Question

Express $\frac{2}{5}$ as a rational number with numerator:
(i) −56
(ii) 154
(iii) −750
(iv) 500

Answer 1

2/5 as a rational number with numerator:

(i)
$$\begin{gathered} -56\mathrm{is}: \\ \frac{2\times 28}{5\times -28}=\frac{-56}{-140}(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}-28) \end{gathered}$$

(ii)
$$\begin{gathered} 154\mathrm{is}: \\ \frac{2\times 77}{5\times 77}=\frac{154}{385}(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}77) \end{gathered}$$

(iii)
$$\begin{gathered} -750\mathrm{is}: \\ \frac{2\times -375}{5\times -375}=\frac{-750}{-1875}(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}-375) \end{gathered}$$

(iv)
$$\begin{gathered} 500\mathrm{is}: \\ \frac{2\times 250}{5\times 250}=\frac{500}{1250}(\mathrm{multiplying}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\text{by}250) \end{gathered}$$