IDENTIFY EQUIVALENT RATIOS
About "Identify equivalent ratios"
Identify equivalent ratios :
Whenever the simplified form of two ratios are equal, then we can say that the ratios are equivalent ratios.
For example ,
6 : 4 and 18 : 12 are equivalent ratios, because the simplified form of 6 : 4 is 3 : 2 and the simplified form of 18 : 12 is also 3 : 2.
How to get an equivalent ratio ?
We can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.
Example 1 :
Fill in the blanks
Solution :
The three given ratios are equal,
In order to get the first missing number, we consider the fact that 21 = 3 × 7. i.e. when we divide 21 by 7 we get 3. This indicates that to get the missing number of second ratio, 14 must also be divided by 7.
When we divide, we have, 14 ÷ 7 = 2
Hence, the second ratio is 2/3
Similarly, to get third ratio we multiply both terms of second ratio by 3.
Hence, the third ratio is 6/9
So, 14/21 = 2/3 = 6/9 = [These are all equivalent ratios.]
Example 2 :
Fill in the blanks
Solution :
(i) In order to get the first missing number, we consider the denominators of first and second fraction.
When we divide 18 by 3, we will get 6, like wise if we divide numerator of first fraction by 3, we will get 5.
Hence the second fraction is 5/6
(ii) Comparing 5/6 = 10/?, if we multiply the numerator 5 by 2 we will get 10
Like wise, if we multiply the denominator 6 by 2, we will get 12.
Hence the third fraction is 10/12
(iii) Comparing 10/12 = ?/30 ,
We cannot say that the number 12 is to be multiplied by which number in order to get 30.
So, let us consider the missing number be "x".
10/12 = x/30
10 x 30 = 12x
x = (10 x 30)/12 = 2.5
(10/12) x (2.5/2.5) = 25/30
Hence the fourth fraction is 25/30.
Example 3 :
Consider the statement: Ratio of breadth and length of a hall is 2 : 5. Complete the following table that shows some possible breadths and lengths of the hall.
|
Breadth of the hall (in meters) |
10 |
? |
40 |
|
Length of the hall (in meters) |
25 |
50 |
? |
Solution :
Let "x" be and "y" be the two unknowns
Breadth and lengths are in the ratio 2 : 5.
If two ratios are equivalent then
Product of means = product of extremes
10 : 25 = x : 50
25 x = 10 (50)
x = 500/25
x = 20
By comparing the first and third column
Product of means = product of extremes
10 : 25 = 40 : x
10 x = 40 (25)
x = 1000/10
x = 100
After having gone through the stuff given above, we hope that the students would have understood "Identify equivalent ratios".
Apart from the stuff given above, if you want to know more about "Identify equivalent ratios", please click here
Apart from the stuff given in this section, 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
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
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
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
Recent Articles
-
All Silver Tea Cups
Dec 15, 19 09:57 PM
All Silver Tea Cups - Concept in Trigonometry - Examples with step by step explanation
-
All Students Take Calculus
Dec 15, 19 09:57 PM
All Students Take Calculus - Concept - Examples with step by step explanation
-
All Sin Tan Cos Rule
Dec 15, 19 09:52 PM
All Sin Tan Cos Rule - Concept - Examples with step by step explanation
