Question

find find five rational number between 2/3 and 4/5​

Answer 1

Step By Step Explained:-

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converting ⅔ and ⅘ in two rational numbers with same denominators.

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$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \\ ========= \\ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$

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the difference between the numerator=12-10=2

For five rational numbers between ⅔ and ⅘.

The difference should be one more than five=6.

So, we multiply the numerators and denominators of 10/15 and 12/15 by 6/2=3.

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$\frac{10}{15} = \frac{10 \times 3}{15 \times 3} = \frac{30}{45} \\ =========== \\ \frac{12}{15} = \frac{12 \times 3}{15 \times 3} = \frac{36}{45}$

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Five rational numbers between ⅔ and ⅘ are:

$\frac{31}{45} , \: \frac{32}{45} , \: \frac{33}{45} , \: \frac{34}{45} , \: \frac{35}{45}$

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