RATIO AND PROPORTION

PROBLEMS (2)

Do the problem yourself first!

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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