# COMPARISON OF RATIOS

Comparison of ratios :

Here we are going to see how to compare two or more ratios.

To compare two ratios, we need to follow the steps given below.

Step 1 :

Consider the denominators of the given ratios. If they are not same, we have to convert the denominator as same by taking L.C.M

Step 2 :

After converting the denominators as same, we may decide that the ratio is greater which has greater numerator.

Let us look into some examples to understand the above concept.

Example 1 :

Compare 3:5 and 4:7

Solution :

We have to compare 3/5 and 4/7

The L.C.M of denominator 5 and 7 is 35.

(3/5) ⋅ (7/7)  =  21/35

(4/7) ⋅ (5/5)  =  28/35

By comparing the above fractions 28/35 and 21/35, 28 is greater.

Hence the ratio 4:7 is greater than 3:5.

4:7 > 3:5

Example 2 :

Compare 4:5 and 5:7

Solution :

To compare the above ratios, let us write each ratio in the fractional form

That is,

4:5  =  4/5

5:7  =  5/7

Since the denominators are not same, we have to take L.C.M in order to make the denominators as  same.

L.C.M of 5 and 7 is 35

(4/5)  (7/7)  =  28/35

(5/7) ⋅(5/5)  =  25/35

28/35 is greater than 25/35.That is, 4/5 is greater than 5/7.

Hence the ratio 4:5 is greater than the ratio 5:7.

4:5 > 5:7

Example 3 :

Compare 3:4 and 4:5

Solution :

To compare the above ratios, let us write each ratio in the fractional form

That is,

3:4  =  3/4

4:5  =  4/5

Since the denominators are not same, we have to take L.C.M in order to make the denominators as  same.

L.C.M of 4 and 5 is 20

(3/4)  (5/5)  =  15/20

(4/5)  (4/4)  =  16/20

16/20 is greater than 15/20.That is, 4/5 is greater than 3/4.

Hence the ratio 4:5 is greater than the ratio 3:4.

4:5 > 3:4

Example 4 :

Compare 3:7 and 7:9

Solution :

To compare the above ratios, let us write each ratio in the fractional form

That is,

3:7  =  3/7

7:9  =  7/9

Since the denominators are not same, we have to take L.C.M in order to make the denominators as  same.

L.C.M of 7 and 9 is 63

(3/7) x (9/9)  =  27/63

(7/9) x (7/7)  =  49/63

49/63 is greater than 27/63.That is, 7/9 is greater than 3/7.

Hence the ratio 7:9 is greater than the ratio 3:7.

4:5 > 3:4

After having gone through the stuff given above, we hope that the students would have understood "Comparison of ratios"

Apart from the stuff given on "Comparison of ratios", if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6