Introduction to Algebra – Multiplication and Division

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Please read Introduction to Algebra – Addition and Subtraction first

A Puzzle

What is the missing number?

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:

which can simply be written like this “Put the number next to the letter to mean multiply

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

How to Solve

On the previous lesson 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 both sides by 4:

Which is … Solved!

Just remember …

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 = …”,
  • So, let us have a go at multiplying both sides by 3
x / 3 x 3= 5 x 3
  • A little arithmetic (3/3 = 1 and 5×3 = 15) becomes:
= 15
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:
x = 9

When you get more experienced:

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

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

 

Have a Try Yourself

Now practice on this Simple Algebra Worksheet and then check your answers from the choices.

Try to use the steps we have shown you here, rather than just guessing!

1.

Solve 3x = 9

Choose one:

6

3

12


2
.

Solve x/2 = 3

Choose one:

6

5

9

3.

Solve x/5 + 2 = 6

Choose one:

15

10

20


4
.

Solve 3x – 2 = 7

Choose one:

3

6

1


5
.

Solve 2(x + 3) = 10

Choose one:

3

2

5

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