![]() To do this, we can draw a horizontal line to show 1/2.īut we only want half of 1/3, not the whole thing. So then multiplying 1/3 x 1/2 means, find 1/2 of 1/3. Confused? That’s why visual models are so helpful! Here’s a picture of thirds: In other words, you’re looking for part of the part of the whole. If problem says, 1/3 x 1/2, it means, “What is 1/2 of a third?” The same is true when you multiply fractions by fractions. Using an Area Model to Multiply Fractionsīefore beginning to multiply fractions, begin by reviewing whole numbers multiplied by fractions.įor example, 8 x 1/2 is asking, “What is half of 8?” In other words, the answer will only be part of the whole (8), not more. In the example above, if we were to add them (rather than merely compare them) the final answer would be 11/15. Once they’ve done this, they can add the fractions easily, because they now have a common denominator. ![]() Then overlay the models to find a new, common “part” and rewrite each fraction. They can set up area models for each fraction just as we did before to compare. ![]() To start, kids need each fraction to have the same number of parts (again, a “like denominator”). Using an area model is also helpful in adding and subtracting fractions with unlike denominators. Using an Area Model to Add/Subtract Fractions Looking then at the 2/5, we see that there are 6/15 in that part. We can now look at the model and ask, how many fifteenths is 1/3? We count and see there are 5/15 in the colored 1/3 part. Now my rectangle is divided into 15 parts. I can then overlay the two to get an area divided into smaller pieces. You might be thinking, “Ok, how does that help? I still can’t see which one is bigger…” Hang with me. Notice I’ve drawn an area model for each fraction, but one vertically divided and the other horizontally divided. In order to compare, we need a common size for the parts (i.e. We can’t compare these, because they are not equal sized parts (thirds are not the same as fifths). The first is divided equally with vertical lines, and the second with horizontal lines. If students are trying to compare or order fractions with unlike denominators, start by drawing an area model for each fraction. How is this helpful? Let’s explore: Using an Area Model to Compare Fractions with Unlike Denominators An easy way to do this is to use graph paper.įor example, here’s an area model of the fraction 3/5: This is an important component of developing fraction sense.īut what does that mean? What does an area model look like?Īn area model represents a fraction as a rectangle, divided into equal parts. Read our full disclosure here.* Creating Area Models of FractionsĪn area model is a great visual tool because it can be used to make sense of virtually any fraction problem. * Please Note: This post contains affiliate links which help support the work of this site. Today, I want to share a powerful visual, which students can use to compare, add, subtract, multiply and divide fractions: area models. Instead, the focus should be on deep understanding, using concrete, visual models. Learning about fractions doesn’t have to be scary, and it doesn’t have to mean hours of pencil and paper computations. As we continue our series on developing fraction sense, hopefully by now you are feeling a little more confident and equipped.
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