PERCENTS ARE RATIOS

PROBLEMS

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1.   Each percent is what ratio? (What ratio has each percent to 100%?)

Upon studying these, the student will have a "dictionary" which relates percents to ratios. The student should study this dictionary both ways:  From percent to ratio, and from ratio to percent.

Percent      Ratio
50%           Half
25%           A quarter
75%           Three quarters
12½%        An eighth  (Half of a quarter)
33 1
3
%          A third
66 2
3
%          Two thirds
20%           A fifth
40%           Two fifths
60%           Three fifths
80%           Four fifths
10%           A tenth
200%         Two times
300%         Three times
250%         Two and a half times
325%         Three and a quarter times
1000%       Ten times
   1%          One hundredth
100%         All

2.  a)  A blouse is a blend of cotton and rayon.  It is 72% cotton.  What
2.  a)  percent is rayon?  28%

2.  b)  In a survey, 87½% responded Yes.  What percent responded
2.  a)   No?  12½%

2.  c)  The vote in a recent election was split between candidates A, B,
2.  a)  and C.  Candidate A got 42% of the vote; candidate B got 43%.
2.  a)  What percent did candidate C get?  15%

Mental calculation

3.  The Amount

  3.   a)  12 is 50% of 24.   b)  6 is 25% of 24.
 
  3.   c)  18 is 75% of 24.   d)  11 is 20% of 55.
  3.   e)  5 is 33 1
3
% of 15.   f)  10 is 66 2
3
% of 15.
  3.   g)  4 is 12½% of 32.   h)  36 is 300% of 12.
 
  3.   i)  500 is 1000% of 50.   j)  750 is 250% of 300.
 
  3.   k)  75 is 150% of 50.   l)  34 is 425% of 8.

4.  How much is 10% of each of the following?  How much is 1%?

   $300    $275 $50  $3 $28 $5,020
10%   $30 $27.50   $5 $.30 $2.80   $502  
 1%   $3 $2.75   $.50   $.03   $.28   $50.20  

5.  Calculate mentally from 1%.

a)  2% of $300 = $6.00   b)  3% of $900 = $27
 
c)  5% of $70 = $3.50   d)  8% of $60 = $4.80
 
e)  7% of $4000 = $280   f)  6% of $8000 = $480

6.  The Base

a)  14 is 50% of 28.   b)  8 is 25% of 32.
c)  9 is 33 1
3
% of 27   d)  5 is 20% of 25.
e)  14 is 200% of 7.   f)  12 is 300% of 4.
 
g)  10 is 500% of 2.   h)  40 is 1000% of 4.
 
i)  $.25 is 10% of $2.50.   j)  $.25 is 1% of $25.

7.  The Percent.  (The question is, Has what ratio?)

a)  7 is 50% of 14.   b)  8 is 33 1/3% of 24.
 
c)  9 is 25% of 36.   d)  6 is 20% of 30.
 
e)  12 is 200% of 6.   f)  18 is 300% of 6.
 
g)  120 is 1000% of 12.   h)  12 is 100% of 12.
 
i)  $75 is 10% of $750.   j)  $7.50 is 1% of $750.

8.  Complete the following.

 
  8.   a)  12 is 50% of 24.    b)  8 is 25% of 32.    c)  7 is 20% of 35.
  8.   d)  9 is 33 1
3
% of 27.   e)  12 is 300% of 4.   f)  5 is 10% of 50.
  8.   g)  8 is 20% of 40.   h)  8 is 1% of 800.   i)  3.5 is 1% of 350.

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