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Introduction to Algebra - Multiplication

Another Puzzle

What is the missing number?

square

×

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

  • 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!

arb_1

arb_2

arb_3

arrb_4

arb_5

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

(Quick Check: 15/3 = 5)

 


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 5×3 = 15) becomes:

1x = 9

Which is just:

x = 9

(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

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