Question

Of $\frac{3}{4}$ and $\frac{5}{7}$, which is greater and by how much?

Answer 1

Let us compare $\frac{3}{4}\mathrm{and}\frac{5}{7}$.
3 $\times$ 7 = 21 and 4 $\times$ 5 = 20
Clearly, 21 > 20
∴ $\frac{3}{4}>\frac{5}{7}$
Required difference:
$$\begin{gathered} =\frac{3}{4}-\frac{5}{7}\mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}4\mathrm{and}7=\left(2\times 2\times 7\right)=28 \\ =\frac{21-20}{28}\left\{\left[28÷4=7,7\times 3=21\right]\mathrm{and}\left[28÷7=4,4\times 5=20\right]\right\} \\ =\frac{1}{28} \end{gathered}$$
Hence, $\frac{3}{4}\mathrm{is}\mathrm{greater}\mathrm{than}\frac{5}{7}\mathrm{by}\frac{1}{28}$.