Integers
Integers are the set of all whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ... Integers do not include fractions or decimals — 3.5 and -1/2 are not integers. This Grade 7 math skill from Saxon Math, Course 2 establishes the formal number line, extends arithmetic to negative values, and is the foundational vocabulary for signed number operations, coordinate graphing, and algebra. Integers appear in real life whenever quantities can go below zero: temperature, elevation, financial balances, and scores in games.
Key Concepts
Property Integers include all the whole numbers and also the opposites of the positive integers (their negatives). $$ ..., 3, 2, 1, 0, 1, 2, 3, ... $$.
Examples The numbers $ 10$, $0$, and $42$ are all proud members of the integer family. Numbers like $3\frac{1}{2}$ and $ 1.5$ are not integers because they are not whole numbers. A temperature of $ 5$ degrees, a depth of $ 100$ feet, and a profit of $500$ dollars are all described with integers.
Explanation Think of integers as all the whole number steps you can take on a number line, both forward (positive) and backward (negative), including standing still at zero. No fractions or decimals are allowed in this exclusive club! It’s the set of whole numbers and their grumpy, negative twins, plus the very neutral zero who gets along with everyone.
Common Questions
What are integers?
Integers are all whole numbers and their opposites (negatives), including zero: ..., -3, -2, -1, 0, 1, 2, 3, ... Integers do not include fractions or decimals.
Is zero an integer?
Yes. Zero is an integer. It is neither positive nor negative; it is the middle of the number line and belongs to the set of integers.
Are fractions and decimals integers?
No. Fractions (like 3/4) and decimals (like -1.5) are not integers. Only whole numbers and their negatives are integers.
What are negative integers used for?
Negative integers represent quantities below zero: temperatures below zero (like -15°F), elevations below sea level, financial losses, and scores below a baseline.
When do students learn about integers?
Integers are introduced in Grade 6 and studied in depth in Grade 7. Saxon Math, Course 2 covers integers in Chapter 1 as the foundation for all signed number work.
How are integers placed on a number line?
Zero is at the center. Positive integers extend to the right. Negative integers extend to the left. Each integer is one unit from the next. The integers are evenly spaced.
What is the difference between integers and whole numbers?
Whole numbers are 0, 1, 2, 3, ... (non-negative only). Integers extend whole numbers to include negative values: ..., -2, -1, 0, 1, 2, ...