Add and subtract integers

Learning Objectives Define integers and identify them on a number line. Add integers with the same sign accurately. Add integers with different signs correctly. Subtract integers by converting subtraction to addition of the opposite. Solve multi-step problems involving addition and subtraction of integers. Apply integer operations to solve real-world problems. Ever wonder how temperature changes from -5°C to 10°C? 🌡️ Or how your bank balance changes after a deposit and a withdrawal? In this lesson, you'll learn the fundamental rules for adding and subtracting positive and negative numbers, known as integers. Mastering these operations is crucial for understanding more complex math concepts like linear functions and systems of equations, which you'll encounter in...

TermDefinitionExample IntegerWhole numbers (positive, negative, or zero) without fractions or decimals.-3, 0, 5, -100 Positive IntegerAn integer greater than zero.1, 7, 100 Negative IntegerAn integer less than zero.-1, -7, -100 Opposite NumbersTwo numbers that are the same distance from zero on a number line but in opposite directions.5 and -5; -12 and 12 Absolute ValueThe distance of a number from zero on the number line, always non-negative.$|-3| = 3$, $|3| = 3$, $|-10| = 10$ Number LineA line on which numbers are marked at regular intervals, used to visualize integers and their operations.A horizontal line with 0 in the center, positive numbers to the right, negative numbers to the left.

Adding Integers with the Same Sign Add their absolute values and keep the common sign. This rule applies when both integers are positive or both are negative. For example, $3 + 5 = 8$ and $-3 + (-5) = -8$. Adding Integers with Different Signs Subtract the smaller absolute value from the larger absolute value, and keep the sign of the number with the larger absolute value. This rule applies when one integer is positive and the other is negative. For example, $-8 + 5 = -(8-5) = -3$ and $8 + (-5) = +(8-5) = 3$. Subtracting Integers (Keep-Change-Change) $a - b = a + (-b)$ To subtract an integer, change the subtraction problem to an addition problem by adding the opposite of the second number. For example, $7 - (-3)$ becomes $7 + 3$.