RATIO AND PROPORTION

PROBLEMS (3)

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19.  1 the only common divisor.  Each number says its name.

19.  What ratio has

a)  2 to 3?   Two thirds.   b)  3 to 4?   Three fourths.
 
c)  5 to 6?   Five sixths.   d)  2 to 9?   Two ninths.
 
e)  1 to 5?   One fifth.   f)  2 to 5?   Two fifths.
 
g)  3 to 5?   Three fifths.   h)  4 to 5?   Four fifths.

10.  Common divisor; Lowest terms.   Express each ratio with the
10.  lowest terms.

a)  6 to 8?   Three fourths.   b)  12 to 18?   Two thirds.
 
c)  10 to 25?   Two fifths.   d)  9 to 24?   Three eighths.
 
e)  10 to 15?   Two thirds.   f)  15 to 20?   Three fourths.
 
g)  20 to 30?   Two thirds.   h)  6 to 10?   Three fifths.
 
i)  15 to 24?   Five eighths.   j)  90 to 100?   Nine tenths.
 
k)  14 to 35?   Two fifths.   l)  15 to 40?   Three eighths.
 
m)  72 to 81?   Eight ninths.   n)  16 to 20?   Four fifths.
 
o)  21 to 70?   Three tenths.   p)  40 to 100   Two fifths.
 
q)  80 to 100?   Four fifths.   r)  1500 to 3500   Three sevenths.

11.  Complete the following with the smallest numbers -- the lowest
11.  terms -- which have that ratio.

11.  a)  If a is half of b, then a is to b as 1 is to 2.

11.  b)  If a is a third of b, then a is to b as 1 is to 3.

11.  c)  If a is four times b, then a is to b as 4 is to 1.

11.  d)  If a is ten times b, then a is to b as 10 is to 1.

11.  e)  If a is two thirds of b, then a is to b as 2 is to 3.

11.  f)  If a is five eighths of b, then a is to b as 5 is to 8.

11.  g)  If a is nine tenths of b, then a is to b as 9 is to 10.

12.  Complete the following with the smallest numbers -- the lowest
12.  terms -- which have that ratio.

(Compare Section 1, Problems 2 and 3.)

12.  a)  If a is 50% of b, then a is to b as 1 is to 2.

12.  b)  If a is a 25% of b, then a is to b as 1 is to 4.

12.  c)  If a is 75% of b, then a is to b as 3 is to 4.

12.  d)  If a is 200% of b, then a is to b as 2 is to 1.

12.  e)  If a is 300% of b, then a is to b as 3 is to 1.

12.  f)  If a is 20% of b, then a is to b as 1 is to 5.

12.  g)  If a is 40% of b, then a is to b as 2 is to 5.

  h)   If a is 33 1
3
% of b, then a is to b as 1 is to 3.
 
   (Lesson 16, Question 5.)
 
  i)   If a is 66 2
3
% of b, then a is to b as 2 is to 3.

13.  Numbers that end in the same number of 0's.

If two numbers end in the same number of 0's, then we may ignore those 0's

and take the ratio of what remains.

(Because when we do that, we have divided both terms by the same power of 10.  The quotients will then have the same ratio as the numbers divided.)

What ratio has

      a)  50 to 150?  One third.   b)  500 to 1500?  One third.
      c)  5000 to 6000?  Five sixths.   d)  70 to 280?   One fourth.
      e)  900 to 4500?  One fifth.   f)  180 to 60?  Three times.
      g)  3200 to 800?  Four times.   h)  1500 to 50?  Thirty times.
      i)  1000 to 100?  Ten times.   j)  400 to 2000?  One fifth.
      k)  1200 to 1800  Two thirds.   l)  1500 to 2000?  Three fourths.

14.  In a class, the ratio of boys to girls was 4 to 5.  There were 20 girls.
14.  How many boys were there?  16.  Four fifths of 20.

15.  In a survey, the ratio of Yes's to No's was 2 to 3.  There were 150
15.  No's.  How many Yes's were there?  100.  Two thirds of 150.

16.  The ratio of white roses to red was 3 to 4.  There were 32 red roses.
16.  How many white roses were there?  24. Three fourths of 32.

17.  The ratio of white roses to red was 3 to 4.  Out of 28 roses, how
17.  .many were white and how many were red?

12 white and 16 red.  For, 3 out of every 7 roses -- 3 white + 4 red -- were white. That is, three sevenths of them were white, and four sevenths, red. One seventh of 28 is 4, so three sevenths are 12. The rest, 16, were red.

18.  In a survey, the ratio of Yes's to No's was 2 to 3.  Out of 100
11.  responses, how many were Yes and how many No?

40 Yes and 60 No.  For, the Yes's were two fifths of 100, and the No's, three fifths.

  19.   The number of boys in a class is 25% of the number of girls.  The number of boys, therefore, is what percent of the entire class?
 
  By following this sequence, you should come upon the answer.
 
  The number of boys is to the number of girls in the same ratio as which two numbers (in lowest terms)?   1 to 4.
 
  Therefore 1 out of every  5  students are boys.
 
  The boys therefore are 20% of the entire class.

20.  The number of girls in a class was two thirds the number of boys.
20.  The girls, then, were what percent of the entire class?

40%.  For, the ratio of girls to boys was 2 to 3. Therefore, 2 out of 5 -- two fifths of the students -- were girls. And two fifths of 100% is 40%.


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