Question

4. 13, 9, 12 are in proportion, find
Short Answer Que
2. e. 8.). 10 in portion? Give reason is support of our answer
3.1.5. 12. 15 are in proportion are 6.7 11.15 som proportion?
5. 113, and 27 are in continuous proportion, mean proportion
6. Give an example to show that numbers main in proportions, their means are interchanged
7. Give an example to show that numbers remain in proportion. If their extremes are interchanged​

Answer 1

Step-by-step explanation:

Euclid, VII. 13.)

Example 1.   1 : 2 = 5 : 10.

(1 is half of 2;  5 is half of 10.)

Alternately:

1 : 5 = 2 : 10

(1 is a fifth of 5;  2 is a fifth of 10.)

Example 2.   

 Directly :

12 : 36 = 2 : 6.   (Why?)

 Alternately:

12 : 2 = 36 = 6.   (Why?)

Example 3.   Complete this proportion:

5 : 7 = 20 : ?

If we look directly at the ratio of 5 to 7, it is not obvious.  But if we look alternately, we see that 5 is a fourth of 20:

5 : 7 = 20 : 28.

And 7 is a fourth of 28.

If we cannot solve a proportion directly, then we can solve it alternately.

Example 4.  The theorem of the same multiple.   Complete this proportion:

4 : 5 = 12 : ?

Solution.  4 is a third of 12 -- or we could say that 4 has been multiplied by 3.  Therefore, 5 also must be multiplied by 3:

4 : 5 = 12 : 15.



As 4 is to 5, so three 4's are to three 5's.

In fact, as 4 is to 5, so any number of 4's are to an equal number of 5's.

That is called the theorem of the same multiple.  It follows directly from the theorem of the alternate proportion.