Percent and Parts Per 100

Justin, the big boss of the Busy Business Beavers, presents his plan for the upcoming year. The BBBs are a small, but growing company, and they hope to earn enough money to buy a bigger office dam. Justin is going on and on about his plan to grow trees by sowing seeds, and his two assistants, Dustin and Kevin, try to focus on what he says. In order to understand Justin's fail-proof business plan, they’ll need to understand percents and parts per 100. Justin starts by telling his employees about percents and their relationship to ratios. Let's look at the word percent. Cent is a word root that means one hundred. Per-cent is another way of saying parts per one hundred.

For example, let's look at 1 percent. That means it's 1 part per 100, which can be written as the fraction 1 over 100. This is equal to the decimal one hundredth. Justin tells the other beavers about the new plot of land they acquired, which has enough space to grow 10 rows of trees, with 10 trees in each row This looks just like a hundreds chart, which is a model that has ten rows and ten columns. That means there are 100 squares, making it perfect for modeling percents. The busy business beavers want to plant 25 percent maple trees. That means that we can look at the part as 25 and the whole as 100. It can be written as the fraction 25 over 100 or the decimal twenty-five hundredths In the hundreds chart, we can then put in 25 maple trees. The big boss says the remaining trees should be pine. Let's see what that looks like in the hundreds chart 75 trees out of 100 remain. That's the fraction 75 over 100, which gives us 75 percent or the decimal seventy-five hundredths. Adding the 25 maple trees to the 75 pine trees gives us 100 trees. Writing that as a fraction gives us 100 over 100, which is also equal to 100 percent and one whole. It looks like Dustin has something to say. Eh, it’s probably not important. So let’s get back to what Justin is saying. He’s talking about his plans for the trees they will chop down. For every tree they chop down, they will use 20 percent of the tree trunk for their new and bigger office dam, 70 percent to sell, and 10 percent to make skateboards. Justin uses a tape diagram to illustrate his plans. We know a whole log is equal to 100 percent, and a piece of tape represents 1 whole log. How are we going to divide up this tape diagram? Notice that each of the numbers is a multiple of 10 percent. If each part is 10 percent, then each amount will be represented by a whole number of tape pieces. We then divide 100 percent by 10 percent to get 10, which means that we will divide the tape into ten pieces. 20 percent is represented by these 2 parts of the tape, since 2 times 10 percent is equal to 20 percent. 70 percent is modeled by these 7 parts of the tape, and 10 percent is modeled by this last piece of tape. Altogether, that makes 100 percent, which is the same as one whole log. Let’s summarize. Hundreds charts and tape diagrams help us better visualize percents. With hundreds charts, each individual square represents one percent. For example, 15 percent is represented by 15 squares. 35 percent is represented by 35 squares. And 50 percent is represented by 50 squares. With a tape diagram, we divide the whole into equal parts. Depending on the percents, we divide it into different amounts. For example, we could divide it into 5 parts. 2 parts would be equal to 2 over 5, or 40 over 100. That would be equal to 40 percent. 3 parts would be equal to 3 over 5, or 60 over 100. That would be equal to 60 percent Justin and Kevin are confident in their fail-proof plan, but Dustin is still trying to get their attention about one little mistake in their plan unsuccessfully. Well, I guess you reap what you sow...