Multiplication and Division with Decimal

I started reading the book "Practical Shop Math" from Popular Woodworking and one of the first topics was how to do multiplication and division by hand. I remembered most of it from school but one part I had forgotten was how to multiply and divide when working with decimals.

I often find myself doing a lot of math like in the workshop and I don't always have a calculator handy. Im going to include a few articles on math concepts that come up in the shop. A lot of this is simple, but I found it was fun to review.

For simple multiplication, you write the problem like this:

12
 8
---

To multiply numbers with decimals, you still put the two numbers on top of one another and line the numbers up ignoring where the decimal point is:

 125.2
  6.15
 -----
  6260
 12520
751200
------
769980

After doing the multiplication and addition as usual, the last step is to position the decimal in the final product. This is done by adding up the number of decimal places in the two values. So, in 125.2, the decimal point is one place from the right, and in 6.15, it is two places. So we place the decimal point three places from the right in the final product.

We then find that 125.2 times 6.15 equals 769.980.

A division problem is setup so that the number being divided is inside the bracket and the divisor is outside of it. So to solve 124 divided by 8, you would set it up as:

Since eight cannot go into four, we have a remainder of four. You can show the remainder as a fraction by putting the four over the eight which would make the answer 15 and 4/8, or 15 and ½. Or you can put it in decimal form by dividing 4 by eight and getting the answer of 15.5.

Dividing numbers with decimals adds another layer. To divide 125.2 by 6.15 the problem is setup as:

      _____
6.15 )125.2

The first step is to move the decimal point to the right until the divisor is a whole number. The decimal point then also has to be moved the same number of times on the number being divided. This gives us a whole number to work with on the outside of the bracket while not affecting the result. This changes the problem to 12520 divided by 615.

220 divided by 615 is 0.35772357723577235772357723577236. If we round that to two places we get a final answer of 20.36. Sometimes it is necessary to divide a number that is a decimal. For example, 1231.125 divided by 6.

   _________
6 )1231.125

When going through the levels of division, multiplication and subtraction, you ignore the decimal. The first step is to divide 6 into 12.

   _2______
6 )1231125
   12
   --
    031125

Now, since six doesn't go into three we have to put it into 31. It goes five times, so since we skipped the three we have to put a zero there and then put the five above the one, like this:

We end up with a remainder of three and 3 divided by 6 is 0.5 so the answer we get is 205187.5. The last step is to adjust the place of the decimal. Since the decimal was three places from the right in the original number we were dividing, we need to adjust the decimal three places to the right. This gives us a final answer of 205.1875.

Created 2/10/2009 - CleghornCreations.com