CBSE Class 6 Maths Ratio and Proportion Revision Notes: Ratio and Proportion revision notes prepared by expert Maths teachers based on the latest edition of CBSE (NCERT) books. You can register online for Maths coaching at the official website of SpeEdLabs to clarify your doubts.

Ratio and Proportion Class 6 Chapter 12 Maths Notes

Comparison by Taking Difference:

We often employ the approach of taking differences between quantities when comparing quantities of the same type.
In some cases, a comparison by difference is not preferable to a comparison by division.
When we examine the two quantities in terms of ‘how many times,’ this comparison is called ‘Ratio’.

Comparison by Division:

In many cases, division is used to make a more meaningful comparison of amounts, i.e., seeing how many times one quantity is to the other quantity.

Comparison by ratio is the name given to this procedure.

The sign: is used to represent a ratio.
The two quantities must be in the same unit to be compared via ratio. If they aren’t in the same unit, they should be before the ratio is calculated.
By multiplying or dividing the numerator and denominator by the same number, we can derive equivalent ratios.

Example:

Priya weighs 10 kg whereas her father weighs 50 kg. The weights of Priya’s father and Priya are said to be in a 50:10 = 5:1 ratio.

The same ratio can occur in a variety of circumstances.
It’s worth noting that the: b ratio is not the same as b: a. As a result, the order in which quantities are taken to express their ratio is important.

For example, 5: 3 ratios are not the same as the 3: 5 ratios.

A ratio can be expressed as a fraction; for example, the ratio 7 : 9 can be expressed as 7/9.
In its simplest form, a ratio can be represented.

For example, the ratio 78: 39 is considered as 78/39.

In its simplest form, a ratio can be represented as 78/39=2/1

Hence, the lowest form of the ratio 78: 39 is 2: 1.

If the fractions corresponding to two ratios are the same, they are comparable.

Introduction to Ratio and Proportion

Golden ratio

Two quantities are in the Golden Ratio if their ratio is the same as the ratio of their sum to larger of the two quantities.

If two numbers a and b are in golden ratio, then

a+b/a = a/b

It is approximately equal to 1.618.

Ratio

The ratio is the comparison of a quantity with respect to another quantity.
It is denoted by “:“.
Two quantities can be compared only if they are in the same unit.

Example: Father’s age is 75 years and the daughter’s age is 25 years.

⇒The ratio of father’s age to daughter’s age

⇒Father’s Age/Daughter’s Age = 3/1 = 3:1

Difference between Fractions and Ratios

A fraction describes a part of a whole and its denominator represents the total number of parts.

Example: 13 means one part out of 3 parts.

A ratio is a comparison of two different quantities.

Example: In a society, 10 people like driving, 20 people like swimming and the total number of people in society is 30.

The ratio of the number of people liking driving to the total number of people = 10:30.
The ratio of the number of people liking swimming to the number of people liking driving is 20:10.

Same ratio in different situations

Ratios can remain same in different situations.

Example:

Weight of Joe/Weight of James = 50/100 = 1:2
Number of Girls/Number of Boys = 50/100 = 1:2

Comparing quantities using ratios

Quantities can be compared using ratios.

Example: Joe worked for 8 hours and James worked for 2 hours. How many times Joe’s working hours is of James’ working hours?

Solution: Working hours of Joe = 8 hours

⇒Working hours of Sheela = 2 hours

⇒The ratio of working hours of Joe to Sheela = 8/2 = 4

Therefore, Joe works four times more than James.

Equivalent Ratios

When the given ratios are equal, then these ratios are called as equivalent ratios.

Equivalent ratios can be obtained by multiplying and dividing the numerator and denominator with the same number.
Example: Ratios 10:30 (=1:3) and 11:33 (=1:3) are equivalent ratios.

Unitary Method

The method in which first we find the value of one unit and then the value of required number of units is known as Unitary Method.

Example: Cost of two shirts in a shop is Rs.200. What will be the cost of 5 shirts in the shop?

Solution: Cost of 2 shirts = Rs.200

⇒Cost of 1 shirt = 200/2 = 100

⇒Cost of 5 shirts = (200/2) * 5 = 100 * 5

= Rs.500

Proportions

If two ratios are equal, then they are said to be in proportion.

Symbol “::” or “=” is used to equate the two ratios.
Example: Ratios 2:3 and 6:9 are proportional.
⇒ 2:3 :: 6:9 or 2:3 = 6:9

Uses of Ratios and Proportions

Example: Suppose a man travelled 80 km in 2 hours, how much time will he take to travel 40 km?
Solution: If x is the required time, then the proportion is

80:2:: 40: x.

⇒ 80/2 * 40/x

⇒80x=80

⇒ x=1 hour

So, the man takes one hour to complete 40 km.

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Ratio and Proportion: Class 6 Chapter 12 Maths Notes