Understanding integers

Learning Objectives Define integers and identify them in various contexts. Represent integers on a number line. Compare and order integers. Perform addition of integers with different and same signs. Perform subtraction of integers. Calculate the absolute value of an integer. Solve real-world problems involving integers. Ever wonder how temperatures drop below zero 🥶 or how deep a submarine can dive ⚓? Integers help us describe these situations! In this lesson, you'll explore the world of integers, which are whole numbers and their opposites. You'll learn how to represent, compare, and perform basic operations with them, which is crucial for understanding more advanced math like linear equations and proportions. Real-World Applications Temperature readings...

TermDefinitionExample IntegerA whole number (not a fraction or decimal) that can be positive, negative, or zero. Integers include numbers like ..., -3, -2, -1, 0, 1, 2, 3, ...-7, 0, 15, -100 Positive IntegerAn integer greater than zero. They are usually written without a sign or with a '+' sign.1, 5, 23 (+1, +5, +23) Negative IntegerAn integer less than zero. They are always written with a '-' sign.-1, -5, -23 Number LineA line on which numbers are marked at regular intervals. It helps visualize the order and relative values of integers.A line with 0 at the center, positive integers to the right, and negative integers to the left. Opposite NumbersTwo numbers that are the same distance from zero on a number line but in opposite directions.5 and -5 are opposite numbers;...

Adding Integers with the Same Sign $a + b = |a| + |b|$ (if $a, b$ are positive) or $a + b = -(|a| + |b|)$ (if $a, b$ are negative) When adding integers with the same sign, add their absolute values and keep the common sign. For example, $3+5=8$ and $(-3)+(-5)=-8$. Adding Integers with Different Signs $a + b = ext{sign of (larger absolute value)} imes (| |a| - |b| |)$ When adding integers with different signs, subtract the smaller absolute value from the larger absolute value. The sum takes the sign of the integer with the larger absolute value. For example, $-7 + 3 = -4$ and $7 + (-3) = 4$. Subtracting Integers $a - b = a + (-b)$ To subtract an integer, add its opposite. This means 'keep the first number, change the subtraction to addition, and change the sign...