Question

explain the rational number in your​

Answer 1

Correct question:-

1. Explain the rational number in your own words

Answer:-

→ If p and q both are integers and $q \: \neq \: 0,$ then $\rm \dfrac{p}{q}$ is called a rational number.

For example:-

    → $\rm \dfrac{-3}{7}$ is a rational number as -3 and 7 both are integers and $7 \: \neq \:0$

    → $\dfrac{15}{22}$ is a rational number as 15 and 22 both are integers and $22 \: \neq \:0$

Remember:-

  → Zero (0) can be written as $\rm \dfrac{0}{1}, \dfrac{0}{2}, \dfrac{0}{5}, \dfrac{0}{-10}, \dfrac{0}{15}, \dfrac{0}{-22}, etc.$ In each of these cases denominator is not equal to zero.

    So, zero can be expressed as a fraction with a non-zero denominator.

      ⁂ Zero (0) is a rational number.

  → Every natural number, every whole number, every integer and every fraction is a rational number.

   → In the rational number $\rm \dfrac{p}{q}$, where p and q are integers and $\rm q \: \neq \: 0$, integer p is called numerator and integer q is called the denominator

For example:-

(i) In $\rm \dfrac{-8}{15},$ numerator = -8 and denominator =  15

(ii) If numerator = 5 and denominator = -2, the rational number is $\dfrac{5}{-2}.$

4. A rational number is positive, if its numerator and denominator have same signs, whereas a rational number is negative, if its numerator and denominator have opposite signs.

  Thus,

→ each of $\rm\dfrac{5}{8}, \dfrac{-5}{-8}, \dfrac{-12}{-17}, \dfrac{15}{19},etc. \: is \:positive$

→ each of $\rm\dfrac{-5}{8}, \dfrac{5}{-8}, \dfrac{12}{-17}, \dfrac{-15}{19},etc. \: is \: negative$

5. If m is a non-zero integer and $\rm\dfrac{p}{q}$ is a rational number, then

   $\rm\dfrac{p}{q}=\dfrac{p \times m}{q \times m} \: and \dfrac{p ÷ m}{q ÷ m}$

Here $\rm\dfrac{p \times m}{q \times m} and \dfrac{p ÷ m}{q ÷ m}$ are rational numbers each equivalent to $\rm\dfrac{p}{q}$

6. Let $\rm\dfrac{a}{b} \: and \dfrac{c}{d}$ are two rational numbers such that

        $\rm\dfrac{a}{b}=\dfrac{c}{d}$ ⇒ $\rm{ a \times d = b \times c}$

 Conversely, $\rm{a \times d = b \times c}$ ⇒ $\rm\dfrac{a}{b}=\dfrac{c}{d} \: or, \dfrac{a}{c}=\dfrac{b}{d},etc$

7. A rational number $\rm\dfrac{p}{q}$ is said to be in standard form, if :

 → p and q have no common divisor (factor) other than (1)

and q is positive

For example:-

   → $\dfrac{3}{5}$ is a rational number in standard form.

   → The rational number $\dfrac{3}{-5}$ in standard form is $\dfrac{-3}{5}$.

   → $\dfrac{-21}{36}$ is not in standard form as 21 and 36 have 3 as a common divisor

             Since, $\dfrac{-21}{36}=\dfrac{-7 \times 3}{12 \times 3}=\dfrac{-7}{12}$

                        ⁂ $\rm\dfrac{-21}{36} \: in \: standard \: form \: is \: \dfrac{-7}{12}$

Similarly, $\dfrac{36}{-63}=\dfrac{4 \times 9}{-7 \times 9}=\dfrac{4}{-7}=\dfrac{-4}{7}$

     ⇒ $\dfrac{36}{-63}$ in standard form is $\dfrac{-4}{7}$