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Ratio Comparison

Comparison of quantities by division is ratio and the symbol ":" express a ratio. Ratio as the comparison made on the basis of how many times a quantity is that of the other quantity. A ratio may be used to convey an idea that cannot be expressed as a single number.
Let us study about ratio comparison:
Consider a and b as two different quantities, Then
the quotient `a/b ` is called as the ratio between a and b. It can be mentioned as a : b.
The ratio comparison is nothing but comparing the two different ratios as they are equal to one another or not.

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How to Compare Ratios?

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The ratios do not have any unit. Then a and b are said to be as terms of ratio, where ‘a’ is the first term which is termed as antecedent and ‘b’ is the second term which is termed as consequent. Always ratios are used to express in their lowest terms.

The inequality of ratios are also considered as greater inequality, lesser inequality and the other as equality, which are as follows:

Greater inequality as if a > b

Lesser inequality as if a < b

Equality as if a = b

If a:b and c:d are said to be two different ratios then their ratio comparison will be as follows:

a:b > c:d if ad > bc

a:b < c:d if ad < bc

a:b = c:d if ad = bc

Ratio Problems

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Below you could see problems on ratio

Solved Examples

Question 1: Consider the two ratios as 3:4 and 1:2. Find which one of the two ratios is greater.
Solution:
The two given ratios are a : b = 3 : 4 and c : d = 1 : 2.

Multiply the value ‘a’ with ‘d’ and the value ‘b’ with ‘c’ as follows:

3 x 2 = 4 x 1

6 = 4

Compare the value 6 and 4 as follows:

6 > 4 (that is ad > bc).

Therefore the ratio 3:4 is greater than the ratio 1:2 according to the ratio comparison rules.


Question 2: Consider the two ratios as 2 : 3 and 3 : 5. Find which one of the two ratios is smaller.
Solution:
The two given ratios are a : b = 2 : 3 and c : d = 3 : 5.

Multiply the value ‘a’ with ‘d’ and the value ‘b’ with ‘c’ as follows:

2 x 5 = 3 x 3

10 = 9

Compare the value 10 and 9 as follows:

10 > 9 = 9 < 10 (that is bc < ad).

Therefore the ratio 3 : 5 is smaller than the ratio 2 : 3 according to the ratio comparison rules.


Practice Problems

Question 1: Consider the two ratios as 1:3 and 2:3. Find which one of the two ratios is smaller.
Question 2: Consider the two ratios as 3:4 and 2:3. Find which one of the two ratios is greater.
Question 3: Consider the two ratios as x:4 and 1:2. If these two ratios are equal then find the value of ‘x’.
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