Integer operations
Mathematics, Grade 8
Integer operations
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Integer operations
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Integer operations
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Integer operations
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Integer operations
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Study Guide Integer operations Mathematics, Grade 8
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INTEGER OPERATIONS What Are Integer Operations? Integer operations are the mathematical operations that involve integers. Integers are negative numbers, zero and positive numbers. • When adding and subtracting integers, specific rules must be followed. Adding and subtracting integers are useful in everyday life because there are many situations that involved negative numbers such as calculating sea level or temperatures. • When multiplying and dividing integers, specific rules must also be followed. To multiply and divide, first the numbers are either multiplied or divided as stated. Then the sign for the answer is determined based on the following: (+)(+) or (-)(-) = + (+)(-) or (-)(+) = - Equations with integers are solved using inverse operations. Inverse operations are used to isolate a variable. Inverse operations undo an operation; addition and subtraction are inverse operations, and multiplication and division are inverse operations of each other. • Inequalities with integers compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. • Inequalities are also solved by using inverse operations. When solving equations and inequalities, the rules for the mathematical operations must be used in order to achieve the correct answer. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
How to use integer operations Operations with integers involve negative numbers, zero and positive numbers. When performing integer operations, certain rules must be used. • To add integers with different signs, subtract the absolute value of the integers and write the sign of the larger absolute value. • To add integers with the same sign, add the absolute value of the integers and write the common sign. Ex. -8 + 5 = │-8│- │5 │ = -3, the answer is -3 because 8 is larger than 5 -7 + -5 = │-7│ + │-5│ = -12, the answer is -12 because the common sign is negative • To subtract integers with the different signs or the same signs, add the opposite of the second integer. Ex. -6 - 3 = -6 + (-3) = -9 2 - (-8) = 2 + 8 = 10 • To multiply and divide integers, first the numbers are either multiplied or divided as stated. Then the sign for the answer is determined based on the following: (+)(+) or (-)(-) = +; (+)(-) or (-)(+) = -. Ex. (-5)(-7) = +35 (-6)(9) = -54 • Equations and inequalities are solved with inverse operations. When solving with integers, the rules for each mathematical operation must be used. Remember when multiplying or dividing by a negative number, the inequality sign is reversed. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. Add the integers: 9 + (-5) = ? -4 + 6 = ? -3 + (-7) = ? 2. Subtract the integers: 9 - 12 = ? -2 - 3 = ? -6 - (-10) = ? 3. Multiply or divide the integers: (-5)(8) = ? (-7)(-4) = ? -63/-9 = ? 4. Solve for x: -2x = -18 6x = -42 -1/5x = 4 5. Solve the inequality for x: x + 3 ≤ -7 -9x > 36 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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