Negative Numbers

7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team

Negative numbers describe values below zero: temperatures below freezing, money you owe, floors below ground. The sign rules can feel like memorised tricks, but they make sense on a number line. This guide builds the rules from that picture.

The number line

Numbers to the right are bigger. −2 is greater than −8, because it is nearer to zero on the right. The absolute value of a number is its distance from zero, so |−5| = 5.

Adding

Adding a positive moves right; adding a negative moves left. −7 + 4 = −3 (start at −7 and move 4 right). −2 + (−5) = −7. When the signs differ, subtract the smaller size from the larger and keep the sign of the larger.

Subtracting

Subtracting a number is the same as adding its opposite. 5 − (−3) = 5 + 3 = 8. And −4 − 6 = −10. A temperature that goes from −5 °C to 12 °C has risen 12 − (−5) = 17 degrees.

Multiplying and dividing

Same signs give a positive; different signs give a negative. (−6)(−4) = 24 and (−3)(5) = −15. Division follows the same rule: −20 ÷ 4 = −5 and −18 ÷ −3 = 6.

Signs	Result
+ × +	+
− × −	+
+ × −	−
− × +	−

Negatives in real life

An account balance of −$40 means you owe $40. A diver at −12 m is 12 m below sea level. When you pay off a $40 debt, your balance changes by +$40, which is −40 + 40 = 0. Practise on the integers quiz.

Practice questions

Test yourself, then tap to check. Answers are calculated by the tools linked below.

Write 45,000,000 in scientific notation.
Show answer
Scientific notation: 4.5 × 10^7
A rent rises from $1,200 to $1,320. What is the percent increase?
Show answer
Percent change: +10%
Calculate 7^4.
Show answer
7^4: 2,401