Lesson 17 Section 2 ## PROPORTIONS |
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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 We will let the following signify a proportion:
Why is this a proportion? Because 1 is half of 2, and 4 is half of 8. (Can you be innocent and make-believe you never heard of a "fraction"? Fractions we will see (Lesson 20) are based on ratios, not the other way around.) Example 7. Read this proportion, and complete it:
Now, what ratio has 8 to 2? 8 is four times 2. And 20 is four times We say that we have What is taught in most textbooks these days as "ratio and proportion," is not. The student is taught to write the letter A ratio is a relationship we can express in words. To express it requires understanding, and because of that the topic of ratio and proportion is educational. Example 8. Complete this proportion:
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:
Now, 2 is two thirds of 3. What number is two thirds of 12? " In the next lesson we will see how to solve a proportion that looks like this:
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