Question

find 3 rational number between 1/2 and 3/4

Answer 1

Given rationals numbers are, 1/2 & 3/4

We know that, Between two given rational numbers, there exists infinite number of rational numbers. We are required to find out 3 such.

Changing to equivalent fractions.

1/2 = 12/24

3/4 = 18/24

We changed the rationals to have equal denominators.

So now rational numbers between 12/24 & 18/24 would be rational numbers between 1/2, 3/4 ( Because they are equivalent fractions 1/2 = 12/24, 3/4 = 18/24)

Now, Rationals between 1/2 & 3/4 are

• 13/24
• 14/24
• 15/24
• 16/24
• 17/24

We can also find many such rational numbers. And If we wish to find exactly equidistant rational numbers,

Then We can use the Arithmetic progression.

Between two rationals a & b ( b > a), we need to find n equidistant rationals then the distance between consecutive rationals is

d = b - a / n +1

After finding the distance,

The required rationals will be a + d, a + 2d,a + 3d,.....

Hope helped !

Answer 2

Answer:

$Required \:3 \:rational\: numbers \\\:between \:\frac{1}{2}\: and \: \frac{3}{4} \: \\are \: \frac{13}{24},\frac{14}{24},\frac{15}{24}$

Step-by-step explanation:

$Given \\rational \: numbers\: \frac{1}{2} \: and \: \frac{3}{4}$

We write the given rational numbers with denominator 24

$i) \frac{1}{2}=\frac{1\times 12}{2\times 12} = \frac{12}{24}$

$and\\\frac{3}{4}=\frac{3\times 6}{4\times 6}=\frac{18}{24}$

$Required \:3 \:rational\: numbers\\ \:between \:\frac{1}{2}\: and \: \frac{3}{4} \: are\\ \: \frac{13}{24},\frac{14}{24},\frac{15}{24}$

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