Question

Compare the fractions:

(i) $\frac{5}{8}\mathrm{and}\frac{7}{12}$
(ii) $\frac{5}{9}\mathrm{and}\frac{11}{15}$
(iii) $\frac{11}{12}\mathrm{and}\frac{15}{16}$

Answer 1

We have the following:

(i) $\frac{5}{8}\mathrm{and}\frac{7}{12}$

By cross multiplication, we get:
5 $\times$ 12 = 60 and 7 $\times$ 8 = 56
However, 60 > 56
∴ $\frac{5}{8}>\frac{7}{12}$

(ii) $\frac{5}{9}\mathrm{and}\frac{11}{15}$
By cross multiplication, we get:
5 $\times$ 15 = 75 and 9 $\times$ 11 = 99
However, 75 < 99
∴ $\frac{5}{9}<\frac{11}{15}$

(iii) $\frac{11}{12}\mathrm{and}\frac{15}{16}$
By cross multiplication, we get:
11 $\times$ 16 = 176 and 12 $\times$ 15 = 180
However, 176 < 180
∴ $\frac{11}{12}<\frac{15}{16}$