Adding & Subtracting MIXED Fractions!

Just when you thought we were done with the adding and subtracting fraction lesson...haha. There's always more to learn! This week I wanted to focus on how to add and subtract mixed fractions. It's not exactly the same as adding/subtracting regular fractions, and the teaching methods are important here since this can get a little tricky.

To begin, I think it makes sense to get some general definitions out of the way. A mixed fraction is essentially just a whole number and a fraction combined, such as 1 3/4. If you think about it in terms of a pizza pie, it would be one whole pizza pie, and 3/4ths of another pizza pie. So...it would look like this:

To make it easier to add and/or subtract fractions, the first step is to convert the mixed fraction into an improper fraction. Definition time! An improper fraction has a numerator that is larger than or equal to the denominator. So, 1 3/4 would actually be 7/4...because the whole number one is equivalent to 4/4 and you still have 3/4ths of the second pie. So if you add both numerators, you get 7, and if your denominator is 4, then your improper fraction equals 7/4.

So, let's try adding mixed fractions now! Here are the steps:

1) Convert the mixed fraction to an improper fraction
2) Add or subtract the fraction
3) Convert the answer back into a mixed fraction

See below for an example from MathisFun.com:

Subtracting mixed fractions is pretty much the same, but here's a helpful example:

Next week, we'll focus on multiplying and dividing mixed fractions!

Simplifying Fractions

This week, I am focusing on simplifying fractions. This is an important step whenever you are working with fractions, and is used for multiple operations. Simplifying fractions is pretty straightforward, but can be difficult to explain to elementary students. Therefore, having a clear and concise way to share this with elementary students is important.

While researching online, I came across several great resources. I found this particular resource from MathIsFun to be very straightforward, visual and helpful. It explains that the definition of simplifying fractions is to reduce the fraction -- or make it as simple as possible. For example, 4/8 can be simplified to 1/2. Using a pizza pie is a great way to illustrate this to young students, which is exactly what MathIsFun did. In the below example, they take a pizza pie and split it up into 8 sections, then highlight four of those sections to illustrate 4/8. Next, they show that 4/8 is equivalent to 2/4, by taking the same pizza pie and now splitting it up into 4 pieces, then highlighting 2 slices. Lastly, they show that 2/4 is equivalent to 1/2, by taking the same pizza pie, splitting it into 2 pieces, and then highlighting one piece.

This illustration is a great example to use when explaining this concept to elementary students because it is extremely visual. Students can see that visually, 4/8, 2/4 and 1/2 all look the same. By using an illustration such as the one above, students will also understand that even though the fractions look different, they take up the same amount of space on the pizza pie, and therefore are equal.

The next method that MathIsFun uses is the "greatest common factor" method, which is typically what I use when simplifying fractions. For this method, the student should think about the greatest factor that goes into both the numerator and denominator. So, let's take the example above. If we have 4/8, a common factor that goes into both numbers is 2. 4/2=2, and 8/2=4, making your new fraction 2/4. But...is that the GREATEST common factor? NO! Yes, it is one factor that goes into both numbers, but then you're left having to simplify again, because 2/4 can be simplified further by dividing by 2 again, resulting in a simplified fraction of 1/2.

So let's try simplifying the same fraction again by the GREATEST common factor this time. 4 goes into both 4 and 8, and there is no great number that goes into both of these numbers, meaning 4 is the GREATEST common factor. 4/4=1, and 8/4=2, making your new fraction 1/2, just like the pizza pie above.

See below for another example:

Next week, I will begin focusing on mixed fractions. These are slightly more complicated to work with, but elementary students are expected to add, subtract, multiply and divide mixed fractions as part of the core curriculum as well. Tune in next week!

Dividing Fractions

This week, I'm focusing on how to divide fractions. Dividing fractions is probably the trickiest topic I've focused on so far -- and it took me a few minutes to refresh my memory. After looking at a few websites and watching a few videos on YouTube, I figured out how to quickly divide fractions, as well as how to break it down into simple steps for elementary students to follow. While researching various resources online, I came across this video, which I found to be very helpful: Dividing Fractions

After watching the video and looking at online resources, I know it's easiest to divide fractions by focusing on the "keep, change, flip" method. This means:

1) Keep the first fraction as is
2) Change the operation from division to multiplication
3) Flip the last fraction so the numerator becomes the denominator, and the denominator becomes the numerator. For example, 3/5 would then become 5/3.

After following the steps above, you can continue by simply multiplying the fractions and then simplifying at the end. So...let's try an example!

3/4 divided by 5/8 = ___

The first step is to keep the first fraction as is. Easy. 3/4 stays the same. The next step is to change the operation from division to multiplication. The last step is to flip the second fraction. After following all of these steps, my new equation should read: 3/4 x 8/5 -- and now it's the same as multiplying fractions!

3x8=24
4x5=20
24/20 = 1 1/5

This is a problem set I found while googling some worksheets for dividing fractions. This example shows the "keep, change, flip" method nicely in red.

Just like we did above in our own example, this snapshot shows the different steps required to divide fractions. It helps to write it out the same way as it's done in the above picture because it ensures that you aren't missing any important steps. In the first example of 1/4 divided by 2/3, we can see how the "keep, change, flip" method is being used. The first fraction looks the same in red, the division sign is changed to multiplication in red, and the second fraction of 2/3 is flipped to 3/2 in red. After these steps are completed, all that's left to do is to multiply the fraction, and simplify if necessary.

Both of the aforementioned resources helped me figure how to divide fractions again with ease! Every week, I continue to learn that fractions do not need to be so scary for students. It's all about approaching the topic with visual representations and simple steps.

Multiplying Fractions

This week, I wanted to focus on multiplying fractions to continue with my fraction theme. Multiplying fractions, although not super difficult, does require a bit of practice to get back into the hang of how to do it. That was the case for me, at least. When researching different ways to learn, as well as teach, this subject - I came across this website: https://www.mathsisfun.com/fractions_multiplication.html

I found this website to be very useful, because it really broke down the different steps in a clear and concise way. First, the link provides three steps in order to begin the process of multiplying fractions. These steps are:

1) Multiply the top numbers (numerators)
2) Multiply the bottom numbers (denominators)
3) Simplify the fraction (if needed)

Sounds easy enough, right?!

So - lets take 2/3 x 3/5 as an example. If I follow the aforementioned steps, I would first need to multiply the numerators (2 x 3 = 6); then the denominators (3 x 5 =15). The answer would be 6/15. Then to simplify this, I would need to think of a factor that goes into both numbers, and how many times that factor goes into the number. For 6/15, a common factor is 3. 3 goes into 6 two times (3 x 2 =6), and 3 goes into 15 five times (3 x 5 =15). Simplified, the new answer would be 2/5 (both the numerator and denominator were divided by the common factor of 3 to get this result).

The "Math is Fun" website provided these graphic step-by-step directions, which I found to be very useful when thinking about how to explain this concept to elementary students. The website also illustrated this using a "pizza pie" fraction, which I loved! Who doesn't love pizza?!?!

Pizza Pie & Fractions:

Next week, I think I'll focus on dividing fractions. I want to remind myself *how* to divide fractions - but perhaps more importantly, effective ways to *teach* students how to divide fractions. Math doesn't need to be so scary for students if it's taught in a fun and approachable way. In writing these blog posts, that has been the biggest takeaway for me thus far.