Finding a rational number lying between 3/8 and 2/5

To find a rational number lying between 3/8 and 2/5, we need to follow a few steps.

Step 1: Convert the given fractions into equivalent fractions with the same denominator.

The denominators of the given fractions are 8 and 5, respectively. We need to find a common denominator for both fractions. The simplest way to do this is to multiply the denominators together, which gives us 40.

So, we need to convert both fractions into equivalent fractions with a denominator of 40.

3/8 = (3 x 5) / (8 x 5) = 15/40

2/5 = (2 x 8) / (5 x 8) = 16/40

Step 2: Find a rational number between the two equivalent fractions.

Now that we have converted the given fractions into equivalent fractions with a common denominator, we can easily find a rational number lying between them.

To do this, we need to find a fraction whose numerator is between 15 and 16. One possible fraction is:

11/40

Step 3: Check that the answer is correct.

To check that our answer is correct, we need to make sure that our fraction is indeed between 3/8 and 2/5.

We can do this by converting 11/40 into equivalent fractions with the same denominators as 3/8 and 2/5:

11/40 = (11 x 5) / (40 x 5) = 55/200 = 3/16

11/40 = (11 x 8) / (40 x 8) = 88/320 = 11/40

Now we can see that 3/8 < 3/16="" />< 11/40="" />< 2/5,="" so="" our="" answer="" is="" />

Therefore, the rational number lying between 3/8 and 2/5 is 11/40.

Find a Rational Number Between 3/8 and 2/5

A rational number between 3/8 and 2/5 is 31/80

Explanation:

First, take the numbers 3/8 and 2/5 and make the denominators equal.

Thus, 3/8 = 15/40

2/5 = 16/40

Now, multiply both the fractions by 2 (Both in numerator and denominator)

15/40 = 30/80

16/40 = 32/80

Hence, a rational number between 3/8 and 2/5 (30/80 and 32/80) is 31/80.