Question

Simplify using suitable properties of rational numbers: (-3)/5 + (4/7 X 3/5)-4/9 ( 2/3 X 1/5 ) - 15/16 + ( 1/5 X 4/3 ).​

Answer 1

Given :

(-3)/5 + (4/7 * 3/5) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 )

To find :

Simply the problem using suitable properties of rational number .

Solution :

This type of problems can be solved using the rule of BODMAS .

=> (-3)/5 + ( 4/7 * 3/5 ) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 )

=> (-3)/5 + ( 12/35 ) - 4/9 * ( 2/15 ) - 15/16 + ( 4/15 )

=> (-3)/5 + ( 12/35 ) - 8/135 - 15/16 + ( 4/15 )

=> 64/105 - 3/5 - 8/135 - 15/16

=> 1/105 - 8/135 - 15/16

=> (-47)/945 - 15/16

=> -14927 / 15120

(-3)/5 + ( 4/7 * 3/5 ) - 4/9 * ( 2/3 * 1/5 ) - 15/16 + ( 1/5 * 4/3 ) = (-14927)/15120

Answer 2

Step-by-step explanation:

Given that:Simplify using suitable properties of rational numbers: (-3)/5 + (4/7 X 3/5)-4/9 ( 2/3 X 1/5 ) - 15/16 + ( 1/5 X 4/3 ).

Solution:

To simplify the given expression

First solve for brackets

$\frac{ - 3}{5} + \big( \frac{4}{7} \times \frac{3}{5} \big) - \frac{4}{9} \big( \frac{2}{3} \times \frac{1}{5} \big) - \frac{15}{16} + \big( \frac{1}{5} \times \frac{4}{3} \big) \\ \\ \frac{ - 3}{5} + \frac{12}{35} - \frac{4}{9} \times \frac{2}{15} - \frac{15}{16} + \frac{4}{15}$

Now solve the one multiplication

$\frac{ - 3}{5} + \frac{12}{35} - \frac{8}{135} - \frac{15}{16} + \frac{4}{15}$

Now take LCM and solve addition and subtraction

$LCM of (5,35,135,16,15)= {2}^{4} \times {3}^{3} \times 7 \times 5 \\ \\ LCM of (5,35,135,16,15) = 15120$

Thus

$=>\frac{ - 3}{5} + \frac{12}{35} - \frac{8}{135} - \frac{15}{16} + \frac{4}{15} \\ \\=> \frac{ - 9072 + 5184 - 896 - 14175 + 4032}{15120} \\ \\ => \frac{9216 -24143 }{15120} \\\\=>\frac{ - 14927}{15120} \\ \\\\\bold{\frac{ - 3}{5} + \big( \frac{4}{7} \times \frac{3}{5} \big) - \frac{4}{9} \big( \frac{2}{3} \times \frac{1}{5} \big) - \frac{15}{16} }\\\\\bold{ + \big( \frac{1}{5} \times \frac{4}{3} \big) =\frac{ - 14927}{15120}}$

Hope it helps you.