Question

What are the properties of equality?

Answer 1

The properties of equality.

Any equation's truth value is unaffected by addition, subtraction, multiplication, or division on both sides of the equation by the same number.

When both sides of an equation are divided by the same non-zero number, the two sides remain equal.

• Reflexive property of equality:

$n=n$

• Symmetric property of equality:

If $m=n$, then $n=m$.

• Transitive property of equality:

If $m=n$ and $n=p$, then $m=p$

• Addition property of equality:

If $m=n$, then $m+p=n+p$.

• Subtraction property of equality:

If $m=n$, then $m-p=n-p$

• Multiplication property of equality:

If $m=n$, then $m\times p=n\times p$.

• Division property of equality:

If $m=n$ and $p$ is not equal to $0$, then $\frac{m}{p}=\frac{n}{p}$.

• Substitution property of equality:

If $m=n$, then $n$ may be substituted for $m$ in any expression containing $m$.