1. Addition
and
Subtraction
Equations

2. Add & Subtract Equations
An equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign.
12 – 3 = 9 Numerical
3a = 30 Algebraic

3. Add & Subtract Equations
An Equation is like a balance scale. Everything must be equal on both sides. = 29
10+19

4. Add & Subtract Equations
What you do to one side of an equation, you must do to the other side to keep it balanced! = 36
30+6

5. Add & Subtract Equations
x + 3 = 8
Heavier
- 3

6. Add & Subtract Equations
x + 3 = 8
Heavier

7. Add & Subtract Equations
x + 3 = 8
Heavier

8. Add & Subtract Equations
x + 3 = 8
Heavier
What you do to one side of an equation, you must do to the other side to keep it balanced!
So if you subtract 3 from the left you must also subtract 3 from the right!

9. Add & Subtract Equations
x + 3 = 8
- 3 = x 5

10. Add & Subtract Equations
x + 3 = 8
- 3
Algebraically
x + 3 = 8
x = 5

11. Add & Subtract Equations
1) GOAL:
Get the variable on one side
of the equation.
2) You always perform the same operation to
both sides of an equation.
3) To undo an operation you perform its opposite operation to both sides of the equation.

12. Add & Subtract Equations
To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations.
Inverse Operations are like Opposites.

13. Add & Subtract Equations
The inverse of add is
SUBTRACT
The inverse of subtract is
ADD
The inverse of multiply is
DIVIDE
The inverse of divide is
MULTIPLY

14. To solve an addition equation
Add & Subtract Equations
To solve an addition equation
Use the inverse operation for addition which is subtraction.

15. Try to solve this addition equation
Add & Subtract Equations
Try to solve this addition equation
How do you get n all by itself? = 10
n + 8

16. Subtract 8 from both sides.
Add & Subtract Equations
Subtract 8 from both sides. = 10
n + 8 -8 -8 2

17. Subtract 8 from both sides.
Add & Subtract Equations
Subtract 8 from both sides.
Check your answer by substitution! = 10 2
n + 8

18. Try to solve this addition equation
Add & Subtract Equations
Try to solve this addition equation
How do you get n all by itself? = 33
n + 12

19. Subtract 12 from both sides.
Add & Subtract Equations
Subtract 12 from both sides. = 33
n + 12
-12
-12 21

20. Subtract 12 from both sides.
Add & Subtract Equations
Subtract 12 from both sides.
Check your answer by substitution! = 33 21
n + 12

21. Add & Subtract Equations1 1 1 X 1 1 = 1 1 1 1
To solve an equation, you must get the variable alone. X = 1 1 1 1 1
X + 2 = 7
X = 5
Check = = 7
7 = 7

22. Add & Subtract Equations
What you do to one side of an equation, you must do to the other side to keep it balanced! =
m + 7 30

23. Add & Subtract Equations
m + 7 = 30
Get the variable alone.
– 7 – 7
+7 and -7 cancel out
Subtract 7 from both sides.
m = 23
Show your check!
= 30
30 = 30
Finish your check!

24. Add & Subtract Equations
This is called the:
Subtraction Property of Equality
The Subtraction Property of Equality is used to solve addition equations.
It is called a property because you subtract the same number from both sides.

25. To solve a subtraction equation
Add & Subtract Equations
To solve a subtraction equation
Use the inverse operation for subtraction which is addition.

26. Try to solve this subtraction equation
Add & Subtract Equations
Try to solve this subtraction equation
How do you get n all by itself? = 25
n - 5

27. Add & Subtract Equations
Add 5 to both sides. = 25
n - 5 +5 +5 30

28. = 25 30 n - 5 Add 5 to both sides. Check your answer by substitution!
Add & Subtract Equations
Add 5 to both sides.
Check your answer by substitution! = 25 30
n - 5

29. Try to solve this subtraction equation
Add & Subtract Equations
How do you get n all by itself? = 18
n - 3

30. Add & Subtract Equations
Add 3 to both sides. = 18
n - 3 +3 +3 21

31. = 18 21 n - 3 Add 3 to both sides. Check your answer by substitution!
Add & Subtract Equations
Add 3 to both sides.
Check your answer by substitution! = 18 21
n - 3

32. Add & Subtract Equations
What you do to one side of an equation, you must do to the other side to keep it balanced. =
a - 13 36

33. Add & Subtract Equations
Get the variable alone.
a - 13 = 36
Add 13 to both sides.
a = 49
+13 and -13 cancel out
Show your check!
= 36
36 = 36
Finish your check!
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34. Add & Subtract Equations
This is called the:
Addition Property of Equality
The Addition Property of Equality is used to solve subtraction equations.
It is called a property because you add the same number to both sides.

35. Add & Subtract Equations
1) x + 3 = 10
4) 13 = x + 5
x = 7
8 = x
2) y - 8 = 11
5) 12 = n - 3
y = 19
15 = n
3) n + 5 = 11
6) = k
14 = k
n = 6
copyright©amberpasillas2010

36. Add & Subtract Equations
Solve the following equations
AND check your answer!
2) y - 13 = -4
1) x + 8 = 2
x = -6
y = 9
= 2
9 – 13 = -4
-4 = -4
2 = 2

37. Add & Subtract Equations
Solve the following equations
AND check your answer!
1) -4 + x = 15
2) - 4 = m + 9
x = 19
-13 = m
- 4 + (19) = 15
- 4 = (-13) + 9
15 = 15
- 4 = - 4

38. Add & Subtract Equations
Solve the following equations
AND check your answer! 1) 2)
8 + (-5) = 3
- 9 = (-6) - 3
3 = 3
- 9 = - 9

39. Take Out Your Study Guide!!!
Add & Subtract Equations
That's all Folks!
Take Out Your Study Guide!!!
That’s all folks

40. To Solve An Addition Equation#3
Subtract the same number from both sides.
m + 8 = 12
Get the variable alone.
– –8
Subtract 8 from both sides.
m = 4
+8 and -8 cancel each other out.
4 + 8 = 12
Show your check.
12 = 12
Finish your check!

41. To Solve a Subtraction Equation#4
Add the same number to both sides.
a – 15 = 22
Get the variable alone.
Add 15 to both sides.
+15 and -15 cancel out
a = 37
= 22
Show your check!
Finish your check!
22 = 22

42. Teacher Note: The following slides may be inserted at the beginning of the lesson if the lesson is also teaching writing expressions and/or equations.

43. Add Subtract Multiply Divide Key Words REVIEW Flip Flop Numbers plus
minus
times
quotient
difference
sum
product of
increased by
decreased by
less
twice
total
more than
less than
subtracted from
added to
Flip Flop Numbers

44. The product of 5 and a number c The sum of seven and t
Writing Expressions
The product of 5 and a number c
The sum of seven and t
The difference of 6 and d. 5c
7 + t
6 – d

45. Flip Flop Numbers Writing Expressions Add 3 and 7 3 + 7
The sum of 3 and 7
3 + 7
3 increased by 7
3 + 7
The total of 3 and 7
3 + 7
Flip Flop Numbers
3 more than 7
7 + 3
7 + 3
3 added to 7

46. Writing Expressions
3 minus x
3 - x
3 less x
3 - x
The difference of 3 and x
3 - x
3 decreased by x
3 - x
3 less than x
x - 3
x - 3
3 subtracted from x
3 is less than x
3 < x

47. Writing Expressions 5 + x - 3 8y - 7 10m - 7 6m + 8
1) Five plus x minus 3
5 + x - 3
2) Three times y less 4
3) Eight multiplied by y minus 7
8y - 7
4) The product of 10 and m decreased by 7
10m - 7
5) Four more than the quotient of x and 3
6) Six times m plus 8
6m + 8

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