Add and subtract integers

Learning Objectives Define integers and identify their representation on a number line. Add integers with the same sign using rules and models. Add integers with different signs using rules and models. Subtract integers by converting subtraction to addition of the opposite. Solve multi-step problems involving addition and subtraction of integers. Apply integer operations to real-world contexts such as temperature, altitude, and finance. Ever wonder how hot it feels at the equator compared to how cold it is at the North Pole? 🌡️❄️ How do we describe these temperature differences using numbers? In this lesson, you'll learn how to add and subtract integers, which are positive and negative whole numbers, including zero. Understanding these operations is crucial for solving...

TermDefinitionExample IntegerWhole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractions or decimals.Examples of integers are -5, 0, 12, -100. Positive IntegerAn integer that is greater than zero. These are typically written without a sign or with a '+' sign.5, 10, 250 are positive integers. Negative IntegerAn integer that is less than zero. These are always written with a '-' sign.-5, -10, -250 are negative integers. OppositeTwo numbers that are the same distance from zero on a number line but in opposite directions.The opposite of 7 is -7. The opposite of -12 is 12. Absolute ValueThe distance of a number from zero on a number line. Absolute value is always a non-negative number.The absolute value of -8 is 8, written as $...

Adding Integers with the Same Sign To add two integers with the same sign, add their absolute values and keep the common sign. If both numbers are positive, the sum is positive. If both numbers are negative, the sum is negative. For example, $a + b$ where $a, b > 0$ or $a, b < 0$. Example: $3 + 5 = 8$ and $(-3) + (-5) = -8$. Adding Integers with Different Signs To add two integers with different signs, subtract the smaller absolute value from the larger absolute value, and keep the sign of the integer with the larger absolute value. This rule applies when one integer is positive and the other is negative. For example, $a + b$ where one is positive and one is negative. Example: $5 + (-3) = 2$ and $(-5) + 3 = -2$. Subtracting Integers (Add the Opposite) To subtra...