📚 Practice With Worksheets
Strengthen your understanding of integer operations, number lines, opposites, distance, and positive and negative numbers.
▶️ Learn With Videos
Review integer addition and subtraction rules and see how zero pairs and integer tiles model the operations.
🛠️ How to Use This Tool
Choose addition or subtraction mode, or select a random problem to create a new integer expression.
Green chips represent \(+1\), and red chips represent \(-1\). One green chip and one red chip form a zero pair because their combined value is zero.
Remove zero pairs until only one color remains, and then use the remaining chips to determine the value of the expression.
🧠 Things to Notice
Removing a zero pair does not change the value of the model because \(+1+(-1)=0\).
When the integers have different signs, the remaining chip color matches the sign of the number with the greater absolute value.
Subtracting an integer can be modeled by adding its opposite, so subtraction problems can be rewritten as addition problems before the chips are combined.
📘 Vocabulary
Integer: A whole number, its opposite, or zero. Examples include \(-4\), \(0\), and \(7\).
Positive Integer: An integer greater than zero, such as \(3\) or \(12\).
Negative Integer: An integer less than zero, such as \(-3\) or \(-12\).
Opposites: Two numbers that are the same distance from zero but lie on opposite sides of zero, such as \(5\) and \(-5\).
Zero Pair: A positive chip and a negative chip whose combined value is zero.
Additive Inverse: A number that combines with another number to make zero. The additive inverse of \(8\) is \(-8\).
Absolute Value: The distance a number is from zero on a number line. Absolute value is always zero or positive.
Adding the Opposite: Rewriting subtraction as addition of the second number’s opposite.
Expression: A mathematical phrase containing numbers and operations, such as \(-5+7\).
➕ Integer Operation Rules
Integer addition and subtraction use different decision rules from integer multiplication and division. Learning the rules side by side can help prevent them from getting mixed up.
Adding Integers
Same signs: Add the absolute values and keep the common sign.
\((-6)+(-4)=-10\)
Different signs: Subtract the smaller absolute value from the larger absolute value. Keep the sign of the number with the greater absolute value.
\((-9)+5=-4\)
Subtracting Integers
Keep the first integer, change subtraction to addition, and change the second integer to its opposite. Then use the addition rules.
\(7-(-3)=7+3=10\)
After rewriting, look at the signs. Same signs mean add the absolute values. Different signs mean subtract the absolute values.
\((-4)-6=(-4)+(-6)=-10\)
Multiplying and Dividing Integers
Multiply or divide the absolute values first. Then determine the sign from the signs of the two integers.
Same signs: The result is positive.
\((-6)(-4)=24\)
Different signs: The result is negative.
\((-24)\div6=-4\)
Important comparison: For addition, the signs tell you whether to add or subtract the absolute values. For multiplication and division, you always multiply or divide the absolute values, and the signs determine whether the answer is positive or negative.
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