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Find $3$ rational number between $-1$ and $-2$

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Determine the direction of a vector scalar multiple

Full solution

Q. Find

3

rational number between

-1

and

-2

Convert to Fractions: To find rational numbers between $-1$ and $-2$ , we can convert them to fractions with the same denominator and then find numbers in between. $\newline$ $-1$ as a fraction is $-\frac{1}{1}$ and $-2$ as a fraction is $-\frac{2}{1}$ . Let's use a common denominator of $10$ . $\newline$ $-\frac{1}{1} = -\frac{10}{10}$ and $-\frac{2}{1} = -\frac{20}{10}$ .
Find Rational Numbers: Now, we need to find three numbers between $-\frac{10}{10}$ and $-\frac{20}{10}$ . Let's pick $-\frac{11}{10}$ , $-\frac{12}{10}$ , and $-\frac{13}{10}$ as our three rational numbers.
Simplify Fractions: We should simplify these fractions to see if they are different from each other and from $-1$ and $-2$ . $-\frac{11}{10}$ is already in simplest form, $-\frac{12}{10}$ simplifies to $-\frac{6}{5}$ , and $-\frac{13}{10}$ is also in simplest form.

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