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Lesson 18  Section 4


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 7.   What does it mean to express a relationship between numbers in the language of ratio?
  It means to say only the ratio of the numbers, without naming the numbers themselves.

Example 1.   Joan earns $1600 a month, and pays $400 in rent.  Express that fact in the language of ratio.

Answer.  "A quarter of Joan's salary goes for rent."

That sentence, or one like it, expresses the ratio of $400 to $1600, of the part that goes for rent to the whole.  We are not concerned with the numbers themselves, but only their ratio.

Example 2.   In Jim's class there are 30 pupils, while in Jane's there are only 10.  Express that fact in the language of ratio.

Answer.  "In Jim's class there are three times as many as in Jane's."

This expresses the ratio of 30 pupils to 10.

Example 3.   In a class of 24 students, there were 16 B's.  Express that fact in the language of ratio.

Answer.  "Two thirds of the class got B."

This expresses the ratio of the part that got B to the whole number of students:  16 out of 24.  Their common divisor is 8.  8 goes into 16 two times and into 24 three times.  16 is two thirds of 24.

(Lesson 16, Question 4.)

Example 10.   This month's bill is $75, while last month's was only $30.  Express that fact in the language of ratio.

Answer.  "This month's bill is two and a half times last month's."

75 is equal to two times 30 (60) with a remainder of 15, which is half of 30.

75 = 60 + 15.

75 is two and a half times 30.

The student will hear this language, will read it, and should be able to understand it and speak it.

At this point, please "turn" the page and do some Problems.


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