Ch. 12. Ratio and proportion
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM.
10/4/10/2/2022
Ratio
Ratio: A method of comparing two quantities of same kind and same unit by division.
Ratio can be obtained only for quantities with same units.
* How Many Times comparison between two quantities is known as the Ratio. We denote ratio using colon symbol ‘ : ’
* Ratio a : b can be shown as a/b.
* Thus Ratio is used to compare two quantities in terms of ‘how many times’.
* Quantities can be compared only if they are in the same unit otherwise not.
Equivalent Ratio same as Fraction.
* Therefore, we can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.
* Two ratios are equivalent, if the fractions corresponding to them are equivalent.
Proportion
* If two ratios are equal, we say that they are in proportion and use the symbol ‘ :: ’ or ‘ = ’ to equate the two ratios.
If two ratios are not equal, then we say that they are not in proportion. In a statement of proportion, the four quantities involved when taken in order are known as respective terms.
First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
1st : 2nd : : 3rd : 4th
1st & 4th –> Extreme Terms
2nd & 3rd –> Middle Terms
Unitary Method
The method in which we first find the value of one unit and then the value of the required number of units is known as the unitary method.
What have we discussed?
1. For comparing quantities of the same type, we commonly use the method of taking difference between the quantities.
2. Comparison By Ratio
In many situations, a more meaningful comparison between quantities is made by using division, i.e. by seeing how many times one quantity is to the other quantity. This method is known as comparison by ratio.
For example, Isha’s weight is 25 kg and her father’s weight is 75 kg. We say that Isha’s father’s weight and Isha’s weight are in the ratio 3 : 1.
3. For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.
4. The same ratio may occur in different situations.
5. Note that the ratio 3 : 2 is different from 2 : 3. Thus, the order in which quantities are taken to express their ratio is important.
6. A ratio may be treated as a fraction, thus the ratio 10 : 3 may be treated as 10/3.
7. Two ratios are equivalent, if the fractions corresponding to them are equivalent.
Thus, 3 : 2 is equivalent to 6 : 4 or 12 : 8.
8. A ratio can be expressed in its lowest form. For example, ratio 50 : 15 is treated as 50/15 ; in its lowest form 50/15 = 10/3. Hence, the lowest form of the ratio 50 : 15
is 10 : 3.
9. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.
Thus, 3, 10, 15, 50 are in proportion, since 3/15 = 10/50.
We indicate the proportion by 3 : 10 :: 15 : 50, it is read as 3 is to 10 as 15 is to 50. In the above proportion, 3 and 50 are the extreme terms and 10 and 15 are the middle terms.
10. The order of terms in the proportion is important. 3, 10, 15 and 50 are in proportion, but 3, 10, 50 and 15 are not, since 3/10 is not equal to
50/15 .
11. The method in which we first find the value of one unit and then the value of the required number of units is known as the unitary method. Suppose the cost of 6 cans is Rs 210. To find the cost of 4 cans, using the unitary method, we first find the cost of 1 can. It is Rs 210/6 or Rs 35. From this, we find the price of 4 cans as Rs 35 × 4 or Rs 140.
CHAPTER-12
Ratio and Proportion
Points to remember:
It can be expressed in its simplest form.
Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.
Example: If 4, 8, 24 and 48 are in proportion, then
4/24 = 48
Four quantities are in proportion if Product of extreme terms is equal to product of middle terms.
Example: If a b c d then axd=bxc
Unitary Method: The method in which we find the value of one unit is known as Unitary Method.
Example: 4 kg apples cost T 480, then find the cost of 7kg apples.
Cost of 4 kg apples = ₹ 480
Cost of 1 kg apples = 480/4
= 120
Cost of 7 kg apples = 120x7840.
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