HappyGrace Posted January 28, 2013 Share Posted January 28, 2013 Everything online I see just explains that you divide the numerator by denominator to get the decimal. She can see that with something like 1/2, that it is dividing the 1 into two parts. But how can I visually explain something like 3/13? (I am trying to make sure she truly understands the conceptual behind things, not just do the formula). Quote Link to comment Share on other sites More sharing options...

regentrude Posted January 28, 2013 Share Posted January 28, 2013 Does she understand that a fraction means simply numerator divided by denominator? So, whether I write the fraction as the ratio of two integers (3 divided by 13) or actually calculate that 3 divided by 13 is 0.2307 makes no difference. That IS conceptual, there is no "formula" - it is simply what 3/13 means. Understanding the fraction as a division or ratio is more efficient than still clinging to the visual pizza model. Of course, you can always explain that you have three pizzas which you need to divide among 13 children - each child gets a little less than a quarter pizza. Quote Link to comment Share on other sites More sharing options...

Karen in CO Posted January 28, 2013 Share Posted January 28, 2013 Does she understand that a fraction means simply numerator divided by denominator? So, whether I write the fraction as the ratio of two integers (3 divided by 13) or actually calculate that 3 divided by 13 is 0.2307 makes no difference. That IS conceptual, there is no "formula" - it is simply what 3/13 means. Understanding the fraction as a division or ratio is more efficient that still clinging to the visual pizza model. Of course, you can always explain that you have three pizzas which you need to divide among 13 children - each child gets a little less than a quarter pizza. Fractions are a way to represent division. You can start easy and prove to her that 1 divided by 2 is, in fact, .5 then work your way through fractions that she knows before you comback to the th 3/13 fraction. It will help her a lot in future maths to really understand this concept and to abandon the pizza-crutch. Quote Link to comment Share on other sites More sharing options...

HappyGrace Posted January 28, 2013 Author Share Posted January 28, 2013 :blush: I guess I prbly should have said *I* don't exactly understand how to explain it because I didn't learn math conceptually. I'm trying really hard to remedy that by watching Crewton Ramone, MUS, etc. So isn't 3/13 like a pizza that is divided into 13 parts and it is 3 of the parts? So why would you divide it? I know it's a really stupid question :( I did really well in math in school, but I just knew how to do the formulas, not the WHY! Quote Link to comment Share on other sites More sharing options...

8filltheheart Posted January 28, 2013 Share Posted January 28, 2013 :blush: I guess I prbly should have said *I* don't exactly understand how to explain it because I didn't learn math conceptually. I'm trying really hard to remedy that by watching Crewton Ramone, MUS, etc. So isn't 3/13 like a pizza that is divided into 13 parts and it is 3 of the parts? So why would you divide it? I know it's a really stupid question :( I did really well in math in school, but I just knew how to do the formulas, not the WHY! Yes, it would be like taking 3 of the 13 parts. However, the real question is what is the value of each part? For an easier example, what is half of a dollar? You know it is 50cents or .50. Written as a fraction it is 50/100 or 50 divided by 100. What is 1/4 of a dollar? 25/100 or 25 divided by 100 = .25 1/10= .10, 2/10=.2 So, what does 1/13= ? It is 1 divided by 13 or 0.07692. So 1 slice of pizza would be slighltly less than 8% of the pizza. 3 slices would be 3/13 or 3 divided by 13= .2307 or about 23% of the pizza. Does that help? Quote Link to comment Share on other sites More sharing options...

wendyroo Posted January 28, 2013 Share Posted January 28, 2013 At its heart a fraction is just another way to express a quantity. It could be a whole number: 1 = 1/1 = 2/2 = 303/303 It could be a non-integer quantity more than one: 1.5 = 3/2 = 6/4 = 51/34 It could be a non-integer quantity less than one: .4 = 2/5 = 4/10 = 22/55 In order to find out what decimal quantity a fraction represents, the easiest, most reliable method is dividing. That is what a fraction means: the numerator divided by the denominator. If you look at the examples I provided above, you will see how the division works: 6 divided by 4 = 1.5, 22 divided by 55 = .4 3/13 does not divide out neatly, which is why it is more convenient to represent that quantity as a fraction as opposed to a repeating decimal (3/13 = .230769 repeating). Yes, 3/13 could be shown as cutting a pizza into 13 pieces and eating 3 of them. If you picture the pizza with a clock face over it, you can see that if it was divided into 12 pieces (like the numbers on a clock) then 3 of those pieces would equal 1/4 of the clock/pizza. But your pizza is divided into 13 pieces meaning that each pieces is a bit smaller than if it was divided into 12 pieces. 3 of your 13ths would be a bit less than 1/4. That is exactly what the division told us: 3/13 = .230769 repeating which is a bit less than .25. However, that is far from the only model that would accurately represent 3/13. In a previous comment the model of 3 pizzas divided by 13 was mentioned - that's fine too. If you had 3 pizza and you wanted to share among 13 people, one way to do that would be 4 people would each have to share 1 of the pizzas and the person who is left over would get to take a sliver from every person in such a way that he ended up with the same amount of pizza as all the other people. Well, if 4 people are sharing a pizza they would each get 1/4 of the pizza and then if the 13th person took a bit from each of them they would all end up with a little less than 1/4. Again, that is what the division told us: 3/13 = .230769 repeating. Another way to think about this is that 3/13 is the same as (1/13) * 3. In the one pizza example you divided one pizza by 13 and then "multiplied" your result by 3 pieces to see the quantity. In the 3 pizza example we started with 3, divided by 13 and our result was the quantity. Hope that helps. Wendy Quote Link to comment Share on other sites More sharing options...

HappyGrace Posted January 28, 2013 Author Share Posted January 28, 2013 Yes, thank you, this helps a lot. I think the 3 pizzas divided by 13 before screwed me up. It's just a bad time anyway here-totally questioning homeschooling and this was the icing on the cake :( Quote Link to comment Share on other sites More sharing options...

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