Rivalry2

HTML Diff

0 added 0 removed

Original 2026-01-01

Modified 2026-02-28

1 Below are the key Properties of Equality in mathematics, basic principles that help us maintain the balance<a>of equations</a>. These rules are important for<a>solving equations</a>and forming justifiable mathematical<a>arguments</a>.

2 1. Reflexive Property of Equality

3 Definition:Every<a>real number</a>is equal to itself.

4 Mathematical Expression:\( a = a\).

5 Example:For any number x, \(x = x\)

6 2. Symmetric Property of Equality

7 Definition:If one quantity equals a second, then the second equals the first.

8 Mathematical Expression: If \(a = b\), then b = a.

9 Example:If \(5 = 3 + 2 \), then \(3 + 2 = 5\)

10 3. Transitive Property of Equality

11 Definition:When one value is equal to the second value, and that second value is equal to a third, then the first and third values are also equal.

12 Mathematical Expression:If \(a = b\) and\( b = c\) then \(a = c\).

13 Example:If \(2 + 3 = 5\) and \(5 = 3 + 2 \), then \(2 + 3 = 3 + 2\)

14 Another example: If \(6 + 1 = 7\) and \(7 = 14 ÷ 2\), then \( 6 + 1 = 14 ÷ 2\).

15 4. Addition Property of Equality

16 Definition:If the same number is added to both sides of an<a>equation</a>, the equality is still true.

17 Mathematical Expression:If \(a = b\), then \(a + c = b + c\).

18 Example:If \(x = 4\), then \(x + 3 = 4 + 3\), so \(x + 3 = 7\).

19 5. Subtraction Property

20 Definition:When two values are equal, and then taking away the same amount from each side, so that the equation remains balanced

21 Mathematical Expression:If \(a = b\), then \(a - c = b - c\).

22 Example:If \( y = 10\), then \(y - 3 = 10 - 3\), so \(y - 3 = 7\)

23 6. Multiplication Property

24 Definition:If two quantities are equal, multiplying both sides by the same number maintains equality.

25 Mathematical Expression:

26 If \(a = b\),

27 then \(a × c = b × c\),

28 where \(c ≠ 0\)

29 Example:

30 If \(6 = 6\)

31 Then \(6 × 3 = 6 × 3\) ⇒ \(18 = 18\)

32 If you multiply both sides of an equation by the same number, equality will remain the same.

33 7. Division Property

34 Definition:If two quantities are equal, dividing both sides by the same non-zero number maintains equality.

35 Mathematical Expression:

36 If \(a = b\),

37 then \(a ÷ c = b ÷ c\),

38 where \(c ≠ 0\)

39 Example:If \(12 = 12\), then \(12 ÷ 4 = 12 ÷ 4 \) ⇒ \(12 ÷ 4 = 12 ÷ 4 \)

40 8. Substitution Property

41 Definition:If two quantities are equal, one can be substituted for the other in any<a>expression</a>.

42 Mathematical Expression:If \(a = b\), then a can be replaced by b in any expression.

43 Example:If \(a = 7\), then in the expression \(a + 3\), a can be replaced with 7, resulting in \(7 + 3 =10\).

44 9. Square Root Property

45 Definition:If two quantities are equal, and a<a>variable</a>is squared, you can take the square root of both sides to solve for the variable. Always remember to include both the positive and negative roots.

46 Mathematical Expression:\(x^2 = 16 \;\;\implies\;\; |x| = 4 \;\;\implies\;\; x = \pm 4 \)