### Abacus Algebra - Gary Flom

A fun way to use the abacus, is to perform bead arithmetic in mixed operations. Doing algebra on the abacus is a good way to practice, and break up your computing and thinking away from simply doing one sort of arithmetic operation repeatedly.

Try:

X / 7 + 6 = 9.

We want to isolate X on the left side of the equation by "undoing" the operations we see here. Whatever we do on one side of the equation, we must do the same on the other side, standard algebra stuff :-)

Start by subtracting 6 from both sides. We will get:

X / 7 = 9 - 6.

On your abacus, do 9 - 6.

The next and final step is to multiply both sides by 7.

The equation then becomes:

X = 7 times ( 9 - 6 ).

Take the number showing on your abacus (should be 3) and multiply it, using bead arithmetic, by 7.

You should now have 21 on your abacus, the final answer. ( X = 21 ).

Check the result by plugging into the original equation:

21 / 7 + 6 does that equal 9?

It does, so we did it right.

Another example:

56 - ( X times 5 ) = 16.

One way to solve this is to start by adding X times 5 to both sides.

We now have:

56 = ( X times 5 ) + 16.

Now subtract 16 from both sides (no cheating, use your abacus :-)

The equation becomes:

56 - 16 = X times 5.

On your abacus, you should have the result of 56 - 16.

Finally, divide both sides by 5.

The equation becomes:

(56 - 16) / 5 = X.

Take the number on your abacus and divide
it by 5.

You should get 8 as the answer.
( X = 8 ).

Does:

56 - (8 times 5) equal 16?

Yes.

If you solve a problem such as:

X / 6 - 3 = 1.5

then, with the check of your answer, you will get practice in all 4 of the fundamental arithmetic operations.

Try it!

Gary Flom