Mathograpy: Hi Cate Community, I'm Dylan Ell and I'm a boarding freshman. Math has always been one of my favorite subjects and Math 25 has been really fun so far. I chose to explain percentages and on this page I'm going to show you how to use percentages and why they're important.
Percentages are numbers expressed as a fraction of 100, and of course they also have the percent sign. Percent means out of 100 or per 100. Percentages are used to compare the quantity of one thing to another. For example, my calculator is 50% the size of hers. My calculator is 100% compared to itself, but compared to hers its only half of the size.
Khan Academy does a thorough explanation of how percents work and what they actually mean in this video:
Problem 2.1: Woolworth's had a going out of business sale. The price of a telephone before the sale was $39.98. What was the price of the telephone after a 30% discount? If the sale price of the same telephone had been $23.99, what would the percentage discount have been?
This is an easier percentage problem as all you have to do is a couple simple equations to get the answers. But as shown in the answer, in the equation 23.99/39.98 = 0.60 basically means that 60% of 39.98 is 23.99, or inversely 23.99 is 60% of 39.98.
Problem 21.9: What is greater, 73% of 87 or 87% of 73?
In this problem you take a number and multiply it by a percent, and then flip the two numbers. Both of those turn out to be equal, no matter the number you use. This is because you are multiplying the same numbers and only changing which one is the percent.
Problem 20.1: Jess and Taylor go into the cookie-making business. The chart shows how many dozens of cookies were baked and sold (at $3.50 per dozen ) during the first six days of business. (a) What was their total income during those six days? (b) Which was more profitable, the first three days or the last three days?
(c) What was the percentage decrease in sales from Tuesday to Wednesday? What was the percent increase in sales from Wednesday to Thursday?
(d) Thursday's sales were what percent of the total sales? (e) On average, how many dozens of cookies did Jess and Taylor bake and sell each day?
(c) What was the percentage decrease in sales from Tuesday to Wednesday? What was the percent increase in sales from Wednesday to Thursday?
(d) Thursday's sales were what percent of the total sales? (e) On average, how many dozens of cookies did Jess and Taylor bake and sell each day?
I liked this problem because there were many percentage questions being asked and it covers many uses of percentages. Part A was getting the total amount of dozen cookies and then multiplying it by the price which is $3.50. Part B also required adding the cookies of the days, but this time it was split into the first 3 days and the last 3. I found which of these had the most cookies baked, which was the last 3. Part C was finding the percentage difference of cookies sold between 2 days. Part D involved finding the percentage of 1 days sale compared to the total amount of sales. And finally Part E was just finding the average dozen of cookies sold per day by using the total dozens divided by the total days.
Problem 24.8: The population of a small town increased by 25% two years ago and then decreased by 25% last year. The population is now 4500 people. What was the population before the two changes?
This is an interesting problem because you have to work backwards with percentages to find the population before the two changes using division.
Problem 42.8: If the price of a stock goes from $4.25 per share to $6.50 per share, by what percent has the value of the stock increased?
This is a simpler percentage problem where you can use the equation (New-Old)/Old. I just plugged the numbers into that and I was able to find that the stock increased 53% from $4.25.
Conclusion: Percentages are ways that we express and compare numbers and objects to each other. Per cent means per 100, so saying multiplying by 57% is equivalent to multiplying by 0.57. They are a simple concept but can get complex as shown in problem 24.8 when using division. Percentages are essential in math at any level and they have multiple uses.