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Q.2: Find five rational numbers between
3//5 and 4/5.

Q. $2$ : Find five rational numbers between $3 / 5$ and $4$ / $5$ .

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Estimate square roots

Full solution

Q. Q.

2

: Find five rational numbers between

3 / 5

and

4

/

5

.

Convert to Common Denominator: To find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ , we need to find numbers that are greater than $\frac{3}{5}$ and less than $\frac{4}{5}$ . A good strategy is to convert these fractions to have a common denominator that is greater than the number of rational numbers we want to find. Since we want to find five numbers, let's use a common denominator of at least $10$ . We can convert $\frac{3}{5}$ and $\frac{4}{5}$ to fractions with a denominator of $10$ .
Convert $\frac{3}{5}$ to $\frac{6}{10}$ : First, convert $\frac{3}{5}$ to a fraction with a denominator of $10$ . To do this, multiply both the numerator and the denominator by $2$ . $\newline$ $\frac{3}{5} = \left(\frac{3 \times 2}{5 \times 2}\right) = \frac{6}{10}$
Convert $\frac{4}{5}$ to $\frac{8}{10}$ : Next, convert $\frac{4}{5}$ to a fraction with a denominator of $10$ . Similarly, multiply both the numerator and the denominator by $2$ . $\newline$ $\frac{4}{5} = \left(\frac{4 \times 2}{5 \times 2}\right) = \frac{8}{10}$
Find Five Numerators: Now we have the two fractions $\frac{6}{10}$ and $\frac{8}{10}$ . We need to find five rational numbers between them. We can do this by simply choosing five numerators that are between $6$ and $8$ .
Write as Fractions: The five numerators between $6$ and $8$ are $7$ , $7.1$ , $7.2$ , $7.3$ , and $7.4$ . We can write these as fractions over $10$ to get the five rational numbers: $\newline$ $\frac{7}{10}$ , $\frac{7.1}{10}$ , $8$ $0$ , $8$ $1$ , and $8$ $2$

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