Inequality Transitive Property Calculator

What is the Inequality Transitive Property?

The Inequality Transitive Property is like a chain of comparisons. If we know that A is greater than B, and B is greater than C, then we can say that A is greater than C. It's like lining up your friends by height - if Tom is taller than Sarah, and Sarah is taller than Mike, then we know Tom is taller than Mike too!

How to Use the Inequality Transitive Property

To use this property, we look at three numbers or values (let's call them A, B, and C) and two inequality statements. If both statements are true, we can make a new statement about A and C.

Formula

We can write the Inequality Transitive Property like this:

\[ \text{If } A > B \text{ and } B > C, \text{ then } A > C \]

This means:

• \(A\), \(B\), and \(C\) are our three values
• \(>\) means "greater than" (but it could also be <, ≥, or ≤)
• If both parts before "then" are true, the part after "then" must be true too

Calculation Steps

1. Choose three values: A, B, and C
2. Compare A to B (Is A > B, A < B, A ≥ B, or A ≤ B?)
3. Compare B to C (Is B > C, B < C, B ≥ C, or B ≤ C?)
4. If both comparisons are true, we can make a new statement about A and C
5. Check if the new statement about A and C is true

Example and Visual Representation

Let's use an example with numbers:

A = 10, B = 7, C = 3

We know: 10 > 7 and 7 > 3

So, we can say: 10 > 3

Let's show this with a picture:

In this picture, we can see that A (10) is to the right of B (7), and B is to the right of C (3). The black arrows show the direct comparisons we know. The red dashed arrow shows the new comparison we can make using the Inequality Transitive Property: A is greater than C!