BECE Mathematics 2018 Paper

Concept:To compare unlike fractions, rewrite them with a common denominator and compare their numerators.Explanation:The given fractions are $\frac{2}{3}$, $\frac{4}{9}$, and $\frac{3}{7}$.Find the L.C.M. of the denominators $3$, $9$, and $7$.Prime factorisation gives $3 = 3$, $9 = 3^2$, and $7 = 7$.So, L.C.M. $= 3^2 \times 7 = 9 \times 7 = 63$.Now convert each fraction into an equivalent fraction with denominator $63$.$\frac{2}{3} = \frac{2 \times 21}{3 \times 21} = \frac{42}{63}$$\frac{4}{9} = \frac{4 \times 7}{9 \times 7} = \frac{28}{63}$$\frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63}$Since all the denominators are equal, compare the numerators: $27 < 28 < 42$.Ascending order means smallest to largest.Therefore, the required order is $\frac{3}{7} < \frac{4}{9} < \frac{2}{3}$.Answer:$\frac{3}{7}, \frac{4}{9}, \frac{2}{3}$Option D.