matematik yang mudah

Introduction to Algebra

Algebra is great fun - you get to solve puzzles!

A Puzzle

What is the missing number?

-

2

=

4

OK, the answer is 6, right? Because 6 - 2 = 4. Easy stuff.

Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we would write:

x

-

2

=

4

It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable.

And when you solve it you write:

x

=

6

Why Use a Letter?

	Because:
	it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box").
	if there were several empty boxes (several "unknowns") we can use a different letter for each one.

So x is simply better than having an empty box. We aren't trying to make words with it!

And it doesn't have to be x, it could be y or w ... or any letter or symbol you like.

How to Solve

Algebra is just like a puzzle where you start with something like "x-2 = 4" and you want to end up with something like "x = 6".

But instead of saying "obviously x=6", use this neat step-by-step approach:

• Work out what to remove to get "x = ..."
• Remove it by doing the opposite (adding is the opposite of subtracting)
• Do that to both sides

Here is an example:

We want to remove the "-2"	To remove it, do the opposite, in this case add 2:	Do it to both sides:	Which is ...	Solved!

Why did we add 2 to both sides?

To "keep the balance"...

	Add 2 to Left Side	Add 2 to Right Side Also
In Balance	Out of Balance!	In Balance Again

Just remember this:

To keep the balance, what you do to one side of the "=" you should also do to the other side!

Another Puzzle

Solve this one:

x

+

5

=

12

Start with:	x + 5 = 12
What you are aiming for is an answer like "x = ...", and the plus 5 is in the way of that! If you subtract 5 you can cancel out the plus 5 (because 5-5=0)
So, let us have a go at subtracting 5 from both sides:	x+5 -5 = 12 -5
A little arithmetic (5-5 = 0 and 12-5 = 7) becomes:	x+0 = 7
Which is just:	x = 7
	Solved!
(Quick Check: 7+5=12)

Introduction to Algebra - Multiplication

Please read Introduction to Algebra first

A Puzzle

What is the missing number?

×

4

=

8

The answer is 2, right? Because 2 × 4 = 8.

Well, in Algebra we don't use blank boxes, we use a letter. So we might write:

x

×

4

=

8

But the "x" looks like the "×"! ... that could be very confusing ... so in Algebra we don't use the multiply symbol (×) between numbers and letters, we simply put the number next to the letter to mean multiply:

4x

=

8

You would say in English "four x equals eight", meaning that 4 x's make 8. And the answer would be written:

x

=

2

How to Solve

On the previous page we showed this neat step-by-step approach:

• Work out what to remove to get "x = ..."
• Remove it by doing the opposite
• Do that to both sides

It still works, but you have to know that dividing is the opposite of multiplying. Have a look at this example:

We want to remove the "4"	To remove it, do the opposite, in this case divide by 4:	Do it to both sides:	Which is ...	Solved!

Why did we divide by 4 on both sides?

Because of the need for balance ...

	Divide Left by 4	Divide Right by 4 Also
In Balance	Out of Balance!	In Balance Again

Just remember ...

To keep the balance, what you do to one side of the "=" you should also do to the other side!

Another Puzzle

Solve this one:

x

/

3

=

5

Start with:	x/3 = 5
What you are aiming for is an answer like "x = ...", and the divide by 3 is in the way of that! If you multiply by 3 you can cancel out the divide by 3 (because 3/3=1)
So, let us have a go at multiplying by 3 on both sides:	x/3 ×3 = 5 ×3
A little arithmetic (3/3 = 1 and 5×3 = 15) becomes:	1x = 15
Which is just:	x = 15
	Solved!
(Quick Check: 15/3 = 5)

Have a Try Yourself

Now practice on this Algebra Multiplication Worksheet and then check your answers on the page after. Try to use the steps we have shown you here, rather than just guessing!

More Complicated Example

How would you solve this?

x

/

3

+

2

=

5

It might look hard, but not if you solve it in stages.

First let us get rid of the "+2":

Start with:	x/3 + 2 = 5
To remove the plus 2 use minus 2 (because 2-2=0)	x/3 + 2 -2 = 5 -2
A little arithmetic (2-2 = 0 and 5-2 = 3) becomes:	x/3 + 0 = 3
Which is just:	x/3 = 3

Now, get rid of the "/3":

Start with:	x/3 = 3
If you multiply by 3 you can cancel out the divide by 3:	x/3 ×3 = 3 ×3
A little arithmetic (3/3 = 1 and 3×3 = 9) becomes:	1x = 9
Which is just:	x = 9
	Solved!
(Quick Check: 9/3 + 2 = 3+2 = 5)

When you get more experienced:

When you get more experienced, you can solve it like this:

Start with:	x/3 + 2 = 5
Subtract 2 from both sides:	x/3 + 2 -2 = 5 -2
Simplify:	x/3 = 3
Multiply by 3 on both sides:	x/3 ×3 = 3 ×3
Simplify:	x = 9

Or even like this:

Start with:	x/3 + 2 = 5
Subtract 2:	x/3 = 3
Multiply by 3:	x = 9