LESSON 2†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††Previous††††††††† Next

 

Now we can start adding our fractions, decimals and percentages together.When you add percentages, itís just like adding any other numbers.Then just put the percent sign behind it.If youíre adding decimals, put the decimal points in a line, one on top of the other.The decimal point stays in the same place, so a problem could be set up like this:

 

1.4

3.52

2.033

6.953

 

You could also just use your calculator, entering 1.4 + 3.52 + 2.033 =

 

That will get you 6.953.Donít be afraid to use the calculator.Itís not important what anyone else is doing.Itís also a good idea to use your calculator if you can do something faster that way.You will have a limited time to do your state exam, and the 15 or 30 seconds youíre wasting on each math problem might add up to time needed for one or two questions at the end.

 

It probably wonít be necessary to add fractions, but itís not all that difficult if you need to know.The numbers on the bottom of the fraction (which are referred to as denominators) must be the same.Then you can just add the top numbers (which are called numerators).For example:

 

††† Notice the bottom number stays the same all the way across.

 

If the bottom numbers are not the same, then you must find a common denominator.One way of doing this would be to multiply BOTH the numerator and the denominator by the denominator of the other fraction, so if we were adding ĺ and ⅓ together, we would set it up like this:

 

This would give us:

 

Then to get it down to one number, you can put 13 divided by 12 into your calculator.

 

Sometimes it wonít be necessary to change all of the fractions.If you wanted to add Ĺ + ľ + ⅛, you could multiply both the numerator and denominator in Ĺ by 4, and the numerator and denominator in ľ by 2.That would give you:

 

 

Anyway, you should have the idea.The denominators have to be the same.Finding the lowest common denominator will allow for the easiest addition.For example if your denominators were 4 and 6, you might notice that they both can be divided evenly into 12, so you could multiply the 4 by 3 and the 6 by 2.Donít forget to multiply the numerator by the same number as the denominator.There is a way of determining the lowest common denominator, but we wonít need that for our purposes.

 

The other option we have is to convert everything to decimals.Since we can use a calculator, this might work better in most cases.If you wanted to add Ĺ + ľ + ⅛, you could convert that to .5 + .25 + .125.If you added that on your calculator, you would get .875, which is the same as ⅞.

 

If you are adding fractions and decimals and percentages, you should convert EVERYTHING to either percentages or decimals, and then just add as shown above.

 

Now that weíve mastered addition, letís move on to multiplication.If youíre multiplying percentages or decimals, just do it on your calculator.Enough said.Any exceptions to this will be brought up when we need to.When you are multiplying fractions, they do not have to be converted like they do when you are adding.You would just multiply straight across, i.e. the numerators are multiplied together and the denominators are multiplied together.For example:

 

If you multiplied ⅔ x ⅝, you would multiply 2 x 5 to get 10 on top (the numerator), and 3 x 8 to get 24 on the bottom (the denominator).If you multiply a whole number times a fraction, you can put the whole number over 1 and still have the same number.For example, if you wanted to multiply 75 x ⅔, then:

 

Notice we multiplied 75 x 2 and 1 x 3.You could also just memorize that multiplying by is the same as DIVIDING by 3, multiplying by ľ is the same as DIVIDING by 4, multiplying byĹ is the same as DIVIDING by 2, and so on (whenever the numerator is 1).

 

We also need to be able to average numbers together.To average numbers together, add together all of the numbers, and then divide by the number of things you are averaging.So if we were averaging five numbers, we would add them all together, and then divide by FIVE.For example, 5 + 7 + 23 + 8 + 12 = 55, divided by 5, gives us an average of 11.

 

Previous†††††††††††††††††††††††††††††††††††††††††††††††††††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††Next

 

You donít fail when

you donít get enough points.

You only fail when

you stop trying.

 

 

 

 

©2000 Douglas R. Barry