# Ratio and Proportion Class 6 Maths NCERT Chapter 12

## Key Features of NCERT Material for Class 6 Maths Chapter 12 – Ratio and Proportion

In the last chapter 11, We studied variables, constants, equations and their applications. We also looked at methods to solve an equation. In chapter 12 of Class 6 Maths NCERT book: Ratio And Proportion, we will learn about ratios, comparison of amounts using ratios, proportions and how to solve problems using the unitary method.

### Quick Revision notes

There are two distinct methods of assessment:

(I) By comparison.

(ii) By division.

The (ii) way is prefered more.

The correlation got through division is called ratio. Thus, we see how often one amount is to the other amount.

For example: If Meeta got 50 marks and Geeta got 25 marks in a test, by then we can say that the marks obtained by Meeta are multiple times the marks obtained by Geeta.

#### Ratio

If we take a look at the two amounts with respect to ‘how often’, the comparison is known as the Ratio. They are the mathematical numbers used to compare two things which are similar to each other in terms of units.

The ratio is demonstrated by ‘:’

For example, Reeta’s weight is 20 kg and her father’s weight is 60 kg. We express that Reeta’s father’s weight and Reeta’s weight are in the ratio = 3: 1.

For correlation by Ratio, the two amounts must be in comparable units. On the off chance that they are not, they ought to be turned in comparable units before the ratio is taken.

A similar ratio may occur in different conditions.

For example,

(I) The length of a room is 10 m and the breadth is 20 m. Along these lines, the ratio of the length of the room to the breadth of the room = 1: 2

(ii) There are 30 ladies and 20 men in a room. Here, the ratio of the quantity of ladies to the amount of men = 3 : 2.

A ratio may be treated as a division.

A ratio proportional to a given ratio can be procured by multiplying the numerator and denominator by a comparative number. In this way, a few ratios equal to 2 : 3 are 4 : 6, 6 : 9, 8 : 12, etc.

In like manner, a few ratios equivalent to 64 : 32 can be  32 : 16, 16 : 8, 8 : 4, 4 : 2, 2 : 1, etc. when the divisions contrasting with proportionate ratios are equivalent, the two ratios are identical.

The order in which the amounts are considered is important. Note that the ratio 2 : 3 is not in relation to 3: 2.

A ratio can be expressed in its most diminished form. For example, ratio 60 : 24 is as a section. In its least structure = 5 : 2. thus, in its most minimal proportion 60 : 24 is treated as 5 : 2.

#### Comparing amounts utilizing ratios

Amounts can be compared with utilizing ratios.

For instance: James laboured for 8 hours and Joe laboured for 2 hours. How frequently Joe’s working hours are James’ working hours?

Answer: Working hours of James = 8 hours

⇒Working hours of Joe = 2 hours

⇒The ratio of working hours of James to Joe =8:2=4.

Consequently, James works 4 times more than Joe.

#### Proportion

Ratios are said to be in proportion when they are equal and we use ‘::’ to equate the ratios.

For instance, 2 : 4 = 60 : 120

we create 2 : 4 :: 60 : 120

It shows that 2, 4, 60 and 120 are in proportion.

Again,

2 : 5 ≠ 60 : 15

Thus 2, 5, 60 and 15 are not in proportion.

When the ratios are not equivalent we state that they are not in proportion.

Four amounts should be in proportion if the ratio of the first and the subsequent amounts is equivalent to the ratio of the third and the fourth amounts. In this way, the four amounts – 3, 10, 15, 50 are in proportion, since =

We create 6 : 25 :: 12 : 50 and read as 6 is to 25 as 12 is to 50.

Here, the first and the fourth terms, i.e., 6 and 50 are known as the extreme terms while the second and the third terms, i.e., 25 and 12 are known as the centre terms.

The request for terms in a proportion is important, 3, 10, 15, 50 are in proportion yet 3, 10, 50, 15 are not, since ≠ .

#### Unitary Method

The strategy where we initially find the estimation of one unit and later the estimation of the necessary number of units is known as the Unitary Method.

For example, if the cost of 6 toys is ₹ 90 and we are to find the expense of 4 toys,  we initially find the expense of 1 toy as ₹ or ₹ 15. From this, we find the expense of 4 toys as ₹ 15 × 4 or ₹ 60.

October 29, 2020

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