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. 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? "3 goes into 12 four times. Four times 2 is 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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