Negative Number Line: Add, Subtract, Multiply and Divide Negatives

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Opens on Chapter 4’s example: the overnight drop from 5 degrees to −8: 5 − (−8).

First number

Sign

Second number

The gap between two numbers, and an average

Higher

Lower

A list to average separate with commas

−x² against (−x)²

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Enter your numbers, then press Work it out.

How it works

On the line, + means move right and − means move left; a negative number reverses the move, so taking away −8 is the same as adding 8. For × and ÷, same signs give a positive and different signs a negative; the pattern shows why: each step down in the first number changes the answer by the same amount, and the pattern carries straight on past zero. The gap between two numbers is the higher minus the lower, whichever side of zero they sit. A power belongs to what sits right before it, so −x² is −(x²) while (−x)² squares the negative.

From the book, Chapter 4. From 5 degrees to −8 is a drop of 13 degrees; $40 less $65 leaves −$25; −3 − (−7) = 4; (−1) × (−2) = 2; from 12 ft below to 30 ft above is 42 ft; temperatures −4, 2, −6, 0 and 3 average −1; at x = 3, −x² is −9 and (−x)² is 9. Every chapter and its calculator →

Numbers can be typed as 1,450, $38, 0.40, 12%, 1/6 or 2 3/8. The algebra is done with exact fractions, so 1/3 stays 1/3; decimals are rounded half up, the way the book rounds. Everything stays in your browser: no sign-up, nothing stored or sent.