Fill in the blanks to summarize how to add, subtract, multiply, and divide integers. Addition 1. If the two integers being added have the same sign, - add their absolute values. - use their sign for the answer. 2. If the two integers being added have different signs, - find the difference of their absolute values. - use the sign of the number with the greater absolute value. Subtraction 1. While subtracting one number from another, find the additive inverse of the second number and add it to the first using the rule of addition. Multiplication and Division 1. While multiplying or dividing two integers, - find the product or quotient of the absolute values. - identify the sign of the result by following the rules below: - positive x positive = positive - positive x negative = negative - negative x positive = negative - negative x negative = positive - When the signs are the same, the answer is positive. - When the signs are different, the answer is negative. - positive ÷ positive = positive - positive ÷ negative = negative - negative ÷ positive = negative - negative ÷ negative = positive Fill in the blanks with 'Yes' or 'No' to summarize the properties of integers. | Property/Operation | Addition | Subtraction | Multiplication | Division | |-------------------|----------|-------------|----------------|----------| | Closure Property | Yes | No | Yes | No | | Commutative Property | Yes | No | Yes | No | | Associative Property | Yes | No | Yes | No |
Answer (1)
Adding, subtracting, multiplying, and dividing integers involve understanding different rules for each operation:
Addition of Integers
If the two integers have the same sign:
Add their absolute values.
Use the common sign for the answer.
If the two integers have different signs:
Subtract the smaller absolute value from the larger absolute value.
Use the sign of the integer with the larger absolute value for the result.
Subtraction of Integers
When subtracting one integer from another:
Find the additive inverse of the second integer (change its sign).
Add this to the first integer using the addition rules.
Multiplication and Division of Integers
When multiplying or dividing two integers:
Calculate the product or quotient of their absolute values.
Determine the sign of the result using these rules:
Multiplication:
Positive × Positive = Positive
Positive × Negative = Negative
Negative × Positive = Negative
Negative × Negative = Positive
Division:
Positive ÷ Positive = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative
Negative ÷ Negative = Positive
If both numbers have the same sign, the result is positive.
If the numbers have different signs, the result is negative.
Properties of Integer Operations
Property/OperationAdditionSubtractionMultiplicationDivisionClosure PropertyYesNoYesNoCommutative PropertyYesNoYesNoAssociative PropertyYesNoYesNo
These rules and properties help ensure consistency and accuracy when working with integers across different mathematical operations.
