# COMPARING RATIOS

"Comparing ratios"  is sometimes difficult job for some students who study math in school level.

Actually it is not a difficult one, once we have understood the concept.

Here, we explain you step by step to compare two ratios.

Step 1 :

We have to write the given ratios in the form of fractions.

Step 2 :

We have to make them to be like fractions. (Having same denominators)

Step 3 :

We have to compare the numerators. To have better understanding on this, let us look at an example.

Compare the two ratios given below.

3:4 and 2:3

Step 1 :

Let us write the given ratios as fractions.

3:4 -------------> 3/4

2:3 -------------> 2/3

Step 2 :

Let us make 3/4 and 2/3 to be like fractions as given below. (Making the denominators to be same)

To make the denominators to be same, first we have to find L.C.M of the denominators 4 and 3.

L.C.M of 4 and 3  = 12

So, we have

(3x3) / (4x3) = 9/12  (multiplied by 3)

(2x4) / (3x4) = 8/12 (multiplied by 4)

Now, the denominators are same.

Step 3 :

Now, we have to compare  the numerators of 9/12 and 8/12.

Numerator in the first fraction is greater than the numerator of the second fraction.

So, the first ratio 3:4 is greater than the second ratio 2:3

Note: In this stuff "comparing ratios", sometimes we may have to do some additional steps in case the terms of the ratio are decimal numbers  or mixed numbers.In that kind of problems, first we have to make the terms of the ratio to be integers.

Let us look at an example for the above mentioned case.

Compare the two ratios given below.

2 1/3 : 3 1/3 and 3.6 : 4.8

Step 1 :

Let us convert the mixed numbers in to improper fractions in the first ratio.

2 1/3 : 3 1/3 = 7/3 : 10/3

Now multiply both the terms of the ratio by 3 in order to get rid of the denominator 3

(7/3)x3 : (10/3)x3 = 7 : 10 (both the terms are integers)

Step 2 :

Let us convert the decimals in to integers in the second ratio by multiplying 10.

(3.6x10) : (4.8x10) = 36 : 48

To simplify the ratio 36:48 to its lowest term, let us divide both the terms of the ratio by 12.

When we do so, 36 : 48  = 3 : 4

Step 3 :

From step 1 and step 2,

we get  first  ratio = 7:10 and the second ratio = 3:4

Let us write them as fractions.

7:10 ---------> 7/10

3:4 -----------> 3/4

Step 4 :

Let us make 7/10 and 3/4 to be like fractions as given below. (Making the denominators to be same)

To make the denominators to be same, first we have to find L.C.M of the denominators 10 and 4.

L.C.M of 10 and 4  = 20

So, we have

(7x2) / (10x2) = 14/20  (multiplied by 2)

(3x5) / (4x5) = 15/20 (multiplied by 5)

Now, the denominators are same.

Step 5 :

Now, we have to compare  the numerators of 14/20 and 15/20.

Numerator in the second fraction is greater than the numerator of the first fraction.

So, the second ratio 3.6 : 4.8 is greater than the first ratio    2 1/3 : 3 1/3.

After having gone through the stuff and examples related to "comparing ratios", we hope that the students would have understood  "comparing ratios".

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