Working with Percentages

We are now moving away from decimals and looking at percentages. We need to know a few little tricks for working with percentages.

The first thing we need to know how to do find a percentage from a small set taken out of a whole. For example, you need to know how to find what percentage say 18 out of a group of 50 is.
The easiest way I have found to do this is to make a fraction with our small set as the numerator (top number) and the whole group as our denominator (bottom number).

So in the example above we would have the fraction 18/50, because 18 is our smaller set and 50 is our total group. 

Next, we use our conversion skills to convert the fraction into a percentage. To do this we divide our numerator by our denominator, then multiply this new number by 100. If you do not know how to do this, see a previous post titled "Converting between fraction, decimals, and percentages". 

So for the example above, we would have

18 ÷ 50 = 0.36 x 100 = 36%

We now know that 18 out of 50 is 36%

The next skill we need is finding a number from a given percentage. So for example, I may want to find what 27% of 500 is. 

To do this, we first convert the percentage to a decimal, and then multiply this by our whole group. So for the example above, we would convert 27% to a decimal (by dividing by 100), which gives us 0.27. Next we would multiply this new decimal by our whole group (500). This gives us: 

0.27 x 500 = 135

We now know that 27% of 500 is 135. 

These are the first two skills (and probably the most important skills) when working with percentages. 

To practice these skills, go through the following worksheet. For now just work through the first page of questions. You can access the worksheet by clicking here, or it can also be found in the "Worksheets" tab. 

As always, if you have any questions, feel free to comment on this post, or email or chat to me in person. 

Converting a Recurring Decimal into a Fraction

In a previous section of this unit we looked at converting a decimal to a fraction. This method would only work for terminating decimals. It is impossible to write an irrational number as a fraction, however with a few little tricks, we can write a recurring decimal as a fraction.

To do this, we want to get rid of the repeating part of the decimal. For example, if we had the decimal 0.1543434343434343.... (going on forever), we want to get rid of the "43434343....." part. To do this, we call our original number "x" (i.e. x = 0.1543434343434343.... (going on forever)). Next, we want to multiply by a power of 10 (i.e. 10, 100, 1000, 10000, etc) that has the same number of zeros as the number of repeating digits. In this case we have two repeating digits (4 and 3) so we will multiply by 100 (because it has two zeros).
This gives us 15.434343434343..... (going on forever). So from this, we can say that 100x = 15.4343434343.... (going on forever) because we multiplied our original number (which we called "x") by 100.
Now we get a bit fancy. We then take this 100x and subtract our original x, so we get:

100x - x = 15.434343434343.... - 0.15434343434343....

Now if we do the left hand side of this sum we get 99x
If we do the right hand side of this sum, we see that the repeating pattern (the 43434343.... part) actually disappears (gets cancelled out), leaving us with 15.28

So what we now have is:

99x = 15.28

Solving this equation then gives us:

x = 15.28/99

x = 382/2475


Now this may seem quite complicated, but with a little practice it does get a whole lot easier. I have added a few more examples below.

I have uploaded a worksheet that has some questions on this, as well as general working with decimals questions. This can be found in the "Worksheets" tab. Work through this and have as much as you can completed by Monday's lesson. 

If you have any questions on this content, feel free to comment on this post, or email or chat to me in person. 

Terminating and Recurring Decimals, and Irrational Numbers

We spent some time looking at 3 special types of decimal numbers. They are:

1. Terminating Decimals
2. Recurring Decimals
3. Irrational Numbers

All the information, as well as some problems on these, can be found by clicking here. 

This document will also be uploaded into the Worksheets tab. 

If you do have any questions on this content, feel free to comment on this post, or email or chat to me in person.

Converting between fractions, decimals, and percentages

Our first unit of work will deal with decimals, percentages, and rates and ratios. To start with we will look at how to convert between fractions, decimals, and percentages. These are essential skills, so make sure you know how do do all of the following. If you do need help with this, please feel free to comment on this post, or email or chat with me in person. 

Converting percentage to decimals

This is quite easy. All you really need to do is to divide the original percentage by 100 and you have your decimal.

For example: 47% to a decimal. All you would do is divide 47 by 100, giving you an answer of 0.47

Converting decimal to percentage

Again, this is quite easy. All we need to do is multiply the original decimal by 100 and you have your percentage.

For example: 0.82 to a percentage. Simply multiply 0.82 by 100, giving you an answer of 82%

Converting fractions to decimals

This is also quite simple. All that needs to be done is dividing the numerator by the denominator.

For example: 3/8 to a decimal. Divide 3 by 8, and you get 0.375, which is your answer.

Converting decimals to fractions

This is slightly more difficult. It involves a few steps. First, we need to make a fraction with the original decimal as the numerator, and the number 1 as the denominator. Once we have done this, we need to convert this decimal to a whole number by multiplying by a multiple of 10 (i.e. 10, 100, 1000, 10000, etc). We then need to multiply our denominator, 1, by this same factor of 10. Once we have done all of this, we simplify our fraction. Hopefully a few examples will help make sense of this.

Example 1:

 Example 2:

Converting percentages to fractions

This is much simpler than converting the decimals to fractions. Since we know that a percentage is a part out of 100, all we need to do is to make a fraction with the percentage as the numerator and 100 as the denominator. You then need to simplify your fraction.

For example: 36% as a fraction. Set up your fraction with 36 as the numerator and 100 as the denominator. You should get 36/100. Now simplify to get 9/25

Converting fractions to percentages

This is quite simple, as long as you have followed the skills I have gone thru above. The first thing you will need to do is to convert your fraction to a decimal, by dividing the numerator by the denominator. You then want to convert this decimal to a percentage by multiplying by 100.

For example: 6/20 as a percentage. First convert it to a decimal by dividing the numerator (6) by the denominator (20). You should get an answer of 0.3. You then want to convert this to a percentage by multiplying by 100. This will give you a final answer of 30%

Now in this post, and more specifically when I talk about fractions, I am talking about simplifying fractions. Now this should have been covered last year, but briefly it is basically finding a number that both the numerator and denominator of the fraction can be divided by, and then going out and actually dividing them by this number. This should keep the overall value of your fraction the same, but the numbers will be a little smaller. For example, if I had 2/6 as a fraction, both the numerator (2) and the denominator (6) can be divided by 2 to give a whole number as an answer. So if we divide the numerator and denominator by 2 we get a simplified fraction of 1/3. The value of the fraction is still the same, but the numbers are a little smaller, so we say the fraction has been simplified. 

For more help on simplifying fractions, check out the following website; 

http://www.mathsisfun.com/simplifying-fractions.html

As mentioned above, if you do have questions about any of this, feel free to comment on this post, or email or chat to me in person. 

A worksheet on this content can be found in the "Worksheets" tab above. I want all of the questions completed on this worksheet.