Properties of Equality

Properties of Equality

by Kelley Roseen

​Addition Property

• ​If a = b, then a+c = b+c

​

• ​Explanation:

  • ​The same number can be added to both sides

​Subtraction Property

• ​If a = b, then a-c = b-c

​

• ​Explanation:

  • ​The same number can be subtracted to both sides

​Multiplication Property

• ​If a = b, then a*c = b*c

​

• ​Explanation:

  • ​The same number can be multiplied to both sides

Division Property

• ​If a = b, then a/c = b/c

​

• ​Explanation:

  • ​The same number can be divided to both sides

Reflexive Property

• ​a=a

• Explanation:

  • ​Any number is equal to itself

Symmetric Property

​

• If a = b, then b=a

• Explanation:

  • ​Any equation my be written in the opposite order

Transitive Property

​

• If a = b and b=c, then a = c

• Explanation:

  • Two quantities that are equal to the same thing are equal to each other

Substitution Property

​

• If a = b, then b can be replaced by a.

• Explanation:

  • Plug in a value into an expression to replace the original variable.

Multiple Choice

165 = 165

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive property of equality

• substitution property of equality

Multiple Choice

10 *4 = (5 *2) *4

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

23+5 = (20+3)+ 5

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

$$If\ x\ =\ 3,\ then\ \frac{x}{3}=1$$  

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

If x=y, then x-2 = y-2

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

Multiple Choice

9 + 9 = 18, so 18 = 9 + 9

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive property of equality

• substitution property of equality

Multiple Choice

If (4+5)x=18, then 9x = 18

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive property of equality

• substitution property of equality

Multiple Choice

3 + 4 = 7 and 2+5 = 7, so 3+4 = 2+5

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive property of equality

• substitution property of equality