Question

the ratio equivalent to 2/3:1/4:5/6​

please explain step by step​

Answer 1

Answer:

Give two equivalent ratios of 8 : 18.

Solution:

We will find the first equivalent ratio of 8 : 18 by using multiplication.

So, first we need to write the given ratio as fraction,

= 8/18

= (8 × 2)/(18 × 2)

= 16/36

= 16 : 36 (one equivalent ratio),

So, 16 : 36 is an equivalent ratio of 8 : 18.

Now we will find another equivalent ratio of 8 : 18 by using division.

Similarly, first we need to write the given ratio as fraction,

= 8/18

= (8 ÷ 2)/(18 ÷ 2)

= 4/9

= 4 : 9 (another equivalent ratio)

So, 4 : 9 is an equivalent ratio of 8 : 18.

Therefore, the two equivalent ratios of 8 : 18 are 16 : 36 and 4 : 9.

2. Frame two equivalent ratios of 4 : 5.

Solution:

To find two equivalent ratios of 4 : 5 we need to apply multiplication method only to get the answer in integer form.

First we need to write the given ratio as fraction,

= 4/5

= (4 × 2)/(5 × 2)

= 8/10

= 8 : 10 is one equivalent ratio,

Similarly again, we need to write the given ratio 4 : 5 as fraction to get another equivalent ratio;

= 4/5

= (4 × 3)/(5 × 3)

= 12/15 is another equivalent ratio

Therefore, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

Note: In this question we can’t apply division method to get the answer in integer form because the G.C.F. of 4 and 5 is 1. That means, 4 and 5 cannot be divisible by any other number except 1.

3. For the following ratio find the two equivalent ratios of 11 : 13.

Solution:

To find two equivalent ratios of 11 : 13 first we need to write the given ratio as fraction,

11/13

= (11 × 2)/(13 × 2)

= 22/26

= 22 : 26 is one equivalent ratio

Similarly again, to get another equivalent ratio of 11 : 13;

11/13

= (11 × 4)/(13 × 4)

= 44/52

= 44 : 52 is another equivalent ratio

Therefore, the two equivalent ratios of 11 : 13 are 22 : 26 and 44 : 52.

Note: If a : b and x : y are two equivalent ratios, we write a/b = x/y.

Solved example to find three equivalent ratios:

4. Find three equivalent ratios of 3 : 8.

Solution:

3 : 8 = 3/8 = (3 × 2)/(8 × 2), [Multiply both numerator and denominator by 2]

= 6/16

= 6 : 16 is the first equivalent ratio.

3 : 8 = 3/8 = (3 × 4)/(8 × 4), [Multiply both numerator and denominator by 4]

= 12/32

= 12 : 32 is the second equivalent ratio.

3 : 8 = 3/8 = (3 × 6)/(8 × 6), [Multiply both numerator and denominator by 6]

= 18/48

= 18 : 48 is the third equivalent ratio.

Therefore, the three equivalent ratios of 3 : 8 are 6 : 16, 12 : 32 and 18 : 48.