What does it mean to divide a fraction by another fraction? During a class activity involving the division of 2/8 by 3/4, two 6th graders realized 1/3 of 3/4 would fit inside 2/8, meaning 2/8 ÷ 3/4 = 1/3. WOW!! That was some heavy thinking. Does it make sense to you?? Incorporated into this discussion was an introduction to multiplying by the reciprocal. Here are what some students wrote about this activity…
Allie:
The equation 2/8 divided by 3/4 is asking how many times 3/4 can fit into 2/8.
Danya:
When you are dividing fractions by fractions, such as 2/8 ÷ 3/4, 3/4 can’t go into 2/8 one whole time, so you know your answer will be less than one whole. You can split one whole into 8 pieces and make groups of 2 within your 8 pieces. The are three groups of 2 pieces in your whole (3/4). Only 1/3 of 3/4 can fit into 2/8.
Ben:
For the problem 2/8 ÷ 3/4, you would have a picture of a group of 8 pieces and a group of 4 pieces and you are trying to find how much of the 3/4 can fit into 2/8. Only 1/3 of the 3/4 can fit into 2/8.
Emily:
In math we learned how to divide by fractions when the thing you want to divide is smaller than how many pieces you’re going to divide it into. To find, for example, 4/16 ÷ 6/8 you need to make the denominator (6/8) easier to divide with. You can multiply 6/8 x 8/6 = 48/48 = 1. You have to do the same for 4/16 so 4/16 x 8/6 = 32/96. Now you have 32/96 ÷ 1 which is the same as 32/96. After that you have to simplify. 32/96 = 1/3
Myles:
The way you divide fractions is that when you divide it you have to do the reciprocal which in this case is multiplying. A reciprocal is like the inverse operation.
Matt:
What we learned to do in math today was how to divide a fraction by a fraction. The funny part about it was we ended up multiplying when we were dividing!
Cassandra:
In math today we had to understand why 2/8 ÷ 3/4 is like multiplying 2/8 x 4/3. You can take a shape and make 8ths, then shade in 2/8, then make another shape and shade in 3/4, since you are trying to find how many times 3/4 goes into 2/8. I really understood why it works and how it gets there. The part that we visualized really helped. I finally understand this.
nice job. I figured out the triplet pattern with the fractions in 1st grade…but I was never able to find an example of it oddly. Here it is.
Hey Aaron – that’s really cool! I’m glad to hear from you and that you are keeping up with the blog!
Why did you put mine up there? There is only 6 or 7 up on the blog. Why choose mine?
I like how you explained the process of dividing fractions Cass! Great way to visualize fractions, nice work
Years ago before TCPS started, I used to tutor students in math. Whether the students were in 2nd grade or high school, usually the biggest issue was that they did not understand the “whys” in math. The study of fractions is a perfect example. Great math writing!
man you smart you can divided