Grade 7 Mathematics

1. PROPERTIES OF EQUALITY

2. OBJECTIVES:
• Illustrate and model the different properties of equality.
• Use the different properties of equality to solve literal
equations.

3. PROPERTIES OF EQUALITY:
• Addition Property of Equality (APE)
• Subtraction Property of Equality (SPE)
• Multiplication Property of Equality (MPE)
• Division Property of Equality (DPE)
• Substitution Law
• Reflexive Property
• Symmetric Property
• Transitive Property (TPE)

4. ADDITION PROPERTY:
If x = y, then x + z = y + z
Equals may be added on both
sides of the equation

5. SOLVE EACH EQUATION USING
ADDITION PROPERTY
x – 7 = 10

6. THIS IS HOW IT WORKS:
x – 7 = 10 WRITE THE ORIGINAL EQUATION

7. THIS IS HOW IT WORKS:
x – 7 = 10 WRITE THE ORIGINAL EQUATION
x – 7 + 7 = 10 + 7 ADD 7 ON BOTH SIDES

8. THIS IS HOW IT WORKS:
x – 7 = 10 WRITE THE ORIGINAL EQUATION
x – 7 + 7 = 10 + 7 ADD 7 ON BOTH SIDES
x = 17 SIMPLIFY

9. ADDITION PROPERTY IN PROBLEM
SOLVING:
The water level fell 12.5 feet from a
high tide to a low tide. The water
level at the pier was 9.25 feet at low
tide. Find the water level at the pier
at high tide.

10. REPRESENT EACH GIVEN BY THE USE
OF VARIABLES
Let x = be the high tide water level
in feet
12.5 = drop in water level
9.25 = low tide water level

11. FORMULATE YOUR EQUATION
x – 12.5 = 9.25

12. SOLVE EACH EQUATION USING
ADDITION PROPERTY
x – 12.5 = 9.25

13. THIS IS HOW IT WORKS:
x – 12.5 = 9.25 WRITE THE ORIGINAL
EQUATION

14. THIS IS HOW IT WORKS:
WRITE THE ORIGINAL
EQUATION
x – 12.5 + 12.5 = 9.25 + 12.5 ADD 12.5 ON BOTH
SIDES
x – 12.5 = 9.25

15. THIS IS HOW IT WORKS:
WRITE THE ORIGINAL
EQUATION
x – 12.5 + 12.5 = 9.25 + 12.5 ADD 12.5 ON BOTH
SIDES
x – 12.5 = 9.25
x = 21.75
SIMPLIFY

16. SUBTRACTION PROPERTY:
If x = y, then x - z = y - z
Equals may be subtracted from
both sides of the equation

17. SOLVE EACH EQUATION USING
SUBTRACTION PROPERTY
x + 5 = 11

18. THIS IS HOW IT WORKS:
x + 5 = 11 WRITE THE ORIGINAL EQUATION

19. THIS IS HOW IT WORKS:
x + 5 = 11 WRITE THE ORIGINAL EQUATION
x + 5 - 5 = 11 - 5 SUBTRACT 5 ON BOTH SIDES

20. THIS IS HOW IT WORKS:
x + 5 = 11 WRITE THE ORIGINAL EQUATION
x + 5 - 5 = 11 - 5 SUBTRACT 5 ON BOTH SIDES
x = 6 SIMPLIFY

22. MULTIPLICATION PROPERTY:
If x = y, then xz = yz
Both sides of the equation may be
multiplied by equals

23. SOLVE EACH EQUATION USING
MUTIPLICATION PROPERTY
8x = 72

24. THIS IS HOW IT WORKS:
8x = 72 WRITE THE ORIGINAL EQUATION

25. THIS IS HOW IT WORKS:
8x = 72 WRITE THE ORIGINAL EQUATION
8x/8 = 72/8 DIVIDE 8 ON BOTH SIDES

26. THIS IS HOW IT WORKS:
8x = 72 WRITE THE ORIGINAL EQUATION
8x/8 = 72/8 DIVIDE 8 ON BOTH SIDES
x = 9 SIMPLIFY

27. DIVISION PROPERTY:
If x = y and z ≠ 0 then
𝒙
𝒛
=
𝒚
𝒛
Both sides of the equation may be
divided by a non-zero real
number

28. SUBSTITUTION PROPERTY:
If x + y = z and x = y, then
𝒚 + 𝒚 = 𝒛 𝒐𝒓 𝒙 + 𝒙 = 𝒛
Equals may be substituted for
equals

29. REFLEXIVE PROPERTY:
x = x, y = y, z = z
Any number or expressions is
equal to itself

30. SYMMETRIC PROPERTY:
x = y then, y = x
The expressions on both sides of
an equation may be interchanged

31. TRANSITIVE PROPERTY:
x = y and y = z, then x = z
If two quantities are both equal to
a third quantity, then they are
equal to each other

32. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36
2. 5t + 5 = 20
3. 3k – 4 = 30
4. n + 25 = -723
5. 9c + 1 = 82

33. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36 (w = 40)
2. 5t + 5 = 20
3. 3k – 4 = 30
4. n + 25 = -723
5. 9c + 1 = 82

34. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36 (w = 40)
2. 5t + 5 = 20 (t = 3)
3. 3k – 4 = 30
4. n + 25 = -723
5. 9c + 1 = 82

35. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36 (w = 40)
2. 5t + 5 = 20 (t = 3)
3. 3k – 4 = 30 (k = 34/3)
4. n + 25 = -723
5. 9c + 1 = 82

36. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36 (w = 40)
2. 5t + 5 = 20 (t = 3)
3. 3k – 4 = 30 (k = 34/3)
4. n + 25 = -723 (n = -748)
5. 9c + 1 = 82

37. COPY AND ANSWER ON YOUR
NOTEBOOK
1. w – 4 = 36 (w = 40)
2. 5t + 5 = 20 (t = 3)
3. 3k – 4 = 30 (k = 34/3)
4. n + 25 = -723 (n = -748)
5. 9c + 1 = 82 (c = 9)