Percentages, Decimals, and Fractions

Today we will be looking at how decimals, percentages, and fractions relate to one another.

We have spent a lot of time looking at decimals and fractions, but percentages are new to us. The word "percent" comes from the latin word "percentum", with centum meaning 100 (i.e. century is 100). So really "percent" means "per 100" or parts per 100. It is represented by the symbol %. To break this down, if we have a room with 100 students, and 12 of these students have birthdays in June, we can say that 12 out of the 100 have birthdays in June. We can say this even simpler, stating that 12 percent of the students have birthdays in June.

Still looking at percentages, if we say 80%, what we really mean is 80 parts out of 100. So for example, if 80% of teachers at Taroona High School drive a car to school, we know that 80 out of every 100 teachers drive a car to school.

Now, since we know percent means per 100, we can think "divide 100" instead. So if we wanted to write 35% and a fraction, we could just divide by 100 or make a fraction with 100 as the denominator. So 35% would be 35/100, which we can easily simplify down to 7/20, using our skills from our unit on fractions (if you need a reminder on this: http://www.mathsisfun.com/simplifying-fractions.html).
For more reading on percentages, this link is really good: http://www.mathsisfun.com/percentage.html


The main skill you need to take from today's lesson is the ability to convert between fractions, decimals, and percentages. I will go through the steps for converting each.

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.

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%


For practice, look at section 4.7 of your booklet. The questions you need to do are:
1 - a, c, f, h
2 - a, c, f, h
3 - a, c, e, g, i, k
4 - a, c, f, h

If you need some extra reading to help you out, this site is really helpful and has some good examples: http://www.mathsisfun.com/decimal-fraction-percentage.html
As always, if you have any question feel free to comment on here, or email me or chat to me in person.

Thursday's Lesson

Today we spent the lesson finishing off the work on decimal division. A lot of students did not do their homework, so they should still have lots of work to go on with for homework. This work is due on Friday, as we need to move on to new work in Friday's lesson.

The work that needs to be completed is in 4.6 of your booklets. We need to be finishing off the first columns of questions 1 and 3, as well as questions 6, 7, and 9. If you would like some extension work or some practice for A and B standard questions, look at questions 17 and 18.

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

Decimal Division

Today we looked at how we divide decimals. As with addition, subtraction, and multiplication, we do this in a similar way to how we would divide if we had whole numbers. For a refresher on how we do that, the following links are quite helpful.

Division: http://www.wikihow.com/Do-Short-Division#/Image:Do-Short-Division-Step-4-Version-2.jpg
http://www.mathsisfun.com/numbers/division.html
http://www.youtube.com/watch?v=2X0Cjy7oEgw

Now we looked at doing division using decimals. An example of this could be 8.942 divided by 2.

Another example could be to divide 37.14 by 5.

A final example could be to divide 4.96 by 0.02. This one is slightly more difficult, because our divisor (0.02) is not a whole number. To get around this, we can multiply both our divisor and our dividend (4.96) by a number which will make our divisor a whole number. The numbers we generally multiply by are factors of 10 (so 10, 100, 1000, 10000, etc). In this case we want to multiply both numbers by 100, because multiplying 0.02 by 100 gives us 2, which is a nice easy whole number to divide by.

Now, we multiplied by 100 when we had 0.02, because that made 0.02 a nice easy number. If however, we had a divisor of say 0.0007, we would multiply by 10000, because this would make 0.0007 a nice easy number (7) to divide by. It is very important that we multiply both our divisor and dividend by the same number. It doesn't matter what the number is, as long as we multiply both by this same number, we will always get the correct answer.

Now, for homework we are still working out of that same booklet. If you have not finished the work in section 4.5 on multiplying with decimals, complete that first. Then move onto section 4.6 which is dividing with decimals. We will be doing questions 1 and 3 (the first column only for these) as well as questions 6, 7, and 9. If you are after some harder extension problems have a look at 17 and 18. By Thursday's lesson I need all for 4.5 (Multiplying) complete as well as the first columns of questions 1 and 3 in section 4.6 (Dividing).

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

Decimal Multiplication

Today we looked at decimal multiplication. Again, it is very similar to standard multiplication. If you need a refresher on this (as it should have been covered in primary school) this websites have some great information and examples.

Multiplication: http://www.mathsisfun.com/numbers/multiplication-long.html

This next website is a link to the video. Once you have watched the video you can click on the green "Practice this concept" button in the top right corner to get a few practice problems. These practice problems are great because if you are getting stuck, you can click on a "Hint" button, and it will help you out a little. The website is: http://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication/v/multiplication-6-multiple-digit-numbers


The way I multiply decimals is slightly different compared to others I have seen, however I have found it to be quite an easy method. The first step I take is to look at the problem and count the number of numbers after the decimal points in the numbers I am multiplying. I then record this off to the side because I will use it later. Next I completely ignore all the decimals and just multiply like I normally would if they were whole numbers. When I get an answer, I then need to modify this slightly. Off to the side I have recorded the number of digits after the decimal points in my question. I recorded this, because this is the number of digits that need to be after my decimal point in my answer. I then put the decimal point back into my answer in the appropriate spot so that it has the same amount of number after the decimal point as my question did. This is then my final answer.
I understand this sounds very complicated, however hopefully I can work through a few examples and it will make a little more sense.


Clicking on any of these images will enlarge them if you are having trouble viewing these.

Example 1:

Example 2:

Example 3:

If you are still having troubles, the following website is also handy

Multiplying decimals: http://www.mathsisfun.com/multiplying-decimals.html

To practice this, look in your booklet is section 4.5 "Decimal Multiplication". I want you to do the following problems:

1 and 3 -> first columns only 

7, 8, 11

Extension: 17 and 18

Our next class for maths is on Tuesday the 28th of July. I need you all to complete the first columns of 1 and 3, and then either 7, 8, or 11 by then for homework. 

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

Addition and Subtraction of Decimals

Today we looked at the addition and subtraction of decimals. This is very similar to the addition and subtraction of larger number, which should have been covered in primary school. If you are struggling with this or would like a refresher, the following websites are very handy.

Addition: http://www.mathsisfun.com/numbers/addition-column.html
Subtraction: http://www.mathsisfun.com/numbers/subtraction-regrouping.html

Adding and subtracting decimals is pretty much exactly the same as adding whole numbers. The key is to keep your working and setting out neat and tidy. When you write the numbers to add, be sure to line up your decimal points. You should also fill in any blank place values with zeros. Once you have done this you can simply add or subtract as you normally would. For example:

Again, some great websites for extra information on this, as well as some more examples can be found here

Addition of decimals: http://www.mathsisfun.com/adding-decimals.html
Subtraction of decimals: http://www.mathsisfun.com/subtracting-decimals.html

As far as work goes, in class we looked at section 4.4 of our booklets. We are working through the following questions:
1 and 2 -> first column of each
4, 5, 8, 10, 11, 15
Note that questions 10, 11 and 15 are more advanced questions, however all students should be able to complete up to and including question 8. If you are missing your booklet or would like further worksheets, I have included some links to further worksheets under the "Worksheets" tab.

If you have any questions or comments regarding this topic feel free to comment on here and I will get back to you.