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EQUATIONS
The important thing to remember about equations is that
both sides must balance (both sides must equal each other).
e.g.
5+2 = 3+4
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. 5 + 2 = 3 + 4
2
5
5
If you take 2 away
from the first part
YOU MUST ALSO take 2
of the equation
away from the second part
So you can see, the equation is still balanced!
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Look at this example, and remember the balance!
e.g.
6+4 = 3+7
10
10
Remember, if you do something to one side of
the equation you must also do the same to the
other:
e.g. 6 + 4
2 = 3+7
3
6
6
If you take 4 away
from the first part
YOU MUST ALSO take 4
of the equation
away from the second part
So you can see, the equation is still balanced!
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You can do anything to the equation, IF you do the same to
both sides.
e.g.
6+4 = 3+7
10
10
So, if you ADD something to one side of the
equation you must also ADD the same to the
other:
e.g. 66
6+++44++44=== 3
33++77 + 4
If you add 4 to the
first part of the
equation
14
14
YOU MUST ALSO add 4 to
the second part
So you can see, the equation is still balanced!
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You can do anything to the equation, IF you do the same to
both sides.
e.g.
6+4 = 3+7
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. 66++44 == 33++77
If you DIVIDE the
first part of the
equation by 2
2
5
2
5
YOU MUST ALSO DIVIDE
the second part by 2
So you can see, the equation is still balanced!
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You can do anything to the equation, IF you do the same to
both sides.
e.g.
6+4 = 3+7
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
6+4
4) x 2 === (3
33 ++ 7
7)
7 x2
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!
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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.
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EQUATIONS MUST ALWAYS BALANCE.
This fact will help you to answer the following questions.
Have a go at them.
1. 40
….. + 60 = 100
What must you add to
60 to make 100
1. 10
….. - 7 = 3
What number take away
7 makes 3
The equation is now
balanced, because
both sides equal 100
The equation is now
balanced, because
both sides equal 3
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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
40 - 60
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!
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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
….. -+ 760
……
60=
=3
=33
10+ 7
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!
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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 + 40
60 = 60
20- 40
Take
away 40
Find the value of y
Take
away 40
What we must do is take 40 away from BOTH SIDES to
leave the y by itself
This left us with the answer we needed! y = 20
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Now try these – they’re easy!!!!
z + 60
3 = =1515
12- 3
Take
away 3
Take
away 3
y + 20
60 = 35
15 - 20
Take
away 20
Take
away 20
Find the value of z
Take 3 away from BOTH SIDES
to leave the z by itself
Find the value of y
Take 20 away from BOTH SIDES
to leave the y by itself
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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
z +- 3
60= =1515
18+ 3
ADD 3 to get
rid of the -3
ADD
3
y +- 20
60 = 35
55+ 20
ADD 20 to
get rid of
the -20
Add 3 to BOTH SIDES to leave
the z by itself
Add
20
Find the value of y
Add 20 to BOTH SIDES to leave
the y by itself
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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= 5-3
SO……..
2 = 2
If it is a MINUS on one side of the
equation, it becomes a PLUS on the other.
-
+
88+- 33 == 55 + 3
SO……..
8 = 8
What you are doing is
KEEPING THE
BALANCE
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Try these. Click the mouse for answer / help
Find the value of x
Find the value of x
+
x + 8 = 21
-
x - 19 = 5
xx++88==21
13- 8
Find the value of y
y - 8 = 22
-
+
z + 19 = 21
+
-
z + 19===212
21- 19
+
x - 19
= ==24
55+ 19
Find the value of b
b - 5 = 26
y
8
=
22
yy + 8 == 22
30 + 8
Find the value of z
-
-
+
bb - 5 == =26
31
26 + 5
Find the value of a
a + 7 = 21
+
-
a + 7 = =21
= 14
21 - 7
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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:This is balanced (because 4x3 is 12)
4 x 3 = 12
To get rid of the x3 we must divide by 3, ON BOTH SIDES
OF THE EQUATION
Not yet balanced!!!
4x3=4
12 ÷ 3
Balanced
again!
Divide by
So divide
3 to get
rid of x3
this side by
3
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Keep your equation balanced
Look at this equation:-
This is balanced (because 4 ÷ 2 is 2)
4÷2=2
To get rid of the ÷ 2 we must multiply by 2, ON BOTH
SIDES OF THE EQUATION
4x
÷ 23 == 24
2x2
Multiply by 2
to get rid of
÷ 2
So multiply
this side by
2
Not yet balanced!!!
Balanced
again!
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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!!!
yy x
÷x233===816
88 x 2
Multiply by 2
to get rid of
÷ 2
So multiply
this side by
2
Balanced
again!
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Look at this equation:yx2=8
To get rid of the x 2 we must DIVIDE by 2, ON BOTH
SIDES OF THE EQUATION
Not yet balanced!!!
yx3
2=4
8÷2
Divide by 2
to get rid of
x 2
So divide
this side by
2
Balanced
again!
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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
22 +x33== 66÷ 3
÷
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
÷
x
SO……..
KEEPING THE
88+÷32== 44x 2
8 = 8
BALANCE
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Try these. Click the mouse for answer / help
Find the value of b
b x 8 = 24
Find the value of a
x
÷
a x 7 = 49
bb+x+888===24
24
3 ÷8
Find the value of y
y÷4=9
Find the value of z
z÷8=6
÷
x
yy÷+48==936
Y
x4
÷
x
z ÷ 8 == 66
48
x8
Find the value of b
b x 5 = 40
x
÷
a x 7= =749 ÷ 7
x
÷
b x 5 ==40
40
8 ÷5
Find the value of a
a÷3=7
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÷
x
aa ÷ 3 ==7721x 3