Pythagorist
Long Division

Negative Numbers Calculator

Add, subtract, multiply and divide negative numbers with full step-by-step working. The calculator applies the correct sign rules and explains the reasoning behind each step.

-5 + 3

-2

How it works

  1. Identify the signs

    First number: -5 (negative). Second number: 3 (positive).

  2. Apply the rule

    Adding a positive to a negative: move 3 to the right on the number line.

  3. Calculate

    −5+3=−2-5 + 3 = -2

    -5 + 3 = -2.

    Result:-2

Sign rules

(+)×(+)=+(−)×(−)=+(+)×(−)=−(+) \times (+) = + \quad (-) \times (-) = + \quad (+) \times (-) = -
+×+=++ × + = +Positive × positive = positive
−×−=+− × − = +Negative × negative = positive
+×−=−+ × − = −Different signs = negative

Example substitution

−5×−3=+15−5+(−3)=−8-5 \times -3 = +15 \qquad -5 + (-3) = -8

Two negatives multiplied give a positive. Adding a negative is the same as subtracting.

Worked examples

Calculate −5 + (−3).

  1. 1
    Adding a negative: same as subtracting
  2. 2
    Calculate: −5 − 3 = −8
Answer: −8

Calculate −4 × (−6).

  1. 1
    Sign rule: − × − = +
  2. 2
    Calculate: 4 × 6 = 24
Answer: +24

Calculate −12 ÷ 3.

  1. 1
    Sign rule: − ÷ + = −
  2. 2
    Calculate: 12 ÷ 3 = 4
Answer: −4

Frequently asked questions

What is −3 + (−5)?+

−3 + (−5) = −8. Adding a negative number is the same as subtracting.

What is −4 × −3?+

−4 × −3 = +12. Two negatives multiplied give a positive.

What is −6 ÷ 2?+

−6 ÷ 2 = −3. A negative divided by a positive gives a negative.

What is the rule for multiplying negative numbers?+

Positive × Positive = Positive. Positive × Negative = Negative. Negative × Negative = Positive.

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