Learn about integers through these example problems with detailed step-by-step solutions.
Example 1: Adding Integers
Calculate the value of \(-5 + 8\).
Step 1: Identify the integers: \(-5\) (negative) and \(+8\) (positive).
Step 2: Since the signs are different, subtract the smaller absolute value from the larger: \(|8| - |-5| = 8 - 5 = 3\).
Step 3: The sign of the result is the same as the integer with the larger absolute value, which is \(+8\). So, the result is positive.
Step 4: Therefore, \(-5 + 8 = 3\).
Example 2: Subtracting Integers
Calculate the value of \(7 - (-3)\).
Step 1: Subtracting a negative is the same as adding the positive: \(7 - (-3) = 7 + 3\).
Step 2: Add the integers: \(7 + 3 = 10\).
Step 3: Therefore, \(7 - (-3) = 10\).
Example 3: Comparing Integers
Compare the integers \(-4\) and \(2\) using the correct symbol (<, >, or =).
Step 1: On a number line, negative numbers are to the left of zero, and positive numbers are to the right.
Step 2: \(-4\) is negative and lies to the left of zero, while \(2\) is positive and lies to the right.
Step 3: Therefore, \(-4 < 2\).
Practice Mode
Enter your own problem related to integers, and get a step-by-step solution.
Note: This basic solver can currently handle addition and subtraction of integers (e.g., Calculate -3 + 7; Calculate 5 - (-2)) and comparison of integers (e.g., Compare -6 and 4).
Related Concepts
Explore these related mathematical concepts to deepen your understanding of integers.
Integers
Integers include all whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...).
Number Line
A number line visualizes integers, with negative numbers to the left of zero and positive numbers to the right.
Absolute Value
The absolute value of an integer is its distance from zero on the number line, always non-negative.
Operations with Integers
Addition and subtraction of integers follow specific rules based on their signs.
