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As a pharmacist, Gerald must dispense a certain amount of drugs that have been prescribed to a patient. The prescription shows how much of the medicine the patient is required to have. Gerald takes that prescription and makes sure that the prescription is created exactly as stated. Therefore, there are times that pills must be cut in half or ground to a powder in order for the person to get the exact dosage. In Gerald’s case, the patient’s prescription requires that each dosage contains 45 milligrams of the medicine in a pill. However, Gerald’s pills come in 81 milligrams each. Gerald realizes that he needs to crush up some of 81-milligram pills into smaller sections. Then pour 45 milligrams of the pill powder into separate containers. Each container will be a separate dosage for his patient. Use the factors of 81 to solve Gerald’s situation.
The factors for the number, 81, are only five. It is not an even number, so that eliminates 2 being a factor. Most numbers have an even number of factors because each factor has a partner. When multiplied together, they will equal the original number. However, a few numbers, like 81, have a factor that have the same factor partner.
Let’s find out the factors for eighty-one. To find out, we will see which numbers 81 or fewer can equally divide into 81. The number will not be a factor of 81 if there is a remainder when dividing. Let’s gather the factors!
Since there are not a lot of factors for 81, it is always best to look twice at the factors when you realize that you have only a few factors for a number.
So, Gerald needs to use the factors of 81 which are 1, 3, 9, 27, and 81. To do this, he first needs to grind the 81-milligram pills into a powder. Then divide it into 9 equal groups. Using the factors of 81, you will know that in each group, there will be 9 milligrams of medicine because 9 times 9 equals 81. Now, Gerald needs 45-milligrams in a pouch, so take 5 groups of 9-milligrams and put it into a pouch. You will have 4 groups of 9 milligrams of medicine left or 36 milligrams. So, Gerald doesn’t waste any of the medicine, you need to make sure that all of the medicine is used up. You need to see a common amount for both 45 and 81. In this case, it is 810. So, take 9 more pills and crush them, then you can make 18 pouches with 45-milligrams in each.
Over many years, 81 episodes of the TV show, Planet of the Donkeys, was made. Since it was such a huge success, you decide to binge watch it on your next day off. Most TV shows make the same number of episodes for each season. Based on this information, how many seasons do you think there were for Planet of the Donkeys?
To figure out the answer to this question, you must look at the factors of 81. The factors of 81 are 1, 3, 9, 27, and 81. You must also use reasoning to answer the question. So, the options are 1, 3, 9, 27, or 81 seasons, but we can probably rule out 1 and 81 seasons because those are too extreme. There are usually more than 3 episodes in a season, so we can also rule out 27. Also, we can rule out 27 episodes because that is high also. Therefore, the best answer would be 9 episodes in each of the 9 seasons.
Sylvia looked into her closet and counted her shoes. There were 81 shoes in her messy closet. She could match up her shoes, but instead she wants to know if there is a shoe missing from her closet. Use the factors of 81 to explain whether or not there is a possibility of there being a missing shoe from the closet.
There is a shoe missing. The reason is because 2 would need to be a factor of 81 in order for there to be all pairs of shoes in the closet. However, there is at least 1 missing shoe, but there could be more.
A bride addresses 81 invitations for her wedding. Then she starts to make the seating arrangements at the tables. She and her groom will be seated at the front of the reception hall. Then she wants to rent as few tables as possible to keep the costs down. She looks at her options. From her options, the most any table will hold is 12. That would be the largest table. Even though you don’t know the other sizes of tables, what might be the best options?
The best options would be round or rectangular tables that seat 9 people because then the bride would only have to have 9 tables and every person would have a seat. There would not be any remainders.
Yes, 1 is always a factor for any number including 81.
There are 5 factors for 81.
Two isn’t a factor for 81 because 81 is not an even number.
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