All Labs

Integer Operations & Absolute Value Lab

See integer arithmetic come alive on a number line. Watch directional arrows show addition and subtraction of positive and negative numbers. Discover the sign rules for multiplication and division, and explore absolute value as distance from zero.

Guided Experiment: Subtraction as Adding the Opposite

What happens when you subtract a negative number? Is a − (−b) the same as a + b?

Write your hypothesis in the Lab Report panel, then click Next.

Number Line

-2-10123456789-3start= 2

Controls

Addition & Subtraction

Step-by-Step
5+(−3)5 + (-3)
=5−3= 5 - 3
=2= 2
Rule

Adding a negative is the same as subtracting its absolute value

Result
=2= 2

Data Table

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#ExpressionStartOperationResultRule Applied
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0 / 500

Reference Guide

Adding & Subtracting Integers

Adding a positive number means moving right on the number line. Adding a negative number means moving left.

a−b=a+(−b)a - b = a + (-b)

Subtraction is the same as adding the opposite. To subtract b, add negative b instead.

Sign Rules for Multiplication

When multiplying or dividing two integers, the sign of the result depends on the signs of the inputs.

(+)(+)=(+),(−)(−)=(+),(+)(−)=(−)(+)(+) = (+), \quad (-)(-)= (+), \quad (+)(-) = (-)

Same signs give a positive result. Different signs give a negative result. This also applies to division.

Absolute Value

The absolute value of a number is its distance from zero on the number line. It is always non-negative.

∣−5∣=5,∣3∣=3,∣0∣=0|{-5}| = 5, \quad |3| = 3, \quad |0| = 0

Absolute value strips the sign. Both 5 and negative 5 are the same distance from zero.

Distance Between Integers

The distance between two integers a and b is the absolute value of their difference.

d(a,b)=∣a−b∣d(a,b) = |a - b|

For example, the distance between negative 3 and 4 is |negative 3 minus 4| = |negative 7| = 7.