Solving Simple Equations (2 of 3)
Equations With Multiplication and Division
We can use the same "do the same thing to both sides" idea that we use to solve equations with addition and subtraction to solve equations that involve multiplication and division.
Multiplication and Division Recap
| When we multiply we combine groups of equal numbers ..... | |
o
o o o
o
o o o
o
o o o |
3 groups of 4 3 x 4 |
o
o o o o o o o o o o o |
3 x 4 = 12 |
... and when we divide we split into equal groups |
|
o
o o o o o o o o o |
10 |
o
o o o o o
o
o o o o o |
10 divided into 10 ÷ 2 = 5 |
We use these operations and the fact that they are opposite operations to help us solve equations.
Dividing Both Sides By The Same Number
We can solve the equations below by "getting rid of" or "cancelling out" the multiplication by dividing (doing the opposite operation.)
Note: There is a short way to write multiplication.
Instead of 3 x n
we can write just 3n (we can leave out the x sign)
| Equation | Left | Right |
| 3n = 12 |
n
n
n |
o
o o o o o o o o o o o |
Divide both sides by 3 3n ÷ 3 = 12 ÷ 3 |
n
n
n |
o
o o o
o
o o o
o
o o o |
| n = 4 | n |
o
o o o |
Here is a similar equation.
| Equation | Left | Right |
| 5n = 15 | n
n
n
n
n |
o
o o o o o o o o o o o o o o |
Divide both sides by 5 5n ÷ 5 = 15 ÷ 5 |
n
n
n
n
n |
o
o o
o
o o
o
o o
o
o o
o
o o |
| n = 3 | n |
o
o o |
Multiplying Both Sides By The Same Number
We can solve the equations below by "getting rid of" or "cancelling out" the division by multiplying (doing the opposite operation.)
Note: There are different ways to write division
Instead of 3 ÷ n we can write
3
n
| Equation | Left | Right | |||
|
n |
o o
|
|||
Multiply both sides by 3
|
n
|
o
o
o
o
o
o
|
|||
| n = 6 | n |
o
o o o o o |
The same idea is used to solve the equation below:
| Equation | Left | Right | |||
|
n
|
o
o o o |
|||
Multiply both sides by 5
|
n
|
o
o o o
o o o o
o o o o
o o o o
o o o o
|
|||
| n = 20 | n |
o
o o o o o o o o o o o o o o o o o o o |
You can "get rid of" or "cancel" multiplication by dividing and you can "get rid of" or "cancel" division by multiplying.
More Examples of Solving Equations
| Problem | Solution |
| 3n = 18 | |
| Divide both sides by 3 | 3n ÷ 3 = 18 ÷ 3 1n = 6 n = 6 |
| Problem | Solution | ||||||
|
|||||||
| Multiply both sides by 6 |
n = 6 |
| Problem | Solution |
| 9n = 72 | |
| Divide both sides by 9 | 9n ÷ 9 = 72 ÷ 9 n = 8 |
| Problem | Solution | |||
|
||||
| Multiply both sides by 7 |
n = 77 |
Try the printable worksheets below to practice solving equations through multiplication and division.
- Equations with division e.g. n/2 = 12
- Equations with multiplication e.g. 6a = 18
- Multiplication and division equations (1 of 2) e.g. 3n = 12 and a/7 = 3
- Multiplication and division equations (2 of 2) e.g. 3n = 12 and a/7 = 3
The two worksheets below combine the use of addition, subtraction, multiplication, and division to solve equations.
- Addition, subtraction, multiplication and division equations (1 of 2)
- Addition, subtraction, multiplication and division equations (2 of 2)
The worksheets listed above are included here with more solving equations worksheets.
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