Question

Simplify:

(i) $\frac{2}{3}\times \frac{5}{44}\times \frac{33}{35}$
(ii) $\frac{12}{25}\times \frac{15}{28}\times \frac{35}{36}$
(iii) $\frac{10}{27}\times \frac{28}{65}\times \frac{39}{56}$
(iv) $1\frac{4}{7}\times 1\frac{13}{22}\times 1\frac{1}{15}$
(v) $2\frac{2}{17}\times 7\frac{2}{9}\times 1\frac{33}{52}$
(vi) $3\frac{1}{16}\times 7\frac{3}{7}\times 1\frac{25}{39}$

Answer 1

We have the following:

(i) $\frac{2}{3}\times \frac{5}{44}\times \frac{33}{35}=\frac{2\times 5\times 33}{3\times 44\times 35}=\frac{1\times 1\times 11}{1\times 22\times 7}=\frac{1\times 1\times 1}{1\times 2\times 7}=\frac{1}{14}$

(ii)$\frac{12}{25}\times \frac{15}{28}\times \frac{35}{36}=\frac{1\times 3\times 5}{5\times 4\times 3}=\frac{1\times 1\times 1}{1\times 4\times 1}=\frac{1}{4}$

(iii) $\frac{10}{27}\times \frac{28}{65}\times \frac{39}{56}=\frac{10\times 1\times 3}{27\times 5\times 2}=\frac{1\times 1\times 3}{27\times 1\times 1}=\frac{3}{27}=\frac{1}{9}$

(iv) $1\frac{4}{7}\times 1\frac{13}{22}\times 1\frac{1}{15}$

=$\frac{11}{7}\times \frac{35}{22}\times \frac{16}{15}=\frac{11\times 35\times 16}{7\times 22\times 15}=\frac{1\times 5\times 16}{1\times 2\times 15}=\frac{1\times 1\times 8}{1\times 1\times 3}=\frac{8}{3}=2\frac{2}{3}$

(v) $2\frac{2}{17}\times 7\frac{2}{9}\times 1\frac{33}{52}$

=$\frac{36}{17}\times \frac{65}{9}\times \frac{85}{52}=\frac{36\times 65\times 85}{17\times 9\times 52}=\frac{4\times 5\times 5}{1\times 1\times 4}=\frac{1\times 5\times 5}{1\times 1\times 1}=25$

(vi) $3\frac{1}{16}\times 7\frac{3}{7}\times 1\frac{25}{39}$

=$\frac{49}{16}\times \frac{52}{7}\times \frac{64}{39}=\frac{7\times 4\times 4}{1\times 1\times 3}=\frac{112}{3}=37\frac{1}{3}$