Adding and Subtracting Integers

Key Concepts

Integers are whole numbers that can be positive, negative, or zero. Adding and subtracting integers involves understanding how these numbers interact with each other on the number line.

1. Adding Integers

When adding integers, consider their signs and magnitudes. If both integers have the same sign, add their absolute values and keep the common sign. If they have different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.

2. Subtracting Integers

Subtracting integers can be transformed into addition. To subtract an integer, change the sign of the integer being subtracted and then follow the rules for addition.

Detailed Explanation

Adding Integers

For example, to add -3 and -5, add their absolute values (3 + 5 = 8) and keep the negative sign, resulting in -8. For 7 + (-4), subtract the smaller absolute value from the larger (7 - 4 = 3) and keep the sign of the larger absolute value, resulting in 3.

Subtracting Integers

For example, to subtract -3 from 5, change the subtraction to addition (5 + 3) and follow the rules for addition, resulting in 8. To subtract 7 from -2, change the subtraction to addition (-2 + (-7)) and follow the rules for addition, resulting in -9.

Examples and Analogies

Example 1: Adding Integers

Imagine a bank account where deposits are positive and withdrawals are negative. If you deposit $3 and then withdraw $5, the net effect is a withdrawal of $2, represented as -3 + (-5) = -8.

Example 2: Subtracting Integers

Think of a temperature change. If the temperature drops by 3 degrees from -5 degrees, the new temperature is -5 - (-3) = -5 + 3 = -2 degrees.

Conclusion

Understanding how to add and subtract integers is crucial for various mathematical operations and real-world applications. By mastering these concepts, you can handle complex calculations with ease.