Integer addition and subtraction rules

Learning Objectives Define integers and absolute value. Accurately add integers with the same sign. Accurately add integers with different signs. Convert integer subtraction problems into addition problems. Solve multi-step problems involving integer addition and subtraction. Apply integer operations to real-world contexts. Ever wonder how temperatures drop below zero or how a submarine dives deep into the ocean? 🌡️🌊 These situations use integers! In this lesson, you'll learn the essential rules for adding and subtracting integers, which are whole numbers and their opposites. Mastering these rules is crucial for solving more complex equations and understanding real-world scenarios involving positive and negative values, laying a strong foundation for linear functions....

TermDefinitionExample IntegerWhole numbers and their opposites. Integers include positive numbers, negative numbers, and zero (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...).The numbers -5, 0, and 12 are all integers. Positive IntegerAn integer greater than zero. These are typically written without a sign or with a '+' sign.7, 25, and 100 are positive integers. Negative IntegerAn integer less than zero. These are always written with a '-' sign.-3, -18, and -99 are negative integers. Absolute ValueThe distance of a number from zero on a number line. It is always a non-negative value, denoted by vertical bars around the number.$|5| = 5$ and $|-5| = 5$. Both 5 and -5 are 5 units away from zero. OppositeTwo numbers that are the same distance from zero on a number line but on oppo...

Adding Integers with the Same Sign If $a$ and $b$ have the same sign, then $a + b = \pm (|a| + |b|)$, where the sign is the common sign of $a$ and $b$. When adding two positive integers, the sum is positive. When adding two negative integers, add their absolute values and keep the negative sign. Adding Integers with Different Signs If $a$ and $b$ have different signs, then $a + b = \pm ||a| - |b||$, where the sign is the sign of the integer with the greater absolute value. Find the difference between their absolute values. The sum takes the sign of the number that is further from zero (has the greater absolute value). Subtracting Integers (Add the Opposite) To subtract an integer, add its opposite: $a - b = a + (-b)$. Change the subtraction sign to an addition sign,...