Solve (-2/5+4/9)+(-3/4)=-2/5+(frac{4}{9}+(-frac{3}{4}))

$$( - \frac { 2 } { 5 } + \frac { 4 } { 9 } ) + ( - \frac { 3 } { 4 } ) = - \frac { 2 } { 5 } + ( \frac { 4 } { 9 } + ( - \frac { 3 } { 4 } ) )$$

Verify

Solution Steps

Least common multiple of 5 and 9 is 45. Convert -\frac{2}{5} and \frac{4}{9} to fractions with denominator 45.

$$-\frac{18}{45}+\frac{20}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Since -\frac{18}{45} and \frac{20}{45} have the same denominator, add them by adding their numerators.

$$\frac{-18+20}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Add -18 and 20 to get 2.

$$\frac{2}{45}-\frac{3}{4}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Least common multiple of 45 and 4 is 180. Convert \frac{2}{45} and \frac{3}{4} to fractions with denominator 180.

$$\frac{8}{180}-\frac{135}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Since \frac{8}{180} and \frac{135}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-135}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Subtract 135 from 8 to get -127.

$$-\frac{127}{180}=-\frac{2}{5}+\frac{4}{9}-\frac{3}{4}$$

Least common multiple of 5 and 9 is 45. Convert -\frac{2}{5} and \frac{4}{9} to fractions with denominator 45.

$$-\frac{127}{180}=-\frac{18}{45}+\frac{20}{45}-\frac{3}{4}$$

Since -\frac{18}{45} and \frac{20}{45} have the same denominator, add them by adding their numerators.

$$-\frac{127}{180}=\frac{-18+20}{45}-\frac{3}{4}$$

Add -18 and 20 to get 2.

$$-\frac{127}{180}=\frac{2}{45}-\frac{3}{4}$$

Least common multiple of 45 and 4 is 180. Convert \frac{2}{45} and \frac{3}{4} to fractions with denominator 180.

$$-\frac{127}{180}=\frac{8}{180}-\frac{135}{180}$$

Since \frac{8}{180} and \frac{135}{180} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{127}{180}=\frac{8-135}{180}$$

Subtract 135 from 8 to get -127.

$$-\frac{127}{180}=-\frac{127}{180}$$

Compare -\frac{127}{180} and -\frac{127}{180}.

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