Use the distributivity of multiplication of rational numbers over their addition to simplify : (i) 3/5 x (35/24+10/1) (ii) -5/4 x (8/5+16/5)

Question

Use the distributivity of multiplication of rational numbers over their addition to simplify:

(i) \(\frac{3}{5}\times (\frac{35}{24}+\frac{10}{1})\)

(ii) \(\frac{-5}{4}\times (\frac{8}{5}+\frac{16}{5})\)

(iii) \(\frac{2}{7}\times (\frac{7}{16}-\frac{21}{4})\)

(iv) \(\frac{3}{4}\times (\frac{8}{9}-40)\)

Answer 1

(i) \(\frac{3}{5}\times \frac{35}{24}+\frac{3}{5}\times 10\)

= \(\frac{105}{120}+6\)

= \(\frac{7}{8}+\frac{6\times 8}{8}\)

= \(\frac{55}{8}\)

 (ii) \(\frac{-5}{4}\times (\frac{8+16}{5})\)

= \(\frac{-5}{4}\times \frac{24}{5}\)

= -6

 (iii) \(\frac{2}{7}\times (\frac{7-21\times 4}{24})\)

= \(\frac{2}{7}\times \frac{-77}{16}\)

= \(\frac{-11}{8}\)

(iv) \(\frac{3}{4}\times (\frac{8-360}{9})\)

= \(\frac{3}{4}\times \frac{-352}{9}\)

 = \(\frac{-88}{3}\)