By Brenda Scottsdale Updated Aug 30, 2022
Integers are whole numbers that form the foundation of arithmetic. They appear in every calculation—from simple counting to complex algebraic equations. The concept of integers dates back to ancient Babylon and Egypt, where early mathematicians began using them to solve practical problems.
On a number line, positive integers lie to the right of zero and increase in value as you move rightward. Examples include 1, 2, 3, 4, and 5. The equal spacing between each point on the line means that statements about size are meaningful; for instance, 2 is twice as large as 1, 10 is twice as large as 5, and 100 is twice as large as 50.
Negative integers occupy the left side of the number line, directly opposite their positive counterparts. For every positive integer there is a negative pair—2 pairs with –2, 5 with –5, and 50 with –50. Each pair is the same distance from zero, so –10 is twice as large (in magnitude) as –5.
Use the number line to visualize addition:
Subtraction can be seen as adding the opposite number:
Multiplication is repeated addition. Key rules:
Memorizing multiplication tables speeds up problem solving.
Division asks how many times one integer fits into another. The sign rules mirror multiplication:
Understanding these operations provides a solid foundation for all levels of mathematics and real‑world problem solving.
