Work through addition, subtraction, multiplication, and division when one or both values are negative. Input changes update both signed result and the supporting steps.
For −12.5 × −4, equal signs produce a positive product of 50. By contrast, −12.5 + (−4) moves farther below zero to −16.5.
A correct signed result is reliable for Negative Number only when its setup matches the relationship.
Temperatures, balances, vector components, and changes from a baseline commonly combine signed values. The magnitude and the direction both contribute to the interpretation. A related application of Negative Number is additive opposites.
Rewrite subtraction as addition of the opposite, then use a number line for sums. For products or quotients, calculate magnitudes first and apply the sign rule afterward.
Start the Negative Number cross-check with First signed number. Apply the original Operation and recompute Signed result. Treat a different Second signed number as new Negative Number data. That prevents its Signed result from being attributed to the earlier Negative Number setup.
Subtracting a negative is addition of its opposite. Multiplication and division produce a positive result for equal signs and a negative result for unlike signs.
The Negative Number meaning depends on First signed number. The Negative Number meaning also depends on Operation. Carry those Negative Number roles into any later Negative Number work.
Written work becomes easier to audit when a negative operand is enclosed in parentheses. The expression 7 − (−3) visibly contains subtraction and a negative value; rewriting it as 7 + 3 explains why the result moves right on the number line.
A minus sign can indicate a value below zero or the operation of taking an opposite. Parentheses make that role visible when two signs meet. This result can be carried into magnitude without direction.
Substitute the Negative Number solution into First signed number. This Negative Number check rejects false Negative Number branches and forbidden denominators.
Choose an easy First signed number value before running Negative Number. Predict Operation, then compare it with the Negative Number output.
Test a boundary relevant to First signed number during the Negative Number review. Hold Operation constant and anticipate Signed result. The boundary case can reveal a branch or limit hidden by the original Negative Number numbers.
The sign rule preserves distributive arithmetic and reverses direction twice.
They represent the same mathematical number.
Yes, provided the divisor is not zero.