RATIO AND PROPORTION  1

PROBLEMS

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11.  Express the ratio of each of the following.  Then express the inverse
11.  ratio.

11.  a)  5 to 10.   "5 is half of 10.  Inversely, 10 is two times 5."

11.  b)  7 to 21.

7 is the third part of 21. Inversely, 21 is three times 7.

11.  c)  32 to 8.

32 is four times 8. Inversely, 8 is the fourth part, or a quarter of 32.

11.  d)  72 to 9.

72 is eight times 9. Inversely, 9 is the eighth part of 72.

11.  e)  30 to 5.

30 is six times 5. Inversely, 5 is the sixth part of 30.

11.  f)  200 to 100.

200 is two times 100. Inversely, 100 is half of 200.

11.  g)  1000 to 100.

1000 is ten times 100. Inversely, 100 is the tenth part of 1000.

11.  h)  1 to 12.

1 is the twelfth part of 12. Inversely, 12 is twelve times 1.

11.  i)  40 to 8.

40 is five times 8. Inversely, 8 is the fifth part of 40.

11.  j)  1 to 10.

1 is the tenth part of 10. Inversely, 10 is ten times 1.

11.  k)   63 to 9.

63 is seven times 9. Inversely, 9 is the seventh part of 63.

11.  l)  3 to 30.

3 is the tenth part of 30.  Inversely, 30 is ten times 3.

11.  m)  4 to 36.

4 is the ninth part of 36.  Inversely, 36 is nine times 4.

2.  Percent: Ratio to 100%.  Percents are ratios.  What ratio is each of
2.  the following?

12. a)  50%  Half.   b)  25%  A quarter.   c)  75%  Three quarters.
12.  d)  33 1
3
%   A third.   e)  66 2
3
%   Two thirds.
12.  f)  20%   A fifth.   g)  40%   Two fifths.
 
12.  h)  60%   Three fifths.   i)  80%   Four fifths.
 
12.  j)  1%   One hundredth.   k)  3%   Three hundredths.
 
12.  l)  200%   Two times, or twice as much.
 
12.  m)  300%   Three times.   n)  800%   Eight times.
 
12.  o)  1000%   Ten times.   p)  10%   The tenth part.
 
12.  q)  30%   Three tenths.   q)  90%   Nine tenths.

3.  How much is

50% of 12?  6.   25% of 12?  3.   33 1
3
% of 12?  4.
 
200% of 12?  24.   300% of 12?  36.   400 % of 12?  48.

4.   Each percent is what ratio?

4.  a)  250%  Two and a half times.    How much is 250% of 12?  30

4.  b)  350%  Three and a half times.    How much is 350% of 10?  35

4.  c)  425%  Four and a quarter times.  How much is 425% of 8?  34

  4.  d)  533 1
3
%  Five and a third times.   How much is 533 1
3
% of 6?  32

5.  Compare each "what ratio" question with the "what percent" question.  5. The percent has that same ratio to 100%.

5.  a)  7 has what ratio to 14?  Half.  7 is what percent of 14?  50%

5.  b)  9 has what ratio to 36?  One fourth.

5.  b)  9 is what percent of 36?  25%

5.  c)  4 has what ratio to 20?  A fifth. 4 is what percent of 20?  20%

  5.  d)  5 has what ratio to 15?  A third. 5 is what percent of 15?   33 1
3
%

5.  e)  7 has what ratio to 70?  A tenth. 7 is what percent of 70?  10%

5.  f)  18 has what ratio to 9?  Two times.

5.  f)  18 is what percent of 9?  200%

5.  g)  27 has what ratio to 9?  Three times.

5.  g)  27 is what percent of 9?  300%


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