I must have found this idea on Pinterest somewhere…I would give credit if I remembered where, but it works so well! I love it–Factoring Rainbows! About 2 weeks ago I used this with the fifth graders who were struggling with simplifying fractions. Using this trick really helped them. Below you can see how it works.
![FactorRainbow](https://i2.wp.com/teacherblog.co/wp-content/uploads/2014/02/FactorRainbow.jpg?resize=448%2C336&ssl=1)
There is a rainbow for both the numerator and the denominator. The rainbows always start with 1 and the number itself on the first arch. Then each arch underneath progresses with the next largest factor. With the 15 rainbow, 2 was not a factor, so I skipped to 3. Three and 5 are factor pairs. I could then try the factor of 4, but the only other number that could be a factor would be 4 itself. I know 4 x 4 is 16, so that won’t make 15. Then I could move on to a factor of 5, but I know that 5 has already been used. When the factors repeat in the rainbow, then I know I have found all of the factors. To simplify fractions, circle the largest common number in both rainbows (GCF) and divide both the numerator and denominator by the largest common factor.
![FactorRainbow2](https://i2.wp.com/teacherblog.co/wp-content/uploads/2014/02/FactorRainbow2.jpg?resize=448%2C336&ssl=1)
Here is another example above. I factored both the numerator–16 and the denominator–18. I started the factor rainbow of 16 with an arch having the factor pair 1 and 16. Then I moved on to an arch with the factor pair 2 and 8. Three won’t equally divide into 16, so 3 is skipped. Next, I know 4 and 4 will multiply to make 16. Because these numbers repeat, I know the 16 factor rainbow is complete. The factor rainbow of 18 begins with the first arch’s factor pair 1 and 18. Next 2 and 9 are a factor pair, followed by 3 and 6. Then, I ask myself if 4 would be a factor. What about 5? Nope. So that brings me back to 6. I know that I have found all of the factor pairs because I have reached a repeating factor–6. Then I circle the greatest common factor of 2 and divide the numerator and denominator by 2.
If a fraction is already simplified, the fraction rainbows will help show this, too. The only thing that will be different is that the largest common factor will be a 1. Dividing by 1 doesn’t change the numerator or denominator obviously so the fraction is already simplified.
I hope using fraction rainbows will help your students as well.
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I just love this blog thank you