1. Equations 1
Click mouse

2. EQUATIONS
The important thing to remember about equations is that both sides must balance (both sides must equal each other).
e.g = 7 7
This means that if you do something to one side of the equation you must also do the same to the other:
e.g =
e.g =
e.g = 5 5
If you take 2 away from the first part of the equation
YOU MUST ALSO take 2 away from the second part
So you can see, the equation is still balanced!
Click mouse

3. Look at this example, and remember the balance!
e.g = 10 10
Remember, if you do something to one side of the equation you must also do the same to the other:
e.g =
e.g =
e.g = 6 6
If you take 4 away from the first part of the equation
YOU MUST ALSO take 4 away from the second part
So you can see, the equation is still balanced!
Click mouse

4. You can do anything to the equation, IF you do the same to both sides.
e.g = 10 10
So, if you ADD something to one side of the equation you must also ADD the same to the other:
e.g =
e.g =
e.g = 14 14
If you add 4 to the first part of the equation
YOU MUST ALSO add 4 to the second part
So you can see, the equation is still balanced!
Click mouse

5. You can do anything to the equation, IF you do the same to both sides.
e.g = 10 10
So, if you DIVIDE one side of the equation by a number you must also DIVIDE the other side by the same:
e.g =
e.g =
e.g = 2 5 5
If you DIVIDE the first part of the equation by 2
YOU MUST ALSO DIVIDE the second part by 2
So you can see, the equation is still balanced!
Click mouse

6. You can do anything to the equation, IF you do the same to both sides.
e.g = 10 10
So, if you MULTIPY one side of the equation by a number you must also MULTIPLY the other side by the same:
e.g. (6 + 4) x 2 = (3 + 7) x2
e.g =
e.g. (6 + 4) x 2 = 20 20
If you MULTIPLY the first part of the equation by 2
YOU MUST ALSO MULTIPLY the second part by 2
So you can see, the equation is still balanced!
Click mouse

7. EQUATIONS RULE: Equations must always balance.
Whatever you do to one side you must ALSO do to
the other.
Now that you know these facts they will really help you to solve equations.
Click mouse

8. EQUATIONS MUST ALWAYS BALANCE.
This fact will help you to answer the following questions. Have a go at them.
The equation is now balanced, because both sides equal 100
1. … = 100 40
What must you add to 60 to make 100
The equation is now balanced, because both sides equal 3
1. … = 3 10
What number take away 7 makes 3
Click mouse

9. What we really did was to take 60 away from BOTH SIDES
Both those sums were very easy and you could work them out in your head.
However, if you understand what you are doing it will help you to work out harder sums!!
Let’s look again at the first one we did and think about how we did it:-
…… + 60 = 100
…… + 60 = 100
…… + 60 =
…… + 60 = 40
Take away 60
Take away 60
What we really did was to take 60 away from BOTH SIDES
This left us with the answer we needed!
Click mouse

10. What we really did was to ADD 7 to BOTH SIDES
Let’s look again at the second one we did and think about how we did it:-
It’s important to remember that this is a MINUS 7
… = 3
…… + 60 = 3 + 7
…… + 60= 3
…… + 60 = 10
… = 3
Add 7 ( to get rid of the –7 )
Add 7
What we really did was to ADD 7 to BOTH SIDES
This left us with the answer we needed!
Click mouse

11. Let’s try adding a little algebra!
Instead of leaving the gap … we put a letter into the equation.
Look at this equation and work it out:-
y + 60 =
y + 60 = 20
y + 60 = 60
y + 40 = 60
Find the value of y
Take away 40
Take away 40
What we must do is take 40 away from BOTH SIDES to leave the y by itself
Click mouse
This left us with the answer we needed! y = 20

12. Now try these – they’re easy!!!!
z + 60 = 12
z + 60 =
z + 60 = 15
z + 3 = 15
Find the value of z
Take 3 away from BOTH SIDES to leave the z by itself
Take away 3
Take away 3
y + 60 = 35
y + 60 = 15
y + 20 = 35
y + 60 =
Find the value of y
Take 20 away from BOTH SIDES to leave the y by itself
Take away 20
Take away 20
Click mouse

13. Add 3 to BOTH SIDES to leave the z by itself z - 3 = 15
Now try these with MINUS numbers in them – they’re still easy if you remember the rule!!
Find the value of z
Remember, this is a MINUS
Add 3 to BOTH SIDES to leave the z by itself
z - 3 = 15
z + 60 =
z + 60 = 15
z + 60 = 18
ADD 3
ADD 3 to get rid of the -3
y + 60 = 55
y + 60 =
y - 20 = 35
y + 60 = 35
Find the value of y
Add 20
ADD 20 to get rid of the -20
Add 20 to BOTH SIDES to leave the y by itself
Click mouse

14. What you are doing is KEEPING THE BALANCE
Can you see the pattern?
If it is a PLUS on one side of the equation, it becomes a MINUS on the other. This is called INVERSING
2 + 3 = 5
2 + 3 =
SO……..
2 = 2
If it is a MINUS on one side of the equation, it becomes a PLUS on the other.
What you are doing is KEEPING THE BALANCE
8 + 3 =
8 - 3 = 5
SO……..
8 = 8
Click Mouse

15. Try these. Click the mouse for answer / help
Find the value of x
x + 8 = 21
Find the value of x
x - 19 = 5
x - 19 = 5
x =
x = 24
x + 8 = 13
x + 8 = 21
x + 8 =
Find the value of y
y - 8 = 22
Find the value of b
b - 5 = 26
y - 8 = 22
y =
y + 8 = 30
b = 31
b - 5 = 26
b =
Find the value of z
z + 19 = 21
Find the value of a
a + 7 = 21
z = 2
z =
z + 19 = 21
a = 14
a + 7 = 21
a =
Click mouse

16. The same rules apply – you must keep your equation balanced
Now you’ve got the hang of these, let’s try with multiplication and division
The same rules apply – you must keep your equation balanced
Look at this equation:-
4 x 3 = 12
This is balanced (because 4x3 is 12)
To get rid of the x3 we must divide by 3, ON BOTH SIDES OF THE EQUATION
Not yet balanced!!!
4 x 3 = 4
4 x 3 = 12 ÷ 3
4 x 3 = 12
4 x 3 = 12
Balanced again!
Divide by 3 to get rid of x3
So divide this side by 3
Click mouse

17. So multiply this side by 2
Keep your equation balanced
Look at this equation:-
4 ÷ 2 = 2
This is balanced (because 4 ÷ 2 is 2)
To get rid of the ÷ 2 we must multiply by 2, ON BOTH SIDES OF THE EQUATION
Not yet balanced!!!
4 x 3 = 2 x 2
4 x 3 = 4
4 x 3 = 2
4 ÷ 2 = 2
Balanced again!
Multiply by 2 to get rid of ÷ 2
So multiply this side by 2
Click mouse

18. So multiply this side by 2
So, now that you can see the same rules apply, let’s try it with algebra
Look at this equation:-
y ÷ 2 = 8
To get rid of the ÷ 2 we must multiply by 2, ON BOTH SIDES OF THE EQUATION
Not yet balanced!!!
y x 3 = 16
y x 3 = 8
y ÷ 2 = 8
y x 3 = 8 x 2
Balanced again!
Multiply by 2 to get rid of ÷ 2
So multiply this side by 2
Click mouse

19. Look at this equation:- y x 2 = 8
To get rid of the x 2 we must DIVIDE by 2, ON BOTH SIDES OF THE EQUATION
Not yet balanced!!!
y x 3 = 4
y x 3 = 8 ÷ 2
y x 3 = 8
y x 2 = 8
Balanced again!
Divide by 2 to get rid of x 2
So divide this side by 2
Click mouse

20. What you are doing is KEEPING THE BALANCE
Can you see the pattern?
If it is a MULTIPLY on one side of the equation, it becomes a DIVIDE on the other - INVERSING again!
x ÷
2 + 3 = 6 ÷ 3
2 x 3 = 6
SO……..
2 = 2
If it is a DIVIDE on one side of the equation, it becomes a MULTIPLY on the other.
What you are doing is KEEPING THE BALANCE
÷ x
8 + 3 = 4 x 2
8 ÷ 2 = 4
SO……..
8 = 8
Click Mouse

21. Try these. Click the mouse for answer / help
Find the value of b
b x 8 = 24
Find the value of a
a x 7 = 49
a = 7
x ÷
a x 7 = 49
a = 49 ÷ 7
b + 8 = 3
x ÷
b x 8 = 24
b + 8 = 24 ÷ 8
Find the value of y
y ÷ 4 = 9
Find the value of b
b x 5 = 40
y + 8 = 36
÷ x
y ÷ 4 = 9
Y = 9 x 4
b = 40 ÷ 5
x ÷
b x 5 = 40
b = 8
Find the value of z
z ÷ 8 = 6
Find the value of a
a ÷ 3 = 7
z = 48
z = 6 x 8
÷ x
z ÷ 8 = 6
a = 7 x 3
a = 21
÷ x
a ÷ 3 = 7
Click mouse