Adding Two Numbers with Opposite Signs
When adding a positive and a negative number, the result's sign belongs to whichever number is farther from zero, and the value is the difference between the two absolute values. For example, (+15) + (-6) = +9 because 15 is farther from zero, and 15 - 6 = 9. This Grade 8 math skill from Yoshiwara Core Math Chapter 7 gives students a clear, algorithmic method for handling one of the most confusion-prone operations in pre-algebra. Mastering this rule is fundamental to all signed number arithmetic and directly supports simplifying algebraic expressions and solving equations.
Key Concepts
Property The sum of a positive number and a negative number can be either positive or negative. It depends on which is farther from zero.
If the positive number is farther from zero, the sum will be positive. If the negative number is farther from zero, the sum will be negative.
To find the sum, subtract the unsigned parts of the numbers, and use the sign of the number that is farther from zero.
Common Questions
How do you add a positive and negative number?
Find which number is farther from zero (has the larger absolute value). The result has the same sign as that number. Subtract the smaller absolute value from the larger to get the answer. For example, (+4) + (-11) = -7 because 11 > 4 and 11 - 4 = 7.
What is the rule for adding numbers with opposite signs?
The sign of the result matches the number with the larger absolute value (the one farther from zero). Subtract the smaller absolute value from the larger to find the magnitude.
What is absolute value?
Absolute value is the distance of a number from zero on the number line, always a non-negative number. The absolute value of -7 is 7, and the absolute value of 7 is also 7. It is written with vertical bars: |-7| = 7.
When do 8th graders learn about adding opposite-sign numbers?
Students study adding numbers with opposite signs in Grade 8 math as part of Chapter 7 of Yoshiwara Core Math, which covers signed numbers and all integer operations.
What is a real-world example of adding positive and negative numbers?
If you have $25 and spend $30, your balance is (+25) + (-30) = -5 dollars, meaning you are $5 overdrawn. Combining assets (positive) and debts (negative) is a direct real-world application.
How does adding opposite-sign numbers prepare students for algebra?
In algebra, simplifying expressions requires combining positive and negative terms. Understanding how signs determine the result of addition is prerequisite for simplifying expressions like 3x + (-5x) = -2x.