State whether the given statement is true or false:

Five rational numbers between $\frac{- 3}{2}$ and $\frac{5}{3}$ are $\frac{- 8}{6}, \frac{- 7}{6}, 0, \frac{1}{6}, \frac{2}{6}$ .

True

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False

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Solution

The correct option is A True
Given rational numbers are $\frac{- 3}{2}$ and $\frac{5}{3}$
LCM of the denominators is $6$

Hence $\frac{- 3}{2}$ and $\frac{5}{3}$ can be written as $\frac{- 9}{6}$ and $\frac{10}{6}$

The numbers between $\frac{- 9}{6}$ and $\frac{10}{6}$ are $\frac{- 8}{6}$ , $\frac{- 7}{6}$ , $0$ , $\frac{1}{6}$ , $\frac{2}{6}, . . .$

Hence the statement is true.

Suggest Corrections

Similar questions

State, in each case, whether true or false.

$(i) \sqrt{2} + \sqrt{3} = \sqrt{5}$

$(i i) 2 \sqrt{4} + 2 = 6$

$(i i i) 3 \sqrt{7} - 2 \sqrt{7} = \sqrt{7}$

$(i v) \frac{2}{7}$ is an irrational number.

$(v) \frac{5}{11}$ is a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

\frac{- 3}{2} \times \frac{5}{4} + \frac{- 3}{2} \times \frac{- 7}{6} = \frac{- 3}{2} \times (\frac{5}{4} + \frac{- 7}{6})

Question 71

In the following question, state whether the given statements are true (T) or false (F).

$(- 5)^{- 2} \times (- 5)^{- 3} = (- 5)^{- 6}$

= \frac{\sqrt{3}}{7}

2.357

3.121

3, 3.101101110 . . .

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