Q. a negative plus a negative equals
Answer
If a,b>0 then \( -a + (-b) = -(a+b) \).
So a negative plus a negative is negative; e.g. \( -3 + (-2) = -(3+2) = -5 \).
Detailed Explanation
Answer
The sum of two negative numbers is negative. In general, for positive numbers a and b:
\( (-a) + (-b) = -(a + b) \)
Example:
\( (-3) + (-5) = -(3 + 5) = -8 \)
Brief explanation: adding two negative numbers combines their magnitudes and keeps the negative sign, so the result is the negative of the sum of their absolute values.
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FAQs
What does "a negative plus a negative" equal?
Add their absolute values and keep the negative sign: \( -a + -b = -(a+b)\). Example: \( -3 + -5 = -(3+5) = -8\).
Why does adding two negatives give a more negative number?
On the number line you move left twice; combining debts increases the total debt. Numerically, the magnitudes add and the sign stays negative.
How do I add negatives on a number line?
Start at the first negative position, then move left by the absolute value of the second negative. E.g., start at \(-2\), move left 4 to reach \(-6\).
How is adding two negatives related to subtraction?
\( -a + -b = -(a+b)\) which is the same as \( -a - b\). Adding a negative is equivalent to subtracting the corresponding positive.
What if one number is negative and the other positive?
Subtract the smaller absolute value from the larger and take the sign of the larger absolute value. Example: \( -7 + 5 = -(7-5) = -2\).
How do you add negative fractions or decimals?
Same rule: add absolute values, keep the negative sign. Example: \( -\tfrac{1}{2} + -\tfrac{3}{4} = -\tfrac{5}{4}\); \( -1.2 + -0.8 = -2.0\).
Are there algebraic properties for adding negatives?
Yes: addition is commutative and associative, so \( -a + -b = -b + -a\) and \( (-a + -b) + -c = -a + (-b + -c) = -(a+b+c)\).
Neg plus neg equals a more negative.
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