Ratio and Proportion Class 6, deals with various concepts which are as under:-

- Converting Ratios to Simplest Form
- Equivalent Ratios
- Find the numbers when their ratio and sum are given
- Divide sum of money between two persons when ratio are given
- Divide sum of money among 3 persons when ratio are given
- Are the given number are in proportion
- Find the value of y when four numbers are in proportion

**Ratio and Proportion Class 6 – Converting Ratios to Simplest Form**

In order to convert the given ratio to Simplest Form, we should follow the following steps : –

- Find the HCF of both the numerator and denominator
- Dividing Both numbers by their HCF

The result is the ratio in its simplest form.

**Question 1:**

Convert 16 : 28 into its simplest form

**Explanation:**

Convert the ratio 16 : 28 in its simplest form.

HCF of 16 and 28 is 4

Since, 16 : 28

=

Dividing Both 16 and 28 by their HCF

=

=

= 4 : 7

Hence, the simplest form of 16 : 28 is 4 : 7

**Ratio and Proportion Cla****ss 6 – ****Equivalent Ratios**

In order to find Equivalent Ratios of any given ratio, we multiply or divide the numerator and denominator of the ratio by the same non zero number.

**Question 2:**

Find the Equivalent ratio of 2 : 5?

, , ,

**Explanation:**

On multiplying or dividing each term of a ratio by the same non zero number, we get a ratio equivalent to the given ratio

For,

Both numerator and denominator of given fraction is multiplied by same nonzero number i.e 4

=

is an equivalent ratio of

is not an equivalent ratio of As both 2 and 5 are not multiply by same non zero number

is not an equivalent ratio of As both 2 and 5 are not multiply by same non zero number

is not an equivalent ratio of As both 2 and 5 are not multiply by same non zero number

**Ratio and Proportion Cla****ss 6 – ****Find the numbers when their ratio and** **sum are given**

**Question 3:**

Two numbers are in the ratio 3 : 1 and their sum is 68. Find the numbers?

**Explanation:**

Let the required number be 3a and 1a

Since the sum of these two numbers is given, we can say that

3a + 1a = 68

4a = 68

a =

a = 17

So, the first number is 3a = 3 x 17

= 51

Second number is 1a = 1 x 17

= 17

Hence, two numbers are 51 and 17

**Ratio and Proportion Cla****ss 6 – ****Divide** **sum of money between two persons when ratio are given**

**Question 4:**

Divide ₹ 1500 among X and Y in the ratio 1 : 2

**Explanation:**

Total money = ₹ 1500

Given ratio = 1 : 2

Sum of ratio terms = ( 1 + 2 ) = 3

Give: part of ₹ 1500 to X

Give: part of ₹ 1500 to Y

that is,

X ‘s share = ₹ ( 1500 x ) = ₹ 500

Y ‘s share = ₹ ( 1500 x ) = ₹ 1000

**Ratio and Proportion Cla****ss 6**** – ****Divide sum of money among 3 persons when ratio are given**

**Question 5:**

Divide ₹ 1200 among X , Y and Z in the ratio 2 : 3 : 1

**Explanation:**

Total money = ₹ 1200

Given ratio = 2 : 3 : 1

Sum of ratio terms = ( 2 + 3 + 1 ) = 6

X share = ₹ ( 1200 x ) = ₹ 400

Y share = ₹ ( 1200 x ) = ₹ 600

Z share = ₹ ( 1200 x ) = ₹ 200

**Ratio and Proportion Cla****ss 6**** –**** ****Comparison of ratios**

To Compare two Ratios, we should follow the following steps : –

- Write both the Ratios as Fractions
- Convert both the Fractions into Like Fraction:-

– Find the L.C.M of denominator of both the Fractions

– Make the denominator of each fraction equal to their L.C.M. - In case of Like fractions, the number whose numerator is greater is larger.

**Question 6:**

Compare the ratios ( 2 : 1 ) and ( 1 : 4 )

**Explanation:**

We can write

( 2 : 1 ) = and ( 1 : 4 ) =

Now, let us compare and

LCM of 1 and 4 is 4

Making the denominator of each fraction equal to 4

We have, = =

and = =

In case of Like fractions, the number whose numerator is greater is larger. Hence we can say >

That is >

Hence, ( 2 : 1 ) > ( 1 : 4 )

**Ratio and Proportion Cla****ss 6**** –**** **Four Numbers in Proportion

Let a, b, c, d are four numbers said to be in proportion.

then, a : b = c : d or a : b :: c : d

here a and d are called the extreme terms or extremes.

b and c are called the middle terms or means.

When Four numbers are in proportion

then, **Product of extremes = Product of means.
**i.e, In proportion a : b :: c : d,

(a x d) = (b x c)

**Ratio and Proportion Cla****ss 6**** – ****Are the given number are in proportion**

**Question 7:**

Are 4 , 12 , 6 , 18 in proportion?

**Explanation:**

We have, 4 : 12 = = =

and 6 : 18 = = =

Since, 4 : 12 = 6 : 18

Hence, 4 , 12 , 6 , 18 are in Proportion

Alternative method: Product of extremes = Product of means

Here, Means are 12 and 6

Extremes are 4 and 18

Product of extremes = 4 x 18 = 72

Product of means = 12 x 6 = 72

Since, Product of extremes = Product of means

Hence, 4 , 12 , 6 , 18 are in Proportion

**Ratio and Proportion Cla****ss 6**** – ****Find the value of y when four numbers are in proportion**

**Question 8:**

If 6 : 3 : : y : 2, find the value of y?

**Explanation:**

We know that, Product of means = Product of extremes

In the given numbers, we can say that 3 , y are means and 6 , 2 are extremes

3 x y = 6 x 2

y =

y = 4

Hence, y = 4

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