What this calculator does
The Multiplying Negative Numbers Calculator multiplies any two numbers — positive, negative, whole, or decimal — and clearly shows the resulting sign. It is a quick way to check homework or to understand why the answer is positive or negative when negative signs are involved.
How to use it
Enter the first number and the second number, then read the product. The result table tells you how many of your factors were negative and whether the product is positive or negative. You can enter decimals such as -2.5 as well as whole numbers.
The formula explained
Multiplication of magnitudes is unchanged by signs — you simply multiply the absolute values. The sign is decided by counting the negative factors:
- \((-a) \times (-b) = ab\) — two negatives give a positive.
- \((-a) \times b = -(ab)\) — one negative gives a negative.
- \(a \times b = ab\) — no negatives stay positive.
In general, the sign equals \((-1)\) raised to the number of negative factors: an even count yields a positive result, an odd count yields a negative result.
Worked example
Multiply \(-6 \times -7\). The magnitudes give $$6 \times 7 = 42.$$ There are two negative factors (an even count), so the product is positive: \(-6 \times -7 = 42\). By contrast, \(-6 \times 7\) has one negative factor, so the result is \(-42\).
FAQ
Why do two negatives make a positive? Multiplying by a negative reverses direction on the number line; reversing twice returns to the original direction, which is positive.
What if one number is zero? Any number times zero is zero, which has no sign.
Does it work with decimals? Yes — enter values like -3.2 and the calculator multiplies and signs them correctly.
