COMPARING RATIOS
You can follow the steps given below to compare two ratios.
Step 1 :
Write the given two ratios as fractions.
Step 2 :
Find the least common multiple of the denominators of both the fractions (if the denominators are not same).
Step 3 :
Make the denominators of both the fractions same as the value of least common multiple found in step 1 using multiplication.
Step 4 :
After getting same denominator for both the fractions, compare the numerators and decide which fraction is greater.
The fraction which has larger numerator is greater in value.
Example 1 :
Compare 5 : 7 and 3 : 7.
Solution :
Write the given ratios as fractions.
5 : 7 = 5/7
3 : 7 = 3/7
The fractions 5/7 and 3/7 have the same denominator '7'.
Compare the numerators.
5 > 7
Then,
5/7 > 3/7
5 : 7 > 3 : 7
So, 5 : 7 is greater than 3 : 7.
Example 2 :
Compare 3 : 5 and 4 : 7.
Solution :
Write the given ratios as fractions.
3 : 5 = 3/5
4 : 7 = 4/7
The least common multiple of the denominators 5 and 7 is 35.
Make the denominators of the fractions as 35 using multiplication.
3/5 = (3 ⋅ 7) / (5 ⋅ 7) = 21/35
4/7 = (3 ⋅ 5) / (7 ⋅ 5) = 20/35
Compare the numerators.
21 > 20
Then,
21/35 > 20/35
3 : 5 > 4 : 7
So, 3 : 5 is greater than 4 : 7.
Example 3 :
Compare 5 : 12 and 7 : 18.
Solution :
Write the given ratios as fractions.
5 : 12 = 5/12
7 : 18 = 7/18
The least common multiple of the denominators 12 and 18 is 36.
Make the denominators of the fractions as 36 using multiplication.
5/12 = (5 ⋅ 3) / (12 ⋅ 3) = 15/36
7/18 = (7 ⋅ 2) / (18 ⋅ 2) = 14/36
Compare the numerators.
15 < 14
Then,
15/36 < 14/36
5 : 12 < 7 : 18
So, 5 : 12 is less than 7 : 18.
Example 4 :
Compare 2⅓ : 3⅓ and 3.6 : 4.8.
Solution :
Write the given ratios as fractions.
2⅓ : 3⅓ = 7/3 : 10/3
2⅓ : 3⅓ = (7/3) ⋅ 3 : (10/3) ⋅ 3
2⅓ : 3⅓ = 7 : 10
2⅓ : 3⅓ = 7/10
3.6 : 4.8 = 3.6/4.8
3.6 : 4.8 = (3.6 ⋅ 10) / (4.8 ⋅ 10)
3.6 : 4.8 = 36 / 48
3.6 : 4.8 = 3/4
The least common multiple of the denominators 10 and 4 is 20.
Make the denominators of the fractions as 20 using multiplication.
7/10 = (7 ⋅ 2) / (10 ⋅ 2) = 14/20
3/4 = (3 ⋅ 5) / (4 ⋅ 5) = 15/20
Compare the numerators.
14 < 15
Then,
14/20 < 15/20
2 ⅓ : 3 ⅓ < 3.6 : 4.8
So, 2⅓ : 3⅓ is less than 3.6 : 4.8.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
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
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
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
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 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
©All rights reserved. onlinemath4all.com
Recent Articles
-
Linear Growth and Decay
May 22, 22 03:05 AM
Linear Growth and Decay
-
Worksheet on Probability
May 22, 22 01:15 AM
Worksheet on Probability
-
Probability Worksheet
May 22, 22 01:12 AM
Probability Worksheet