Question

insert six rational numbers between 3/5 and 2/3

Answer 1

Heyya..

First lets take the LCM of the denominators..

LCM of 5 and 3 is 5 × 3 = 15

Hence..Lets make the denominator equal..

$\frac{3}{5} \ * \ \frac{3}{3}\ = \ \frac{9}{15}$

$\frac{2}{3} \ * \ \frac{5}{5} \ = \ \frac{10}{15}$

Therefore we got Like fractions..

Now we need 6 rationals ..Hence we are multiplying the fractions with 7 both to the numerator and denominator

[tex] \frac{9}{15} \ * \ \frac{7}{7} \ = \frac{63}{105} [/tex]

$\frac{10}{15} \ * \ \frac{7}{7} \ = \ \frac{70}{105}$

Hey...The six rationals between these two numbers are

 $\frac{64}{105} \ ,\ \frac{65}{105} \ ,\ \frac{66}{105} \ , \ \frac{67}{105} \ , \ \frac{68}{105} \ , \ \frac{69}{105}$

Hope it helps..

And here CutieBarbie :)

Answer 2

Answer:

The six rational numbers are

$\frac{73}{120}, \frac{74}{120}, \frac{75}{120}, \frac{76}{120}, \frac{77}{120}, \frac{78}{120}$

Step-by-step explanation:

we have to insert six rational numbers between

$\frac{3}{5}$ and $\frac{2}{3}$

$\frac{3}{5}$

Multiply and divide by 24 on both sides

$\frac{3\times 24}{5\times 24}=\frac{72}{120}$

$\frac{2\times 40}{3\times 40}=\frac{80}{120}$

The six rational number between $\frac{72}{120}$ and $\frac{80}{120}$

$\frac{73}{120}, \frac{74}{120}, \frac{75}{120}, \frac{76}{120}, \frac{77}{120}, \frac{78}{120}$