Students can go through AP 6th Class Maths Notes Chapter 12 Ratio and Proportion to understand and remember the concepts easily.
Class 6 Maths Chapter 12 Notes Ratio and Proportion
→ A type of comparison where we compare things or quantities by division is called ratio.
→ When we compare two quantities, we have to take care of order of the quantities.
→ Latha is 6 years old and Siri is 18 years old. The ratio of Latha’s age and Siri’s age is
\(\frac{18}{6}\) = \(\frac{1}{2}\) = 3 : 1. We read it as 3 is to 1.
→ In general the ratio of two quantities a and b is written as a : b and we read it as a is to b.
→ The two quantities a and b are called terms of the ratio, ‘a’ is called the first term or antecedent and ‘b’ is called second term or consequent.
→ A ratio is said to be in the simplest form or in the lowest terms when it is written in terms of whole numbers with no common factors other than 1.
Ex : The simplest form of 35 : 40 is 7 : 8 (∵ \(\frac{35}{40}\) = \(\frac{5 \times 7}{5 \times 8}\) \(\frac{7}{8}\))
→ Equalities of ratios is called proportion. In general if the ratio of ‘a’ and ‘b’ is equal to the ratio of ‘c’ and ‘d\ we say that they are in proportion.
This is represented as a : b:: c : d.
→ Unitary method :
In this method we first find the value of one unit apd then the value of the required number of units.
Ex : If the cost of 15 books is Rs. 120, then find the cost of 10 books.
Solution:
Cost of 15 books = Rs. 120
Cost of 1 book = Rs. 120 ÷ 15 = Rs. 8
Cost of 10 books = Rs. 8 × 10 = Rs. 80.
→ The ratio of two quantities ‘a’ and ‘b’ can be given in any one of the following ways.
- Symbolic form : a : b
- Fractional form : \(\frac{a}{b}\)
- Verbal form : ‘a’ is to ‘b’.