Properties of ratios:
- A ratio is a way of comparing two quantities.
- The ratio between a and b is written as a:b. The colon (:) stands for ratio.
- In the ratio a:b, a and b are called its terms. The first term of the ratio, 'a' is called the "antecedent" and the second term, 'b' is called the "consequent".
- It is same as writing fraction.
- The ratio of two quantities expressed is the simplest form of that fraction.
- If two ratios are equal, then four numbers forming the two ratios in order are said to be in proportion.
- Percent is a part of a whole that is expressed in hundredth.
- Probability is the ratio of the number of ways an event can happen to the total number of possible outcomes.
Example: What is the ratio of 21 and 35?
- Order of terms in a ratio is important. Note that the ratio 3:5 is different from 5:3.
If the antecedent and consequent of a ratio are multiplied or divided by the same number (¹0), its value does not change.
5:3 = 5x2:3x2 = 10:6
30:40 = 30/2:40/2 = 15:20
- It is customary to express the terms of a ratio as natural numbers.
If the antecedent or consequent or both are fractions, find the L.C.M. of the denominators of the fractions and multiply both terms of the ratio by this L.C.M. This will convert fractional terms into natural numbers.
Change the terms of the ratio 1/2:1/3 to natural numbers.
The L.C.M. of the denominators 2 and 3 is 6.
1/2:1/3 = (1/2)x6:(1/3)x6 = 3:2
- To convert a given ratio to its least terms, find the H.C.F. of its antecedent and consequent and divide both terms of the ratio by this H.C.F.
Example: Write 30:36 in its least terms.
The H.C.F. of 30 and 36 is 6.
Therefore, 30:36 = 30/6:36/6 = 5:6
This can be written as 21/35
- To find the simplest form, we find the HCF of the given quantities
- Factors of 21 are 1, 3, 7, 21
- Factors of 35 are 1, 5, 7, 35
- HCF is 7.
- Divide both 21 and 35 by 7.
- The simplest form of this is 3/5.
Directions: Solve the following problems.