Ten Rational Numbers between -4 and -6

To find ten rational numbers between -4 and -6, we can follow the steps below:

Step 1: Find the difference between -6 and -4.

-6 - (-4) = -6 + 4 = -2

Step 2: Divide the difference by 11.

-2 ÷ 11 = -0.18181818...

Step 3: Add the result to -4 to get the first rational number.

-4 + (-0.18181818...) = -4.18181818...

Step 4: Add the result to the previous rational number to get the next rational number.

-4.18181818... + (-0.18181818...) = -4.36363636...

Step 5: Repeat step 4 until we have ten rational numbers.

Here are ten rational numbers between -4 and -6:

-4.18181818...
-4.36363636...
-4.54545454...
-4.72727272...
-4.90909090...
-5.09090909...
-5.27272727...
-5.45454545...
-5.63636363...
-5.81818181...

Explanation

Rational numbers are numbers that can be expressed as a ratio of two integers. To find ten rational numbers between -4 and -6, we need to find the difference between -6 and -4, which is 2. Then we divide 2 by 11 to get the difference between each rational number. We add this difference to -4 to get the first rational number, and then we repeat this process to get the next nine rational numbers.

For example, the first rational number is -4.18181818..., which is obtained by adding the difference (-0.18181818...) to -4. We can check that this is a rational number by expressing it as a ratio of two integers. We can multiply both the numerator and denominator by 1000000 to get rid of the decimals and simplify the fraction.

-4.18181818... = -4181818/1000000 = -20909/5000

Similarly, we can express all the other rational numbers as ratios of two integers.

10 rational numbers between-4 and -6 are as follows
-44/11,-45/11,-46/11,-47/11,-48/11,-49/11,-50/11,-51/11,-52/11,-53/11