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Lesson 17 Section 2 ## PROPORTIONSWhat is taught in most textbooks these days as ratio and proportion, is not. It is algebra. The student is taught to represent a ratio as a fraction, write the letter A ratio requires understanding. It has meanng and is not merely symbolic. Because of that, the topic of ratio and proportion is educational. |
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Example 1. 5 is to 15 as 8 is to 24. That is a proportion because 5 is the third part of 15, just as 8 is the third part of 24. (Lesson 15.) A proportion involves four numbers -- four terms. To explain Example 2. Why is this a proportion? 16 is to 2 as 80 is to 10.
Example 3. Why is this a proportion? 10 is to 15 as 2 is to 3.
Example 4. Complete this proportion: 8 is to 32 as 9 is to ? The 1st term is to the 2nd as the 3rd is to the 4th. Example 5. Complete this proportion: 27 is to 3 as ? is to 5 If the student will speak and use sentences, the answer will be clear. Example 6. In each item below, what ratio has ( a) b)
a) Since 1 is the sixth part of 6, then b) Since 10 is ten times 1, then Symbolic representation The following is the traditional way to symbolize a proportion: 1 : 2 = 4 : 8. "1 is to 2 as 4 is to 8." Why is this a proportion? Because 1 is half of 2, and 4 is half of 8. Again, a proportion has 4 numbers -- 4 terms. The 1st, the 2nd, the 3rd, the 4th. In any problem, we are typically asked to find the 4th, which is called the 4th proportional. Example 7. Read this proportion, and complete it: 8 : 2 = 20 : ?
Now, what ratio has 8 to 2? 8 is four times 2. And 20 is four times We say that we have Example 8. Read this proportion and complete it: 7 : 21 = 4 : ?
What ratio has 7 to 21? 7 is the third part of 21. And 4 is the third part of Example 9. Complete this proportion: 2 : 3 = ? : 12
Now, 2 is two thirds of 3. What number is two thirds of 12? " 2 : 3 = In the next lesson we will see how to solve a proportion that looks like this: 5 : 7 = 20 : ?
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