Adding Two Numbers with the Same Sign
Adding two numbers with the same sign is a fundamental integer rule in Grade 8 math (Yoshiwara Core Math). When both are positive, add their absolute values: (5) + (8) = 13. When both are negative, add their absolute values and attach a negative sign: (−5) + (−8) = −13. A number line model confirms: two negative numbers both move left from zero. The result's sign always matches both addends' sign. This rule is the foundation of signed-number arithmetic throughout Grade 8 algebra.
Key Concepts
Property 1. The sum of two positive numbers is positive. 2. The sum of two negative numbers is negative.
Examples To find $(+8) + (+3)$, we add the numbers $8$ and $3$ to get $11$. Since both numbers are positive, the sum is $+11$.
To find $( 7) + ( 5)$, we add the numbers $7$ and $5$ to get $12$. Since both numbers are negative, the sum is $ 12$.
Common Questions
What is the rule for adding two negative numbers?
Add their absolute values and make the result negative. (−6) + (−9) = −15.
What is (−12) + (−7)?
12 + 7 = 19; both negative → −19.
How does the number line show adding two negatives?
Start at −6, move 9 more units left → −15.
Does the rule apply to two positives?
Yes. Two positives: add values, keep positive. Two negatives: add values, keep negative.
How does same-sign differ from opposite-sign addition?
Same-sign: add absolute values, keep that sign. Opposite signs: subtract smaller from larger, keep sign of larger.