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← Why Simplify - Visualizing Algebra

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Showing Revision 3 created 05/25/2016 by Udacity Robot.

  1. So you're probably saying so what? Why
    would I want to reduce factors first?
  2. Well, what if I wanted to find 3/10*5/12?
    I could draw a diagram of the candy bar
  3. and split up the pieces before it. I could
    split up the 10's and then 12's. But
  4. that's kind of a lot of work and I know I
    just really need to multiply these 2
  5. fractions. Multiplying these two fractions
    together I get 15/120. But now
  6. I have to figure out if I can simplify
    this, and how to simplify this fraction.
  7. This can be frustrating working with large
    numbers, so let's make our work easier and
  8. simplify our fractions first. I know 10
    can be written as 2*5, and 12 can be
  9. written as 3*4. Remember any number
    divided by itself makes 1. Like 4/4 makes
  10. 1, 5/5 makes 1. It doesn't work for zero,
    but we should keep this in mind when we're
  11. simplifying. Here I have 3/3 so that makes
    1 and 5/5, so that also makes 1. Now I'll
  12. just multiply my numerators. So I have
    1 times 1, which is 1 and I have 2 times 1 times 1 times 4 or I
  13. have 2 times 1 times 1 times 4.
    Which I know that's just really 2*4 or 8.
  14. So 15/120 is really the same thing as
    1/8th. I am showing you this longer method
  15. so you can really see why we can cancel
    factors. You can do ahead of the time and
  16. this is what it would look like. I know 5
    and 10 share a common factor of 5, so I
  17. can divide them both by 5, 5/5 makes 1,
    10/5 makes 2. 3 and 12 also share a factor
  18. of 3, so 3/3 makes 1, and 12/3 makes 4.
    Now, I multiply, just like before, 1*1 is
  19. 1, and 2*4 is 8. So either way I do it
    this long way, or this shorter way with
  20. cross-cancelling, I get 1/8.