Algebra Den

Proportion

Explanation
When two Ratios are equal, they are said to be in Proportion. When two Ratios are in Proportion we use the symbol ' :: ' or ' = '. to denote them.

Read the following examples to learn more about Proportion:-

Example = Check and discuss whether the following ratios are in proportion.
        1) 2 : 5 and 5 : 7
        2) 7 : 3 and 56 : 24
        3) 12 : 22 and 15 : 27
        4) 44 : 8 and 22 : 4
        4) 4 : 8 and 7 : 14
Answer = The proceeds is as :
1) 2 : 5 and 5 : 7
Here, both the ratios are in lowest form and
2 : 5 ≠ 5 : 7
So, we can say that the given Ratios are not in proportion.

2) 7 : 3 and 56 : 24
Here, First Ratio(7:3) is in Lowest From: but Second Ratio(56:24) needs to be converted into Lowest Form:
56 : 24 = 7 : 3 (Lowest Form)
Lowest Forms of both ratios are equal,
So, 7 : 3 :: 56 : 24 (both are in proportion)

3) 12 : 22 and 15 : 27
Firstly, convert the ratios into Lowest Form
12 : 22 = 6 : 11(Lowest Form)
15 : 27 = 5 : 9 (Lowest Form)
Lowest Forms of both ratios are not equal,
So, 12 : 22 ≠ 15 : 27 (both are not in proportion)

4) 44 : 8 and 22 : 4
Firstly, convert the ratios into Lowest Form
44 : 8 = 11 : 2 (Lowest Form)
22 : 4 = 11 : 2 (Lowest Form)
Lowest Forms of both ratios are equal,
So, 44 : 8 :: 22 : 4 (both are in proportion)

5) 4 : 8 and 7 : 14
Firstly, convert the ratios into Lowest Form
4 : 8 = 1: 2 (Lowest Form)
7 : 14 = 1 : 2 (Lowest Form)
Lowest Forms of both ratios are equal,
So, 44 : 8 :: 22 : 4 (both are in proportion)