Rules for addition
algebra, numbers•January 27, 2025
<p>Rules for adding and subtracting signed numbers.</p>
<p><strong>Positive + Positive = Positive</strong></p>
<p><strong>Negative + Negative = Negative</strong></p>
<p><strong>Positive + Negative</strong>: The result depends on the magnitudes of the numbers. For example, when $a$ and $b$ have opposite magnitudes, the result is:</p>
<p>$$ext{sign} = egin{cases}<br>
+1 & ext{if } |a| > |b|, <br>
-1 & ext{if } |b| > |a|, <br>
0 & ext{if } |a| = |b| ext{ and } a = -b.<br>
\end{cases}$$</p>
<p><strong>Negative + Positive</strong>: Similarly, the result depends on the magnitudes:</p>
<p>$$ ext{sign} = egin{cases}<br>
+1 & ext{if } |b| > |a|, <br>
-1 & ext{if } |a| > |b|, <br>
0 & ext{if } |a| = |b| ext{ and } a = -b.<br>
\end{cases} $$</p>
<p><strong>Positive - Positive</strong>: The result is positive if the first number is larger.</p>