The sum of two opposites is zero
The rule that the sum of two opposites equals zero is a fundamental Grade 7 integer property in Saxon Math, Course 2: a + (-a) = 0 for any number a. For example, (-92) + (+92) = 0 and a gain of $450 combined with a loss of $450 results in exactly $0. Opposite numbers — also called additive inverses — are the same distance from zero on the number line but on opposite sides. Recognizing this property simplifies computations, supports equation solving, and is the basis for understanding additive inverses in algebra.
Key Concepts
Property The sum of two opposites is zero. For any number $a$, this rule can be written as $a + ( a) = 0$.
Examples $( 92) + (+92) = 0$.
$(+3) + ( 3) = 0$.
Common Questions
What is the sum of two opposite numbers?
The sum of two opposite numbers (additive inverses) is always zero. For any number a, a + (-a) = 0.
What are opposite numbers?
Opposite numbers are two numbers that are equal in absolute value but have different signs (one positive, one negative). For example, 5 and -5 are opposites.
Why does a number plus its opposite equal zero?
On the number line, a positive number moves right and its negative opposite moves the same distance left, ending exactly at zero — perfect cancellation.
How is the sum of opposites used in algebra?
This property explains how additive inverses work in equation solving: adding the opposite of a term cancels it, isolating the variable on one side.
Where is the sum of two opposites taught in Saxon Math Course 2?
This integer property appears in Saxon Math, Course 2, as part of Grade 7 integer operations and number properties.
Can you give a real-world example of opposites summing to zero?
A financial example: gaining $450 and losing $450 results in a net change of $0. A temperature example: rising 15 degrees then falling 15 degrees returns to the original temperature.
How does the zero property of opposites relate to the additive identity?
Zero is the additive identity — adding zero to any number leaves it unchanged. The sum of opposites produces that identity element (zero), reinforcing that opposites perfectly cancel each other.