Find five rational numbers between 3/5 and 4/5.
Solution:
Given:
The rational numbers 3/5 and 4/5
Now, let us find the five rational numbers between 3/5 and 4/5
So we need to multiply both numerator and denominator with 5 + 1 = 6
We get,
3/5 = (3 × 6) / (5 × 6) = 18/30
4/5 = (4 × 6) / (5 × 6) = 24/30
Now, we have 18/30 < 19/30 < 20/30 < 21/30 < 22/30 < 23/30 < 24/30
Hence, the five rational numbers between 3/5 and 4/5 are
19/30, 20/30, 21/30, 22/30, 23/30
Find ten rational numbers between -2/5 and 1/7.
Solution:
Given:
The rational numbers -2/5 and 1/7
By taking LCM for 5 and 7 which is 35
So, -2/5 = (-2 × 7) / (5 × 7) = -14/35
1/7 = (1 × 5) / (7 × 5) = 5/35
Now, we can insert any10 numbers between -14/35 and 5/35
i.e., -13/35, -12/35, -11/35, -10/35, -9/35, -8/35, -7/35, -6/35, -5/35, -4/35, -3/35, -2/35, –
1/35, 1/35, 2/35, 3/35, 4/35
Hence, the ten rational numbers between -2/5 and 1/7 are
-6/35, -5/35, -4/35, -3/35, -2/35, -1/35, 1/35, 2/35, 3/35, 4/35
More Solutions:
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- Prove that √2 is an irrational number.
- Prove that, √3 is an irrational number.
- Prove that √5 is an irrational number.
- Prove that the following numbers are irrational:
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- Write the decimal expansion of each of the following numbers.
- State whether the following rational numbers
- Without actually performing the long division.