Number system practice

Rational Numbers between 2 fractions

Question: Find 5 rational numbers between \\frac{3}{4}) and \\frac{4}{5}).

Video Explanation

Explanatory Answer

Step 1: Express \\frac{3}{4}) and \\frac{4}{5}) as equivalent fractions that have the same denominator.

To do that find the LCM and HCF of 4 and 5.
LCM(4, 5) = 20

\\frac{3}{4}) = \\frac{3 \times 5}{4 \times 5}) = \\frac{15}{20})

\\frac{4}{5}) = \\frac{4 \times 4}{5 \times 4}) = \\frac{16}{20})

Step 2: Compute equivalent fractions with room to fit 5 integers between 15 and 16

If you have to find ā€˜nā€™ rational numbers, multiply and divide both the equivalent fractions that we have computed in step 1 by (n + 1).
We have to find 5 rational numbers. So, multiply and divide both these fractions by (5 + 1) = 6.

\\frac{15}{20}) \\times) \\frac{6}{6}) = \\frac{90}{120})

\\frac{16}{20}) \\times) \\frac{6}{6}) = \\frac{96}{120})

5 rational numbers between \\frac{90}{120}) and \\frac{96}{120}) are \\frac{91}{120}), \\frac{92}{120}), \\frac{93}{120}), \\frac{94}{120}), \\frac{95}{120})