Question

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Answer 1

NOTE : REFER ATTACHMENT FOR ANSWER.

Answer 2

How to find rational numbers between two numbers.

Step 1: Find the LCM of the denominators to make them equal.

Step 2: Multiply any number to the numerator and denominator.

Step 3: Find the rational numbers between the two rational numbers.

So we will solve the questions using the following steps.

a) -1 and 0

Step 1: Here the denominators are equal so we don't need to find the LCM.

$\frac{-1}{1} , \frac{0}{1}$

Step 2: Here I am gonna multiply 6 to the denominator and numerator you can multiply any number you wish.

$\frac{-1*6}{1*6} , \frac{0*6}{1*6}$

$\frac{-6}{6} . \frac{0}{6}$

Step 3: The five rational numbers are-

$\frac{-5}{6},\frac{-4}{6} ,\frac{-3}{6} ,\frac{-2}{6} ,\frac{-1}{6}$

b) -3 and -2

Step 1: Here the denominators are equal so we don't need to find the LCM.

$\frac{-3}{1},\frac{-2}{1}$

Step 2: Here I am gonna multiply 6 to the denominator and numerator you can multiply any number you wish.

$\frac{-3*6}{1*6} , \frac{-2*6}{1*6}$

$\frac{-18}{6} ,\frac{-12}{6}$

Step 3: The five rational numbers are-

$\frac{-17}{6},\frac{-16}{6},\frac{-15}{6},\frac{-14}{6},\frac{-13}{6}$

c) $\frac{1}{2}$ and $\frac{2}{3}$

Step 1: The LCM of 2 and 3 is 6. So now we need to make the denominator equal.

$\frac{1*3}{2*3} , \frac{2*2}{3*2}$

$\frac{3}{6},\frac{4}{6}$

Step 2: I am gonna multiply 6 to the denominator and numerator.

$\frac{3*6}{6*6} , \frac{4*6}{6*6}$

$\frac{18}{36} , \frac{24}{36}$

Step 3: The five rational numbers between $\frac{1}{2}$ and $\frac{2}{3}$ are -

$\frac{19}{36}, \frac{20}{36} , \frac{21}{36} ,\frac{22}{36} ,\frac{23}{36}$

d) $\frac{-4}{5}$ and $\frac{-2}{3}$

Step 1: The LCM of 5 and 3 is 15. So now we need to make the denominator equal.

$\frac{-4*3}{5*3} , \frac{-2*5}{3*5}$

$\frac{-12}{15} , \frac{-10}{15}$

Step 2: I am gonna multiply 3 to the denominator and numerator.

$\frac{-12*3}{15*3} , \frac{-10*3}{15*3}$

$\frac{-36}{45} , \frac{-30}{45}$

Step 3: The five rational numbers between $\frac{-4}{5}$ and $\frac{-2}{3}$ are -

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