Properties of Equality

Here is a quick summary of the Properties of Equality.

List of Properties of Equality, Namely Reflexive Property of Equality, Symmetric Property of Equality, Transitive Property of Equality, Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, Division Property of Equality, and Substitution Property of Equality.

1) Reflexive Property of Equality

For any number a, a=a.

\Rightarrow It states that any quantity is equal to itself.

Examples:

2=2 \\

1+4=1+4 \\

3x^2=3x^2 \\


2) Symmetric Property of Equality

For any numbers a and b, if a=b then b=a.

\Rightarrow If one quantity equals a second, then the second quantity equals the first.

Examples:

If 1+2=3 then 3=1+2.

If 2y = x + y then x + y = 2y.

If {x^2} - {y^2} = \sqrt 2 then \sqrt 2 = {x^2} - {y^2}.


3) Transitive Property of Equality

For any numbers a, b, and c, if a=b and b=c, then a=c.

\Rightarrow If the first quantity is equal to the second quantity, and the second quantity is equal to the third quantity, then the first quantity must be equal to the third quantity.

Examples:

If 7 + 8 = 12 + 3 and 12 + 3 = 15, then 7 + 8 = 15.

If 3 \times 4 = 2 \times 6 and 2 \times 6 = 12, then 3 \times 4 = 12.

If m - n = {k^2} and {k^2} = p + {d^3}, then m - n = p + {d^3}.


4) Addition Property of Equality

For any numbers a, b, and c, if a=b, then a+c=b+c.

\Rightarrow A true equation will remain true and unchanged when the same or common value is added to each side.

Example 1:

one plus 4 equals five

Example 2:

x plus three equals ten

5) Subtraction Property of Equality

For any numbers a, b, and c, if a=b, then a-c=b-c.

\Rightarrow A true equation will remain true and unchanged when the same or common value is subtracted from each side.

Example 1:

seven minus three equals four

Example 2:

x minus nine equals four

6) Multiplication Property of Equality

For any numbers a, b, and c, if a=b, then a \times c = b \times c.

\Rightarrow As long as the same value or quantity is multiplied on both sides of the equation, the new equation remains true and the same in meaning.

Example 1:

five times eight equals forty

Example 2:

6 times y equals twelve

7) Division Property of Equality

For any numbers a, b, and c, if a=b, then a \div c = b \div c.

\Rightarrow As long as the same value or quantity is divided from both sides of the equation, the new equation remains true and the same in meaning.

Example 1:

42/7 = 6

Example 2:

3 times x equals twenty-seven

8) Substitution Property of Equality

If a=b then b can be substituted for a in any expression or equation.

\Rightarrow A quantity can be substituted or replaced by another quantity of equal or the same value in any expression or equation.

Example 1:

If x=y and x+2, then y+2.

Example 2:

If m=5 and m-2, then 5-2.

Example 3:

If x=3 and 5+x=8, then 5+3=8.


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Classifying Real Numbers

Properties of Real Numbers