RATIO AND PROPORTION

PROBLEMS (2)

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4.  What is a proportion?

A statement that two ratios are the same.

5.  Why is each of the following a proportion?

5.  a)  2 is to 6  as  10 is to 30.

2 is the third part of 6, just as 10 is the third part of 30.

5.  b)  12 is to 3  as  24 is to 6.

12 is four times 3, just as 24 is four times 6.

5.  c)  2 is to 3  as  10 is to 15.

2 is two thirds of 3, just as 10 is two thirds of 15.

6.  In each of the following, what ratio has a to b?

6.  a)  a is to b  as  1 is to 5.   a is a fifth of b.

6.  b)  a is to b  as  32 is to 8.   a is four times b.

6.  c)  a is to b  as  2 is to 3.   a is two thirds of b.

7.  Read each proportion.  Why is each one a proportion?

       a)   5
1
 =  10
 2

"5 is to 1 as 10 is to 2."
  5 is five times 1, as 10 is five times 2.

       b)   2
8
 =   6
24

"2 is to 8 as 6 is to 24."
 2 is a fourth of 8, as 6 is a fourth of 24.

       c)    75
100
 =  3
4

"75 is to 100 as 3 is to 4." 
75 is three quarters of 100, as 3 is three quarters of 4.

8.  Complete each proportion.

       a)   1
2
 =   7 
14
  b)   3
9
 =  10
30
  c)   4
1
 =  20
 5
       d)   49
 7
 =  56
 8
  e)   2
3
 =  10
15
  f)    7
28
 =   3 
12
       g)    6
42
 =   9 
63 
  h)   18
 2
 =  45
 5
  i)   3
4
 =  27
36

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