Question

insert three rational number between 1/3 and 4/5

Answer 1

Given: Two rational numbers $\frac{1}{3}$ and $\frac{4}{5}$

To find: Three rational numbers between the given numbers

Solution: The given numbers have different denominators. First we need to make their denominators same.

The LCM of their denominators 3 and 5 = 15

To convert rational numbers with same denominators, we have

$\frac{1}{3} = \frac{1}{3}$ × $\frac{5}{5} = \frac{5}{15}$ and $\frac{4}{5} = \frac{4}{5}$ × $\frac{3}{3} = \frac{12}{15}$

We know that 6, 7, 8, 9, 10 and 11 are the integers between 5 and 12.

We can choose any three.

Hence, three rational numbers between $\frac{1}{3}$ and $\frac{4}{5}$ are: $\frac{6}{15}, \frac{7}{15} \ and \ \frac{8}{15}$ .

Answer 2

Answer:

Three rational numbers between the given rational numbers, $\frac{1}{3}$ and $\frac{4}{5}$ are:

 $\frac{7}{15}$ , $\frac{8}{15}$ and $\frac{9}{15}$

Step-by-step explanation:

The given two rational numbers are: $\frac{1}{3}$ and $\frac{4}{5}$,

Any rational number multiplied and divided by a real number simultaneously gives us the different representation of the same rational number.

Using this, we can find the rational numbers between the given rational numbers, The LCM of the given rational number's denominators is 15.

Now, in order to make the denominators equal, multiplying and dividing the rational numbers  $\frac{1}{3}$ and $\frac{4}{5}$ by 5 and 3 respectively, we get:

$\frac{1}{3}\times \frac{5}{5} =\frac{5}{15}$

and

$\frac{4}{5}\times\frac{3}{3} =\frac{12}{15}$

Now, Three rational numbers between $\frac{5}{15}$ and  $\frac{12}{15}$  would be:

$\frac{7}{15}$ , $\frac{8}{15}$ and $\frac{9}{15}$