## ← Proportions - Visualizing Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

1. Let's keep our same ratio and this time look at using proportion and a table.
2. So, the number of dimes to the number of quarters is still two to three. But
3. this time I have 10 dimes in my hand. How many quarters am I holding? We could
4. solve this problem by extending our table. I could keep adding two dimes and
5. three dimes in each case. So I'd have 8 dimes, 12 quarters, and 20 coins in
6. total. And then 10 dimes, 15 quarters, and 25 in total. So if I add 10 dimes,
7. then that means I have 15 quarters. But, maybe there was a different way to see
8. this. If I take two dimes and if I multiply it by 5, then I also have to
9. multiply my quarters by 5. The same is true for the number of coins. I would
10. have 5 times 5, which is 25. Ratios often have a multiplier. We take our
11. original ratio and multiply it by a number. So to get from 2 dimes to 10 dimes,
12. we multiply by 5. So to get a 3 quarters to 15 quarters we also multiply by 5.
13. The number of the objects continue to increase, so I can have an n multiplier,
14. any number, and this would be 2n. 3n and 5n. These expressions represent the
15. number of coins for our dimes, our quarters, and our total, depending on our
16. multiplier.