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.
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