Opposites
Opposites in math are two numbers that are the same distance from zero on a number line but on opposite sides. The opposite of 5 is -5, and the opposite of -7 is 7. Mathematically, the opposite of a number n is -n. Adding a number and its opposite always gives zero: 5 + (-5) = 0. This is also called the additive inverse. This 7th grade concept from Saxon Math Course 2 is foundational for working with negative numbers, solving equations, and understanding the algebraic addition of signed quantities.
Key Concepts
Property A positive number and a negative number whose absolute values are equal are opposites .
Examples The opposite of 8 is $ 8$. The opposite of $ 25$ is $25$. The opposite of $\frac{3}{4}$ is $ \frac{3}{4}$.
Explanation Imagine a number line is a street and zero is your house. Opposites are like two friends who live the same distance from your house but in opposite directions! So, 7 is seven steps to the right, and its opposite, 7, is seven steps to the left. They're mirror images across zero, perfectly balanced every single time.
Common Questions
What are opposites in math?
Opposites are two numbers that are equal distances from zero on a number line but on different sides. The opposite of 5 is -5; the opposite of -3 is 3. Their sum is always 0.
What is the opposite of a negative number?
The opposite of a negative number is positive. The opposite of -7 is 7, and the opposite of -1/2 is 1/2.
What happens when you add a number and its opposite?
They cancel out to zero. This is called the additive inverse property: n + (-n) = 0 for any number n. For example, 8 + (-8) = 0.
What grade learns about mathematical opposites?
Opposites and additive inverses are a 7th grade topic in Saxon Math Course 2, Chapter 8, foundational to working with integers and rational numbers.
How are opposites used in subtraction?
Algebraic addition converts subtraction to adding the opposite: a - b = a + (-b). Knowing opposites makes this transformation natural and automatic.
What is the opposite of zero?
Zero is its own opposite. Zero is neither positive nor negative, and -0 = 0.