Meet the Opposites
Opposite numbers are pairs like 5 and −5 that are equal distances from zero on the number line but on opposite sides. In Grade 6 Saxon Math Course 1, students learn the property: a + (−a) = 0 — a number and its opposite always sum to zero, making them additive inverses. Opposite numbers have the same absolute value but different signs. This concept introduces signed number arithmetic and is foundational for understanding subtraction of integers and solving equations in algebra.
Key Concepts
Property Numbers like $5$ and $ 5$ are the same distance from zero but are on opposite sides of zero. We say that $5$ and $ 5$ are opposites .
Examples The opposite of $12$ is $ 12$. The opposite of $ 25$ is $25$. On a number line, $7$ and $ 7$ are both 7 steps away from $0$.
Explanation Imagine you and your mirror image standing on opposite sides of a puddle (that's zero). You're both the same distance from it! That's how opposites work in math. Every positive number has a negative twin, and they perfectly balance each other out across zero on the number line.
Common Questions
What are opposite numbers?
Two numbers with the same absolute value but opposite signs. Example: 5 and −5. They sit equal distances from zero on the number line.
What is the sum of a number and its opposite?
Always zero. 5 + (−5) = 0. This is why they are called additive inverses.
What is the opposite of −7?
7. The opposite of a negative number is the corresponding positive number.
What is the absolute value of −5?
5. Absolute value measures distance from zero, always giving a non-negative result.
How does the concept of opposites relate to subtraction?
Subtracting a number is the same as adding its opposite: a − b = a + (−b). This rule extends subtraction to all integers.