Decomposing Fractions with Number Bonds

All right, today we are going to talk about number bonds and number bonds just a quick review. Say I have the number ten, and I say, okay, I need you to break it down or decompose it into two other numbers. You'd say, okay, well, I can add 6 plus four, and that will get me ten. Or I could do ten and do a multiplication. Two times 5, that would also get me ten. By knowing truly had a decomposed numbers, the students will understand a better number sense. And actually understand why they do certain strategies in solving different math problems. We're going to use this number bond concept today as with a fraction. So for example, I'm going to show you this particular picture and we're going to represent this one whole as a fraction with number bonds. And fractions can be decomposed as well. So by looking at this and it's also important to know note that students are not always going to have a nice clean rectangle or a circle or a triangle. They might have some weird irregular shape like this where they've got to figure out the fraction. So the question is, how much is shaded? Well, I know that I've got one, two, three, four, 5, 6, 7, 8, 9, ten, 11, one, two, three, four, 5, 6, 7, 8, 9, ten, 11 total equal parts. So that's going to be my denominator. My bottom number. My shaded ones are one, two, three, four, 5. So right now I've got 5 elevenths showing. 5 elevenths of this actual picture is shaded. So I'm going to go ahead and say, okay, well, that's the same thing as taking one whole, this is what this is, a one whole picture. And I'm going to decompose it into fractions. I know that both of my fractions are going to have a denominator of 11 because they both had 11 equal parts, right? How many was shaded? One, two, three, four, 5, so 5 elevenths is shaded. How many was not shaded? One, two, three, four, 5, 6. 6, 11. Now, can I add 5? Plus 6 elevenths. If I add 5 and 6 together, that will get me 11 elevenths. Which is the same thing. As one whole. We want them to understand if you have the same number in the numerator and the denominator, that is also equal to one. One hull is the same thing as 5 elevenths plus 6 elevenths equals 11 elevenths back to yes. It does equal one whole.