What Is 4 Divided By 1/3 – Division of fractions is one of the topics I often have to work on. It’s definitely one of those “don’t use it, lose it” situations for me. So this post comes from me to refresh my memory on dividing fractions. But why now? This tweet:
After sharing Howie Hua’s tweet in our Visual Math Facebook group, I remembered dividing fractions. And full disclosure, I never thought of splitting as a thing to do. I’m 42 years old and have a master’s degree in math teaching and it never occurred to me. I usually don’t worry too much about how I come across, but I was grateful that the other teachers in the group acknowledged that it never crossed their minds either. It gave us all a chance to learn something new together and I love it when that happens. In a graduate class, we had to write articles about various algorithms taught in math and why they work. Fraction division was one of those algorithms, and after more than a few “repeats” written at the top of my paper, I finally submitted work that could actually be graded. Needless to say, it was a difficult class. Keep it, change it, flip it. Why? I hope to answer with 3 examples in this post. Example 1: (2/3)÷(1/2)
What Is 4 Divided By 1/3
Division asks, “How many of these will fit?” For example, for 10 divided by 2, “How many 2s go into 10?” We ask the same thing when dividing fractions, but it’s a little harder to see. In our first example, (2/3)÷(1/2), we’re asking, “How much 1/2 can go into 2/3?” Answering this question would be easier if our fractions were divided into the same number of parts. Creating a common denominator will make it easier to figure out how many will fit. By creating a common denominator of 6, we can see that our 3 green bars fit into the space occupied by our blue bars. There is room for one more! So all the green bars (a whole) go into the blue space and 3 more bars (1/3). So (2/3)÷(1/2) = 1 and 1/3. Here is a video explanation:
What Is 3x^4 + 2x^3
Connection to “Keep-Change-Flip”: When I posted this video to my Instagram feed, a teacher pressured me to connect to “keep-Change-Flip” (ahem, multiply reciprocal) with the standard algorithm. As with anything in mathematics, there is more than one good way to make a connection. Personally, I like to go back to whole numbers:
If you want to apply the algorithm directly to this fraction example, do this: We see that the numerator of the second fraction becomes the denominator of our answer. This is because we are asking, “How much will the numerator of the second fraction (columns) fit into the numerator of the first fraction [after forming a common denominator]?”
Example 2: (1/2)÷(2/3) This example is like Example 1, we just changed the placement of the fractions, which is fun because it emphasizes that the division is not the common denominator.
In our second example, (1/2)÷(2/3), we ask, “How many 2/3s go into 1/2?” By creating a common denominator, we easily find that 3 of the 4 blue bars fit into the space occupied by the green bars. So (1/2)÷(2/3)=(3/4).
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Example 3: (4/5)÷(2/3) Sometimes creating a common denominator with simple columns can be too complicated to be useful, so we can create a grid instead. We can always do this, I prefer columns when possible because I find them more visible.
With (4/5)÷(2/3) our common denominator is 15, so we can create a grid with 15 spaces. 4/5 takes up 12 places and 2/3 takes up 10 places. So all of our 2/3 goes into 4/5 plus another 2. Then we see that (4/5)÷(2/3) = 1 and 2/10. Here is a video that explains this example:
I also just created this set of fraction division problem cards to go along with this post. The cards can be laminated and used with a dry marker to make them reusable.
And for a fun review, this digital math escape room review. In the number puzzle. 5 students must multiply and divide fractions. Students get 4 answers and then enter the 4 letter code into the verified answer Google form to unlock the puzzle. Fraction review digital math escape room Hope this post was helpful! -Shana McKay. Constructed Math and Science Dividing Fractions can be very difficult for many students. It is difficult to imagine dividing a fraction into other groups of fractions. To divide fractions, many students memorize the keep-change-invert algorithm without knowing why it works.
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Without a conceptual understanding of fraction division, students encounter problems (especially word problems) that require dividing by non-unit fractions such as 2/3 or 3/4, or problems with a divisor greater than the divisor. the dividend
In sixth grade, when students have to divide mixed numbers, they often rely on the multi-step keep-change-flip method, which is difficult to remember and understand.
You can help your students understand how to divide fractions by using fraction lists to move them around. Manipulatives and visual representations are evidence-based strategies that help learn new math concepts. Lists of fractions can help students not only understand the concept of dividing fractions, but literally see how to solve these problems without having to do any calculations.
Collect and research materials. Give each student or pair of students a set of fraction lists. Have students cut each list into unit fractions (with a numerator of 1). For students who struggle with fine motor skills, consider multiple cut sets. You can also create a variety of laminate or cardboard kits for students.
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After cutting each strip into pieces, ask students to put each strip back together so that they have a complete set that matches the one on the button. Give students a copy of the printout or project an image of the printout so they have a visual model to reference.
When students have organized all the lists, they introduce the whole concept again. Remind students that when talking about fractions, visual representation 1 and the words “whole” are often interchangeable. Say, “We have a whole piece at the top of our set.” Then ask students what they notice about the lines underneath the whole piece. An example model. One might say, “I noticed that every fraction line is the same size.” Have students share what they notice with a partner. Then ask a few students to share with the whole class. Remind students of previous lessons where they worked on dividing whole numbers by fractions.
1. Check the fraction division of a whole number. Ask the students to put the whole list 1 on the table. Students place enough 1/4 strips under this strip to equal the size of a whole. Write the equation 1 ÷ 1/4 = 4 on the board and ask students how they know this is true. Students will have to refer to the lists in front of them to explain the answer.
Review all the common ways students can explain their answers, giving the following examples both visually and verbally:
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2. Explain how to use fraction lists to divide a fraction by a fraction. Use the “I do, we do, you do” model (also called the gradual release teaching model) to guide students through the process of using lists.
I do: Explain and model using lists. Say: “Now we can use a similar strategy to solve division problems with two fractions. Let’s look at 1/2 ÷ 1/6. I started by putting the strap 1/2 up like this. I then placed as many 1/6 strips as I could underneath to match the 1/2 strips. We see that it takes one, two, three 1/6 strips to match the 1/2 strip. So I can conclude that 1/2 ÷ 1/6 = 3, or 1/6 goes into three times 1/2.
We do it: we guide students through testing with you. Say: “Now let’s try it together. Start again with 1/2. I’ll put 1/2 on top. Do the same.” Pattern with 1/2 strip above. “This time divide 1/2 by 1/8. We’ll put as many 1/8 lists as possible to match the 1/2 list.” and then walk around to help students who may need help. Ask students who can set it up correctly to write a division and solution problem.
When everyone has finished, discuss the answer as a class. Write a sentence with the division number for students who did not get the answer right. Describe the solution in several ways.
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You do: Choose three division problems using unit fractions for both the divisor and the dividend. Tell the students that they will do it themselves. Say: “Try a few more problems on your own or with your partner. Don’t forget to write a division sentence with the solution when setting up
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