Step $2$ : If the rational number is not in its simplest form, first find Then divide both the numerator and denominator by their HCF to expres Example $1$ : Express (i) $\frac{2}{-7}$ $\newline$ (ii) $\frac{4}{10}$ $\newline$ (iii) $\frac{2}{3}$ and $\newline$ (iv) $\frac{17}{49}$ in their standard Solution: (i) $\frac{2}{-7}$ is not in the standard form as its denominator is negat

Full solution

Q. Step

2

: If the rational number is not in its simplest form, first find Then divide both the numerator and denominator by their HCF to expres Example

1

: Express (i)

\frac{2}{-7}

\newline

(ii)

\frac{4}{10}

\newline

(iii)

\frac{2}{3}

and

\newline

(iv)

\frac{17}{49}

in their standard Solution: (i)

\frac{2}{-7}

is not in the standard form as its denominator is negat

Step $1$ : Simplify $(2)/(-7)$ : (i) Simplify $(2)/(-7)$ . Since the denominator is negative, we multiply both numerator and denominator by $-1$ to make the denominator positive. $(2)/(-7) \times (-1)/(-1) = (-2)/(7)$ .
Step $2$ : Simplify $(4)/(10)$ : (ii) Simplify $(4)/(10)$ . $\newline$ Find the HCF of $4$ and $10$ , which is $2$ . $\newline$ Divide both numerator and denominator by $2$ . $\newline$ $(4)/(10) \div (2)/(2) = (2)/(5)$ .
Step $3$ : Simplify $(\frac{2}{3})$ : (iii) Simplify $(\frac{2}{3})$ . This fraction is already in its simplest form because the HCF of $2$ and $3$ is $1$ . $(\frac{2}{3})$ remains unchanged.
Step $4$ : Simplify $(17)/(49)$ : (iv) Simplify $(17)/(49)$ . $\newline$ Find the HCF of $17$ and $49$ , which is $1$ since $17$ is a prime number. $\newline$ $(17)/(49)$ is already in its simplest form.