Integer addition and subtraction rules

Learning Objectives Define integers and identify their properties. 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 both integer addition and subtraction. Apply integer operations to solve real-world problems. Ever wonder how temperatures drop below zero or how a submarine dives deep underwater? 📉 These situations involve negative numbers, and understanding how to add and subtract them is key! In this lesson, you'll learn the essential rules for adding and subtracting integers, which include positive numbers, negative numbers, and zero. Mastering these operations is crucial for solving more complex equations and understan...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...-5, 0, 12 Positive IntegerAn integer greater than zero. It can be written with or without a '+' sign.+7 or 7 Negative IntegerAn integer less than zero. It is always written with a '-' sign.-10 OppositeTwo numbers that are the same distance from zero on a number line but on opposite sides. Their sum is always zero.The opposite of 5 is -5. The opposite of -3 is 3. Absolute ValueThe distance of a number from zero on the number line, always expressed as a positive value. It's denoted by vertical bars: $| |$.$|-7| = 7$ and $|7| = 7$ Number LineA line on which numbers are marked at regular intervals, used to visualize...

Adding Integers with the Same Sign If two integers have the same sign (both positive or both negative), add their absolute values and keep the common sign. When adding numbers that are both positive, the sum is positive. When adding numbers that are both negative, the sum is negative. For example, $a + b = |a| + |b|$ if $a, b > 0$, and $(-a) + (-b) = -(|a| + |b|)$ if $a, b < 0$. Adding Integers with Different Signs If two integers have different signs (one positive, one negative), subtract the smaller absolute value from the larger absolute value. The sum takes the sign of the integer with the larger absolute value. This rule helps determine if the result will be positive or negative. For example, $a + (-b) = |a| - |b|$ if $|a| > |b|$ and $a > 0$, or $a + (-b) =...