rewrite subtraction as adding the opposite. Keep the first integer, change subtraction to addition, and change the sign of the second integer.
Multiplying Integers
Same signs: The product is positive.
Different signs: The product is negative.
Dividing Integers
Same signs: The quotient is positive.
Different signs: The quotient is negative.
Mixed and Advanced Integer Expressions
Use grouping symbols first. Then complete multiplication and division from left to right, followed by addition and subtraction from left to right.
Negative outside parentheses: A negative sign outside a group changes the sign of every term inside the parentheses.
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