I have to write each of the following percent change into a ratio comparing it to the original quantity. Then I have to write it as a constant multiplier.
This is the example in my book:
3% increase, 103/100, 1+0.03
So I understand how to do single digit numbers, like 8, but the problems i'm stuck on are:
11% decrease
12.5% growth
6 1/4% loss and x% increase.
How would I go about solving these?
To convert each percent change into a ratio comparing it to the original quantity, you can follow these steps:
1. For a percent decrease, subtract the percentage from 100 to find the remaining percentage. For example, for an 11% decrease, the remaining percentage would be 100 - 11 = 89%.
2. Convert the remaining percentage to a fraction by putting it over 100. For example, 89% would be 89/100.
3. To write it as a ratio, divide the remaining percentage by 100. Using the example, the ratio would be 89/100.
4. To write it as a constant multiplier, subtract the remaining percentage from 100 and divide by 100. Using the example, the constant multiplier would be (100 - 89) / 100 = 0.11.
For a percent growth or increase, the process is similar:
1. Add the percentage to 100 to find the new percentage. For example, for a 12.5% growth, the new percentage would be 100 + 12.5 = 112.5%.
2. Convert the new percentage to a fraction by putting it over 100. For example, 112.5% would be 112.5/100.
3. To write it as a ratio, divide the new percentage by 100. Using the example, the ratio would be 112.5/100.
4. To write it as a constant multiplier, add the percentage to 100 and divide by 100. Using the example, the constant multiplier would be (100 + 12.5) / 100 = 1.125.
For the example of a 6 1/4% loss, you can follow a similar process:
1. Convert the mixed number to a decimal. 6 1/4% can be written as 6.25%.
2. Subtract the percentage from 100 to find the remaining percentage. Using the example, the remaining percentage would be 100 - 6.25 = 93.75%.
3. Convert the remaining percentage to a fraction by putting it over 100. In this case, 93.75% would be 93.75/100.
4. To write it as a ratio, divide the remaining percentage by 100. Using the example, the ratio would be 93.75/100.
5. To write it as a constant multiplier, subtract the remaining percentage from 100 and divide by 100. Using the example, the constant multiplier would be (100 - 93.75) / 100 = 0.0625.
For the case of x% increase, you can use a variable to represent the percentage:
1. Add the variable percentage (x) to 100 to find the new percentage. So, the new percentage would be 100 + x.
2. Convert the new percentage to a fraction by putting it over 100. For example, (100 + x)% would be (100 + x)/100.
3. To write it as a ratio, divide the new percentage by 100. Using the example, the ratio would be (100 + x)/100.
4. To write it as a constant multiplier, add the variable percentage (x) to 100 and divide by 100. Using the example, the constant multiplier would be (100 + x)/100.
Remember to substitute the value of x with the specific percentage increase when solving a specific problem.
1 + .03 = 1.03
1 - .11 = .89
1 + .125 = 1.125 = 9/8 (.125 = 1/8)
1 - .0625 = .9375 = 15/16
(.0625 = half of .125 or 1/16)
(1 + x)?
I hope this helps. Thanks for asking.