Question

What is rational number?

Answer 1

Answer:

no which can be written in the form of p/q where q≠0 are called rational numbers

Step-by-step explanation:

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Answer 2

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What is a rational number?

A number which can be expressed as $\dfrac{a}{b}$ where 'a' and 'b' both are integers and b is not equals to 0, is called a rational number.

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In general, the set of rational numbers is denoted by the letter Q.

$\therefore \sf Q = \{ \frac{a}{b} : a, b \in Z \: and \: b \neq 0 \}$

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1) $\: \sf \dfrac{a}{b} \: is \: a \: rational \ number$

1. b ≠ 0
2. $a$ and $b$ have no common factors other than 1 (one) $i.e., \: a$ and $b$ are co-primes.
3. $b$ is usually positive, whereas $a$ may be positive, negative or zero.

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2) Every integer (positive, negative or zero) and a every decimal number is a rational number.

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3) Corresponding to every rational number $\dfrac{a}{b}$, its negative rational number is $\dfrac{-a}{b}$

Also, $\dfrac{-a}{b} = \dfrac{a}{-b} \: e.g. \: \dfrac{-3}{5} = \dfrac{3}{-5} = - \dfrac{3}{5}$ and so on.

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4)

1. A rational number $\dfrac{a}{b}$ , where $a \in I, b \in I \: and \: b \neq 0$, is positive if a and b both have the same sign.

Thus, each of $\dfrac{5}{7} , \dfrac{-5}{-7} , \dfrac{-3}{-11} , \dfrac{12}{17}$ , etc is a positive rational number.

2. $\quad \quad \quad$ A rational number $\dfrac{a}{b}$ is negative, if $a$ and $b$ have opposite signs.

Thus, each of $\: \sf \dfrac{-3}{5} , \dfrac{7}{-12} , \dfrac{-12}{11} , \dfrac{15}{-17}$ , etc. is a negative rational number.

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5) Two rational numbers are $\dfrac{a}{b}$ and $\dfrac{c}{d}$ are equal, if and only if : $a \times d = b \times c.$

$i.e., \dfrac{a}{b} = \dfrac{c}{d} \Leftrightarrow a \times d = b \times c$

Also, $\dfrac{a}{b} > \dfrac{c}{d} \Leftrightarrow a \times d > b \times c \quad and \quad \dfrac{a}{b} < \dfrac{c}{d} \Leftrightarrow a \times d < b \times c$