Adding Numbers With the Same Sign
Add integers with the same sign in Grade 9 algebra by summing their absolute values and keeping the common sign—positive plus positive stays positive, negative plus negative stays negative.
Key Concepts
Property To add numbers with the same sign, add their absolute values. The sum will have the same sign as the addends.
Examples $( 19) + ( 8) = 27$ $( \frac{3}{5}) + ( \frac{1}{5}) = \frac{4}{5}$ $10 + 5 = 15$.
Explanation Imagine you're on a team. If you're on the 'Negative Team' and you add more negative players, your team just gets more negative! Just add up everyone's strength (their absolute values) and stick with your team's sign. You're either building a taller tower or digging a deeper hole together.
Common Questions
What is the rule for adding numbers with the same sign?
Add the absolute values of both numbers and keep the common sign. For positive addends: 4 + 7 = 11 (positive). For negative addends: (-4) + (-7) = -11 (negative). The sign of both numbers carries through.
How do you add -15 + (-23)?
Both numbers are negative, so use the same-sign rule. Add absolute values: 15 + 23 = 38. Keep the negative sign: result is -38. This is equivalent to saying you owe 15 more plus 23 more equals 38 owed.
How does adding same-sign numbers differ from adding opposite-sign numbers?
Same-sign addition: add absolute values, keep the sign. Opposite-sign (different signs): subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value.