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← An Easier Problem - Visualizing Algebra

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Showing Revision 3 created 05/24/2016 by Udacity Robot.

  1. Lets try answering an easier form of the problem. This might help us think about
  2. what we should do. How many batches of brownies could you bake if a recipe
  3. requires 1/2 of a cup of sugar and you have one cup of sugar at home? This seems
  4. a little bit easier. This square is going to represent my one cup of sugar. I
  5. know 1/2 of a cup of sugar will make one batch of brownies. So I'm going to fill
  6. up 1/2 of my cup and make one batch of brownies. So here's a half cup of sugar
  7. and I know I made one batch of brownies. If I use another half cup of sugar, I
  8. know I'll make another batch of brownies. Now I've used my one whole cup of
  9. sugar and I don't have any sugar left at home. Well, I made two batches of
  10. brownies. Let's try this with some math. I have one cup of sugar. And I wondered
  11. how many times did 1/2 go into it? I knew I was able to make 2 batches of
  12. brownies. So 1 divided by a 1/2 must be 2. Remember, when we divide by a number,
  13. we can actually multiply by the reciporical. We learned that from before. So I
  14. could change this to look like 1 times 2 over 1. Well, remember, I could just
  15. put any number over 1. And then, multiply fractions like before. 1 times 2 is 2,
  16. and 1 times 1 is 1. 2 for 1 is just 2. Let's change this problem a little bit
  17. and see what we can find out. What if instead a recipe called for 1/3 a cup of
  18. sugar? I know if I use a 3rd cup of sugar I'll make one batch of brownies. If I
  19. use another 1/3 cup of sugar, I'll make another batch of brownies and if I use
  20. my last 1/3 cup of sugar I'll make one more batch of brownies. So let's put this
  21. with some math. I was wondering how many times does 1/3 go into 1 so I did 1
  22. divided by 1/3. I know that for every 1/3 cup of sugar I get one batch of
  23. brownies so I should get three batches. Remember when I divide by a number it's
  24. the same thing as multiply by the reciprocal. I could change this to
  25. multiplication 1 times 3 over 1. I know 1 is just 1 over 1 and now I can
  26. multiply these fractions together. 1 times 3 is 3 and 1 times 1 is 1, I get 3
  27. over 1, 3 divided by 1 is 3 batches. I hope you're starting to see a pattern.
  28. Let's see if you can figure this one out.