The image above shows a simple way of showing what we do when multiplying fractions. Multiply across the top (1x1=1), and then across the bottom (2x2=4). The circles show the equivalent of half OF a half.
Another way to multiply fractions is by using the area model of multiplication. For example,
I think the image explains it better than I could.
There is yet another way to figure out some problems. Swapping the top numbers, or the bottom numbers - but not from top to bottom or bottom to top. In the last problem, we could have had 3/3 x 2/4. That's actually 1 x 1/2, which is equivalent to 6/12.
This is what swapping looks like when put into action. This is the Commutative Property at work as well.
Next Step
Dividing Fractions! So.... Y'all probably know about flipping the second fraction and multiplying, and ya gotta use improper fractions... yada yada. Why in the world DO we flip a fraction? And why not the first fraction? Let's take a look.
4/5 divided by 3/8
If we take the typical route, we get 8x4 and 3x5. 32/15 which reduces to 2 2/15.
We'll come back.
What if I divide 3/5 by 1/5? You know it's 3. How do the 5's disappear? They don't. You're just dividing 3 by 1 and 5 by 5. 5 by 5 is 1, which can be ignored at the bottom of a fraction. Heeeyyyyy! Those were common denominators!
So what if I found a common denominator between 5 and 8 from the previous problem? 40. If I multiply 5 by 8, then I have to do the same to the 4. If I multiply 8 by 5, then I have to do the same to the 3. We get 32/40 divided by 15/40. If the 40's go to 1, then I'm left with 32/15. That's the same thing as we got above.
When you divide, you're asking how many groups of this number are in the other number. You may not know off the top of your head, but let's see an example.
Oh! They also divided across the top and bottom! That's another way to find easier answers. That all depends on both numbers being easily divided into one another though.
Think that's all... Hope you learned something!
You did a nice job of going through the step by step process of multiplying across the top and bottom in multiplication of fractions as well as displaying the area model, and the commutative property. All three of these ways are really important in order to solve different types of multiplication problems. If the fraction is not top heavy, I would just multiply across the top and bottom, but if it were a mixed number I would use the area model. You also explained the division of multiplication very well and included really nice visuals to help the reader understand the concepts of multiplying and dividing fractions. Good job on your post!!
ReplyDeleteGreat job! This blog does a really great job of explaining thoroughly the process of multiplying fractions. I like the fact that you used images, but the inconsistency on formatting was just a little confusing, but I do appreciated the aid! Your opening example was really funny and relatable, and it helped hook me into the blog to keep reading, and I ended up gaining a clearer understanding of the topic. Great blog thank you!
ReplyDeleteNyna,
ReplyDeleteI think your blog is really great. The way you presented the information made it very easy to read and follow. It wasn't just another blog entry about fractions- but you made it interesting and added some humor and some of your personality into it. The images you used were really helpful and pulled your explanations and information together. Good job!
I really like how you presented all of the information in your blog. The way that you wrote it like you were having a conversation was also nice. I really liked the second picture you included as well. I really like the method of making a square and shading in the pieces and I think it is a very easy method to understand. I also liked the picture you used for division. It was good that you included that having 5/5 is the same as 10/10 and how to make them.
ReplyDeleteThis is a great blog!! Your pictures and descriptions are well put and easy to understand. I think the best picture is the first one. It is good because it is easy to understand and very simple. Sometimes fractions are hard to understand and putting them into context. I also really liked the picture and description of the number swapping. This was a fun and different way to do a problem. Your blog this week was great! Good job.
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