Kilometer – Visualizing Algebra

If you said 10, nice work. This is a little bit tricky, so let’s walk through how to actually do this. I’m going to show you two ways to find the common denominator. The first way is listing out the multiples. I have 5 for one denominator, and I have 10 for the other. I’m going to start by listing out the multiples of 5. I have 5, then 10, then 15, 20, and so on. To get to the next multiple, I just add 5. For 10, I can list out its multiples as well. 10, 20, 30, 40, and 50. And it keeps going. To find the denominator, I want the lowest number that both 5 and 10 go into. When I think about the lowest number they both go into. I see that it’s 10. So I know I’m going to need to split this bar into tenths, and this one into 10ths. Luckily, this one’s already in tenths. Another way to find the common denominator is to find the factors of 5 and 10. I’m going to use a factor tree. I know the common factors for 5 and 10 are 5. So I put that in the middle. The other factors are 5, or 5 and 1. Because 5 times 1 makes 5. The other factor of 10 has to be 2, because 5 times 2 makes 10. If I multiply all these numbers together, 1 times 5 times 2, I get 10. Either way, I can still find the common denominator.

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