A reader in China asked about how to change fractions…not just simple ones, into percent.
“I am trying to assist my 6th grader and my way of doing math works, but it appears complicated when I explain it….”
Professor Homunculus replies:
I know what you mean. I used to be a math teacher, and I understand that each child needs his own method of explanation. There is no “one right way,” but I have learned that there is a need for at least one simple, core explanation (a sort of “summary” or “schematic” explanation) that each teacher can build on.
So, for how to change fractions into percent, I have come up with this: Read the rest here
This is Brian. I’m adding this comment, which is from the original reader. She is in China, and it seems that there are sometimes problems visiting different sites, and sometimes MathMojo.com is hard for her to access. So we’ve been corresponding by e-mail. After I answered her above question in an e-mail, she responded the next day. Here is her comment.
Dear Prof,
WOW! I am so amazed that I heard back from you so quickly and in time to assist my daughter! Thank you very, very much! Her response was “that’s it” …. “that’s so easy”.
She had to fill in a table that had various items given, either a percent, a fraction or a decimal. She did get a little confused trying to keep straight in her head which way to move the decimal to get a percent and which way to move it when changing a % into a decimal. The best we came up with was to think if we need “percent” there is an “r” so we move the decimal to the right and if we need “decimal” there is an “l” in it so we move to the left. We loved the explanation of the whole number being like one whole cookie each and ignoring it till we solved the division problem that was waiting to be done as you appropriately call the fraction and then add how ever many 100%’s to the answer. It certainly worked!! Thanks again!
My only small comment is that for the mixed number example below it may be easier to use a different whole number than is also found in the fraction. My daughter needed clarification since there were two “5′s” as I was giving her your explanation orally. Not a huge deal, but since you asked. :)
Also, I found the explanation using the analogy of money very helpful with my daughter. For example, as she was filling in her table and had to change .25 into a percent I had her also think of money. .25 is saying 25 cents out of a possible 100 to get a dollar. Also, I noticed her math book that was asking her to change large fractions like 9/500 into a percent stated the answer as 1 4/5 % instead of 1.80%. That seemed strange to me since they were asking you to change FROM a fraction….but anyway this is again where money came in handy. She could think of just the .xx part of her percentage answer (ignoring the whole number for the moment) say .80 as 80 cents or 8 out of 10 dimes possible to make a dollar….8 out of 10 looks like 8/10 and that reduces to 4/5. Her book and teacher have approached the above with cross multiplying and dividing and it left my child very confused. Any other tips you use would be much appreciated.
I home schooled my girls from the start and when we moved to China they transitioned to International School. They were 2/3 of the way through grades 3 and 4 when they entered the traditional school setting. Thankfully, they transitioned well. They are still in the same Int’l school in Beijing and fast approaching 2/3 of the way through grades 5 and 6. They use something called Int’l math for the curriculum.
Many thanks!! Feel free to post anything if applicable.
Kindest Regards
Brian, this is exactly the way I taught fractions to my son. I remember being perpetually confused about pi in school. “Pi is a number representing the ratio of a circle’s circumference to its diameter.” How on earth can a decimal number be a ratio? It wasn’t until my senior year in high school that a math teacher bothered to mention the whole 22 over 7 thing. So when my son learned division, I showed him the “fraction arrangement” as one way to write the problem. Then when he learned fractions, we talked about whole numbers being DIVIDED into smaller parts. When he learned ratios, we wrote them with a colon AND as a fraction. And this year, when he learned about pi, he understood right away. If only this concept had been explained to me early on, it could have saved me years of frustrated confusion about math.
hi im a 6th grader who has moved many times so i aways have to catch up on math and i am struggling with changin percents into fractions please help
Rhms Student
Professor Homunculus sez:
Kimmi,
I know what a problem changing schools can be. I wish the education system could make some sort of arrangements to help kids who have to move around, because I know what a disadvantage you are at.
But you seem to have the advantage of being a smart kid who isn’t afraid to ask for help. Good work.
You’re in luck – changing percents into fraction is a piece of cake.
Percents are already a kind of fraction. They’re just fractions with 100 as the denominator.
For example, 78% can also be written 78/100. Then you just reduce the fraction (if you can).
You probably know that percent means “out of a hundred.” So 78 out of 100 is the same ratio as 39 out of 50 (when you reduce).
Therefore, 78% can be written either as 78/100, or as 39/50. Most teachers and tests want the reduced fraction, but there is no real law that says you have to reduce. But give the teachers what they want, and you’ll get what you probably want (good grades). Just keep in mind that 78/100 is perfectly OK outside of school.
Try another? What is 56% expressed as a fraction?
56/100
reduced to 28/50
reduced to 14/25
Any of those would be correct.