Here we are going to learn about Proportions (some portion of this topic taken from ICSE class 10 syllabus).
When any two ratios are equal, we say that the two ratios are in proportion. It is the relationship between two ratios whose output is same and constant.
It is represented by a/b :: c/d
or
a : b :: c : d
Here the ratio of a: b is proportion to c: d. Both symbols :: and = are used to represent the proportionality of two ratios.
If we have a : b : : c : d , it is read as a is to b as c is to d
In the above statement we have 'a' as First term, 'b' as second term , 'c' as third term and 'd' as the fourth term.
In this a and d are called extreme terms or extremes and b and c are middle terms and are also called means
If the given four numbers are in proportion, then the product of means is equal to the product of extremes.
In order to check that the two ratios are in proportion, we simply check if the product of extremes and the product of means are equal.
Let us see how to solve proportion with the help of an example:
Example: solve Proportion problem 60 : 105 :: 84 :147 .
Sol: We first take the product of means ie 105 * 84 = 8820
now we take the product of extremes i.e. 60 * 147 = 8820
Here we observe that the product of means = product of extremes. So the two ratios are in proportion.
This can also be checked by converting both ratios in lowest terms, if both the values are same, they are in proportion
Let us try it for the same data:
60 / 105 ,we divide numerator and denominator by 5 and get
= 12 /21 , again dividing by 3 we get
= 4 / 7
Similarly we write 84/147 , dividing & multiplying by 3 we get
= 28 / 49
Now dividing & multiplying by 7 we get
= 4 /7
So they are in proportion.
In next post we will talk on Estimation of Solutions in Grade VI. For more information on Substitution Method, you can visit our website
When any two ratios are equal, we say that the two ratios are in proportion. It is the relationship between two ratios whose output is same and constant.
It is represented by a/b :: c/d
or
a : b :: c : d
Here the ratio of a: b is proportion to c: d. Both symbols :: and = are used to represent the proportionality of two ratios.
If we have a : b : : c : d , it is read as a is to b as c is to d
In the above statement we have 'a' as First term, 'b' as second term , 'c' as third term and 'd' as the fourth term.
In this a and d are called extreme terms or extremes and b and c are middle terms and are also called means
If the given four numbers are in proportion, then the product of means is equal to the product of extremes.
In order to check that the two ratios are in proportion, we simply check if the product of extremes and the product of means are equal.
Let us see how to solve proportion with the help of an example:
Example: solve Proportion problem 60 : 105 :: 84 :147 .
Sol: We first take the product of means ie 105 * 84 = 8820
now we take the product of extremes i.e. 60 * 147 = 8820
Here we observe that the product of means = product of extremes. So the two ratios are in proportion.
This can also be checked by converting both ratios in lowest terms, if both the values are same, they are in proportion
Let us try it for the same data:
60 / 105 ,we divide numerator and denominator by 5 and get
= 12 /21 , again dividing by 3 we get
= 4 / 7
Similarly we write 84/147 , dividing & multiplying by 3 we get
= 28 / 49
Now dividing & multiplying by 7 we get
= 4 /7
So they are in proportion.
In next post we will talk on Estimation of Solutions in Grade VI. For more information on Substitution Method, you can visit our website
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