Introduction:

To find six rational numbers between 4/6 and 8/10, we need to first understand what rational numbers are and how to compare and generate them.

Understanding Rational Numbers:

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. In this case, both 4/6 and 8/10 are rational numbers.

Comparing Rational Numbers:

To compare the rational numbers 4/6 and 8/10, we need to have a common denominator. The least common multiple (LCM) of the denominators 6 and 10 is 30. So, we can convert both fractions to have a denominator of 30:

4/6 = (4 * 5)/(6 * 5) = 20/30
8/10 = (8 * 3)/(10 * 3) = 24/30

Now, we have:

20/30 < />

Generating Rational Numbers:

To generate six rational numbers between 20/30 and 24/30, we can divide the difference between these two fractions by 7 (6 + 1) and add the resulting value successively to the numerator of 20/30.

Difference between fractions: (24/30) - (20/30) = 4/30

Increment value: (4/30) / 7 = 4/210

Calculating the Rational Numbers:

To generate the six rational numbers, we can add the increment value to the numerator of 20/30 successively:

1. 20/30 + 4/210 = 136/210
2. 136/210 + 4/210 = 140/210
3. 140/210 + 4/210 = 144/210
4. 144/210 + 4/210 = 148/210
5. 148/210 + 4/210 = 152/210
6. 152/210 + 4/210 = 156/210

Simplified Rational Numbers:

The six rational numbers between 4/6 and 8/10 are:
1. 136/210
2. 140/210
3. 144/210
4. 148/210
5. 152/210
6. 156/210

These fractions can be further simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of the numerators and denominators is 2. Dividing each fraction by 2:

1. 68/105
2. 70/105
3. 72/105
4. 74/105
5. 76/105
6. 78/105

Conclusion:

We have successfully found six rational numbers between 4/6 and 8/10, which are:
1. 68/105
2. 70/105
3. 72/105
4. 74/105
5. 76/105
6. 78/105

These fractions can be simplified further if needed.

4/6 = 4×5/6×5=20/30 = 20×10/30×10= 200/300 8/10=8×3/10×3=24/30= 24×10/30×10=240/300 rational no.between 4/6and 8/10 are 201/300.......239/300