What does it mean to divide fractions? To divide fractions, you find out how many groups of a particular fraction can fit into another fraction or a whole number. For example: 10÷1/2. This is asking you "how many halves can fit into 10?". To do this, we can 'keep, change, and flip':
1. We keep the dividend the same.
2. We change the division sign into multiplication. We do this because multiplying by a fraction is a lot much easier.
3. We then "flip" the divisor by it's reciprocal. In the end, the number sentence comes out as this: 10 x 2/1. From there, we can do simple multiplication. 10 x 2/1 is 20/1 = 20.
Here is a visual understanding:
Let's try another problem: There are 6 pies that we made for the party. Each person gets to have 2/3 of pie. How many people can get 2/3 of pie?
I drew a model and a numbers sentence to show how fractions work. For the model, I drew six rectangles to represent the 6 pies, and colored in 2/3 of them to show how much of a pie each person would eat. After coloring in the pies, I saw some pieces of pie left over. So, I grouped those other 1/3's of pie into 2/3 with the other pie pieces. I then counted how many people could eat them. 9 people could each eat 2/3 of pie.
For the number sentence, I first wrote the problem out using numbers.
Then I wrote down the algorithm to find the answer using reciprocals. 6 x 3/2 = 18/2 = 9.
To understand how reciprocals work, we need to look at their relationship between one another. If we look at 1/2 and find the reciprocal 2/1, and multiply them, you get 2/2 or 1. This works for every single fraction. Another example: 5/6 x 6/5 is 30/30 = 1. I know that reciprocals work because dividing by 1/2 is the same as multiplying by 2/1, its reciprocal. So, it always comes out as it's reciprocal. We would write the relationship in this number sentence: