Ratio and Proportion Summary Class 6 Maths Chapter 12

Ratio

• The ratio of two non-zero numbers a and b is the fraction a/b and we write it as a : b read as ‘a is to b’.
• In the ratio a : b, we call a the first term or antecedent and b the second term or consequent.
• Equivalent ratios : On multiplying (or dividing) each term of a ratio by the same non-zero number, we get a ratio equivalent to the given ratio.
• Ratio in simplest form : The ratio a : b is said to be in the simplest form if the HCF of a and b is 1.

Methods of comparing quantities

Comparison by taking difference

• For comparing quantities of the same type, we commonly use the method of taking difference between the quantities. For example: Isha and Neha collected flowers for scrap notebook. Isha collected 20 flowers and Neha collected 35 flowers. So, we may say that Neha collected 35 - 20 = 15 flowers more than Isha. 
• Some times the comparison by difference does not make better sense than the comparison by division.

Comparison by Division

• The comparison of two numbers or quantities by division is known as the ratio. Symbol ':' is used to denote 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.

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.

Four numbers in proportion

• Four numbers a, b, c, d are said to be in proportion if a : b = c : d and we write a : b : : c : d. We read it as ‘a is to b as c is to d’.
• Here a, b, c, d are respectively known as first, second, third and fourth terms of the given proportion.
• The 1st and 4th terms are called the extreme terms or extremes.
• The 2nd and 3rd terms are called the middle terms or means.
• In a proportion a : b : : c : d, we always have (a × d) = (b × c). product of extremes = product of means.

Unitary Method

• The method in which first we find the value of one unit and then the value of the required number of units. 
• For example, the cost of 6 caps is 210. Find the cost of 4 caps. The cost of 6 caps = 210 
  ∴ Cost of 1 cap = 210/6 = 35
  Hence, cost of 4 caps = 35 × 4 = 140.