Lesson 5 — Activity 3: Making Conversions
Completion requirements
Lesson 5 — Activity 3: Making Conversions
Getting Ready
Percentages, or percents, are used all the time in everyday life. Just check out the following ads! Percent means out of one hundred.
Think about This:
Think about other times you have seen ads or signs that talk about percentages.
In this activity, you will see how decimals, fractions, and percents are related to each other.
Here's an example to illustrate this:
Converting from a Fraction to a Decimal to a Percent
Have you ever
received an assignment back and the only mark was how many you got
correct over the total and you wondered what percent you actually got on
the assignment? What mark out of 100?
Or you were asked what percent of the day you spent on a certain activity?
In
this part of the activity, you will learn the steps to convert a fraction into a
decimal and also into a percent, which will allow you to figure out the
answers to the questions above.
Let's say you spent 3 hours at the library yesterday and someone wanted to know what percent of the day you spent there.
You can figure out the answer by clicking on each tab below:
1. Convert from a fraction into a decimal.
There
are 24 hours in a day, so our original fraction would be 3/24. In order
to convert this into a decimal, divide the top number (the numerator) by
the bottom number (the denominator).
3 ÷ 24 = 0.125
2. Convert from a decimal into a percentage.
To
convert from a decimal into a percentage, you have to multiply your
decimal by 100. This is because percentage is always out of 100.
0.125 x 100 = 12.5%
3. Depending upon how accurate you wish to be, you may want to get rid of the decimal in the percent.
Remember the rules; if the number is 5 or higher, you round up. In this case, the number is 5, so you would round up.
12.5% = 13%
You spent 13% of the day in the library.
What about a school mark? Let's say you got 13 out of 16 on a quiz. What percent did you get?
Again, click on the tabs below:
You could either use the two-step method you just learned about above or, if you are comfortable, do it in one step like this:
Divide
the numerator by the denominator and then multiply by 100.
13 ÷ 16 x 100 = 81.25%
If you wished to round it to the nearest whole number, you would look at the first decimal. It is a 2, so you would not round up.
81.25% = 81%
You received 81% on the quiz. Good mark!
Converting from a Percent to a Fraction:
Now consider this situation:
Your boss wants you to spend 75% of today's shift cleaning up the back room. He has been very specific in that you have to spend that exact amount of time working on it, no less and no more.
You are working 8 hours today. What fraction of your day will be spent cleaning up the back room?
In this part of the activity, you will learn the steps to convert a percent into a fraction, which will allow you to figure out the answer to the problem above.
Click on each tab below to see how you do this.
1. Place the percentage over 100: 75/100
2. Reduce the fraction to its lowest form.
In order to do this, you have to find a number that will divide evenly into both the numerator and the denominator. It is best to find the smallest number that will go into both and keep reducing the fraction until you can't reduce it any more.
This may take more than one calculation to do. In this case, since the last digit in each number is either a 5 or a 0, both numbers can be divided by 5.
3. Check to see if the numerator and the denominator of the new fraction are still divisible by any common number.
In this case, both numbers are once again divisible by 5.
There are no numbers that divide evenly into both 3 and 4.
Therefore, you will spend 3/4 of today cleaning up the back room.
You
can also figure out how many hours you will have to spend cleaning up
the back room. You can do this by first converting the percentage to a
decimal and then by multiplying the decimal by the number of hours.
Follow the tabs below:
1. Convert the percentage to a decimal by dividing the percentage by 100.
75 ÷ 100 = 0.75
2. Multiply the number by the decimal.
8 x 0.75 = 6
You will have to work 6 hours cleaning the back room.
Try this:
Solve this two-part problem.
Part 1: A survey asked Aboriginal people about their traditional language.
About 20% said they understood their traditional language.
What percentage do not understand their traditional language?
Part 2: When you have this percentage, answer: what fraction of the people do not understand their traditional language?
Convert the percentage to a fraction. Use the steps above to help.
Part 1: 100% – 20% = 80% do not understand their traditional language
Part 2: 80/100
You have determined that 4/5 of Aboriginal people do not understand their traditional language.
