Question

Which of the following statements are true?
(i) 0 ÷ 4 = 0
(ii) 0 ÷ (−7) = 0
(iii) −15 ÷ 0 = 0
(iv) 0 ÷ 0 = 0
(v) (−8) ÷ (−1) = −8
(vi) −8 ÷ (−2) = 4

Answer 1

(i)
$$\begin{gathered} \mathrm{LHS}=\frac{\left|0\right|}{\left|4\right|}=\frac{0}{4}=0 \\ =\mathrm{RHS} \end{gathered}$$

Because LHS is equal to RHS, the equation is true.

(ii)
$$\begin{gathered} \mathrm{LHS}=-\frac{\left|0\right|}{\left|-7\right|}=-\frac{0}{7}=-0=0 \\ =\mathrm{RHS} \end{gathered}$$

Because LHS is equal to RHS, the equation is true.

(iii)
$$\begin{gathered} \mathrm{LHS}=-\frac{\left|-15\right|}{\left|0\right|}=-\frac{15}{0}=\mathrm{Not}\mathrm{defined} \\ \ne \mathrm{RHS} \end{gathered}$$
Because LHS is not equal to RHS, the equation is false.

(iv)
$$\begin{gathered} \mathrm{LHS}=\frac{\left|0\right|}{\left|0\right|}=\frac{0}{0}=\mathrm{Not}\mathrm{Defined} \\ \ne \mathrm{RHS} \end{gathered}$$

Because LHS is not equal to RHS, the equation is false.

(v)
$$\begin{gathered} \mathrm{LHS}=\frac{\left|-8\right|}{\left|-1\right|}=\frac{8}{1}=8 \\ \ne \mathrm{RHS} \end{gathered}$$
Because LHS and RHS are not equal, the equation is false.

(vi)
$$\begin{gathered} \mathrm{LHS}=\frac{\left|-8\right|}{\left|-2\right|}=\frac{8}{2}=4 \\ =\mathrm{RHS} \end{gathered}$$

Because LHS is equal to RHS, the equation is true.