Question

Find answers to the following. Write and indicate how you solved them.

(i) Is equal to ?
(ii) Is equal to ?
(iii) Is equal to ?
(iv) Is equal to ?

Answer 1

Two fractions are equal when:

Numerator of the first fraction $\times$ Denominator of the second fraction = Numerator of the second fraction $\times$ Denominator of the first fraction
(i)
$$\begin{gathered} 5\times 5=25 \\ 4\times 9=36 \\ \mathrm{So}, \\ 5\times 5\ne 4\times 9 \\ \frac{5}{9}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\frac{4}{5}. \end{gathered}$$
(ii)
$$\begin{gathered} 9\times 9=81 \\ 5\times 16=80 \\ \mathrm{So}, \\ 9\times 9\ne 5\times 16 \\ \frac{9}{16}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\frac{5}{9}. \end{gathered}$$

(iii)
$$\begin{gathered} 4\times 20=80 \\ 16\times 5=80 \\ \mathrm{So}, \\ 4\times 20=16\times 5 \\ \frac{4}{5}\mathrm{is}\mathrm{equal}\mathrm{to}\frac{16}{20}. \end{gathered}$$
(iv)
$$\begin{gathered} 1\times 30=30 \\ 4\times 15=60 \\ \mathrm{So}, \\ 1\times 30\ne 4\times 15 \\ \frac{1}{15}\mathrm{is}\mathrm{not}\mathrm{equal}\mathrm{to}\frac{4}{30}. \end{gathered}$$