1. Solving
Multiplication
and
Division
Equations

2. Multiply & Divide 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.

3. Multiply & Divide 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

4. Multiply & Divide Equations
What you do to one side of an equation, you must do to the other side to keep it balanced. = 30
5 x 6

5. To solve a multiplication equation
Multiply & Divide Equations
To solve a multiplication equation
Use the inverse operation for multiplication which is division.
Get the variable alone, by dividing the same number into both sides.

6. Try to solve this multiplication equation.
Multiply & Divide Equations
Try to solve this multiplication equation.
How do you get x all by itself? = 8x 56

7. Multiply & Divide Equations
Divide 8 into both sides. = 8x 56 7 8 8

8. •7 = 8x 56 Divide 8 into both sides.
Multiply & Divide Equations
Divide 8 into both sides.
Check your answer by substitution! = 8x •7 56

9. Try to solve this multiplication equation
Multiply & Divide Equations
Try to solve this multiplication equation
How do you get x all by itself? = 42 7x

10. Multiply & Divide Equations
Divide 7 into both sides. = 42 7x 6 7 7

11. •6 Divide 7 into both sides. = 42 7x
Multiply & Divide Equations
Divide 7 into both sides.
Check your answer by substitution! = 42 7x •6

12. To Solve a Multiplication Equation
Multiply & Divide Equations
Divide the same number into both sides
To Solve a Multiplication Equation
8x = 32
Get the variable alone.
Divide 8 into both sides.
x = 4
8 divided by 8 cancels out
8 • 4 = 32
Show your check!
32 = 32
Finish your check!

13. Multiply & Divide Equations1) 3) 2) 4)

14. To solve a division equation
Multiply & Divide Equations
To solve a division equation
Use the inverse operation for division which is multiplication.
Get the variable alone, by multiplying the same number to both sides.

15. Try to solve this division equation
Multiply & Divide Equations
Try to solve this division equation
How do you get x all by itself? x 3 = 15

16. Multiply & Divide Equations
Multiply both sides by 3 x 3 = •3 45 •3 15

17. 45 x = 3 15 Multiply both sides by 3
Multiply & Divide Equations
Multiply both sides by 3
Check your answer by substitution! 45 x 3 = 15

18. Try to solve this division equation
Multiply & Divide Equations
Try to solve this division equation
How do you get x all by itself? x 6 = 4

19. Multiply & Divide Equations
Multiply both sides by 6 x 6 = •6 24 4 •6

20. 24 x = 6 4 Multiply both sides by 6 Check your answer by substitution!
Multiply & Divide Equations
Multiply both sides by 6
Check your answer by substitution! 24 x 6 = 4

21. Try to solve this division equation
Multiply & Divide Equations
Try to solve this division equation
How do you get x all by itself? x 7 = -7

22. Multiply & Divide Equations
Multiply both sides by 7 x 7 = •7
-49 -7 •7

23. -49 x = 7 -7 Multiply both sides by 7
Multiply & Divide Equations
Multiply both sides by 7
Check your answer by substitution!
-49 x 7 = -7

24. To Solve a Division Equation
Multiply & Divide Equations
To Solve a Division Equation
Multiply the same number to both sides.
x 3
= 25
Get the variable alone.
3• •3
= 25
x 3
Multiply both sides by 3.
3 divided by 3 cancels out to 1.
x = 75
Show your check!
Finish your check!
25 = 25

25. Try These Equations Show your check!
Multiply & Divide Equations
Try These Equations Show your check!
-3x = 21 m
= 8 -2
(-2)
m = -16
x = -7
-3(-7) = 21
21 = 21
8 = 8

26. Multiply & Divide Equations
Try These Equations 1) 2)

27. Multiply & Divide Equations
Try These Equations 3) 4)

28. Take Out Your Study Guide!!!
Multiply & Divide Equations
That's all Folks!
That’s all folks
Take Out Your Study Guide!!!

29. To Solve a Multiplication Equation#5
To Solve a Multiplication Equation
Divide the same number into both sides
5x = 40
Get the variable alone.
Divide 5 into both sides.
x = 8
5 divided by 5 cancels out to 1.
5 • 8 = 40
Show your check!
40 = 40
Finish your check!

30. To Solve a Division Equation#6
To Solve a Division Equation
Multiply the same number to both sides
x 2
= 20
Get the variable alone.
= 20
2• •2
x 2
Multiply both sides by 2.
2 divided by 2 cancels out to 1.
x = 40
Show your check!
Finish your check!
20 = 20

31. 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.

32. Multiply & Divide Equations
Add
Subtract
Multiply
Divide
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

33. Multiply & Divide Equations
Placement Rule
Always write the variable after the number!
a WRITE IT AS 4a

34. Parentheses mean multiply!
Multiply & Divide Equations
Using Parentheses
8 x is written as
8(x)
(8)x
(8x) 8x
Parentheses mean multiply!

35. Multiply & Divide Equations
Translate the following into equations.
1) Eleven more than a number t is 23.
2) Eight times a number k is equal to 56.
3) Thirteen less m equals 6.
4) The quotient of x and 3 is 18.

36. Multiply & Divide Equations
Write a phrase that describes each variable expression below.
Four times the sum of m and 5 minus 3
Five minus twice the quotient of x and 8
The quotient of a and 7 minus 3

37. Teacher Note: The following slides may be inserted at the end of the lesson if the lesson is also teaching solving equations with fractions.

38. Multiply & Divide Equations
Short Way
Long Way
Easier to multiply
by the reciprocal!

39. Solve the division by multiplying by the reciprocal.
Multiply & Divide Equations
Solve the division by multiplying by the reciprocal.

40. Solve the division by multiplying by the reciprocal.
Multiply & Divide Equations
Solve the division by multiplying by the reciprocal.

41. Solve the division by multiplying by the reciprocal.
Multiply & Divide Equations
Solve the division by multiplying by the reciprocal.

42. To Solve a Fraction Equation#7
Multiply both sides by the reciprocal of the fraction.
Multiply the numerators. Multiply the denominators.
Simplify

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