Question

insert 1 rational no. between 5\7 and 4\9 and arrange in ascending order

Answer 1

5×9/7×9 = 45/63

4×7/9×7 = 28/63

28/63 29/63 45/63


Thanks

Answer 2

Answer:

$\frac{2}{5}$  <  $\frac{4}{9}$  <  $\frac{5}{7}$

Step-by-step explanation:

Given:- The given rational numbers are 5/7 and 4/9.

To Find:- Insert a rational number between 5/7 and 4/9 and arrange them in ascending order.

Solution:-

Here we can insert any rational number between 5/7 and 4/9.

Let's take the rational number = 2/5.

Now to arrange the rational numbers 5/7, 2/5 and 4/9, first we need to find the LCM of 7, 5 and 9.

LCM of 5, 7, 9 = 315

Now we will make the denominator of all the rational numbers equal.

So we will multiply 5/7 with 45/45, 2/5 with 63/63 and 4/9 with 35/35

$\frac{5}{7} * \frac{45}{45}$ = $\frac{225}{315}$ , $\frac{2}{5} *\frac{63}{63}$ = $\frac{126}{315}$, $\frac{4}{9} *\frac{35}{35}$ = $\frac{140}{315}$

Now after observing the numerators of all the number we can write that

126 < 140 < 225

$\frac{126}{315}$  <  $\frac{140}{315}$  <  $\frac{225}{315}$

∴ $\frac{2}{5}$  <  $\frac{4}{9}$  <  $\frac{5}{7}$

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