Solve 1/2-(-3)=6/5+4/9(-3/8)-1

$$\frac { 1 } { 2 } - ( - 3 ) = \frac { 6 } { 5 } + \frac { 4 } { 9 } ( - \frac { 3 } { 8 } ) - 1$$

Verify

Solution Steps

The opposite of -3 is 3.

$$\frac{1}{2}+3=\frac{6}{5}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{1}{2}+\frac{6}{2}=\frac{6}{5}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{2}=\frac{6}{5}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Add 1 and 6 to get 7.

$$\frac{7}{2}=\frac{6}{5}+\frac{4}{9}\left(-\frac{3}{8}\right)-1$$

Multiply \frac{4}{9} times -\frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}=\frac{6}{5}+\frac{4\left(-3\right)}{9\times 8}-1$$

Do the multiplications in the fraction \frac{4\left(-3\right)}{9\times 8}.

$$\frac{7}{2}=\frac{6}{5}+\frac{-12}{72}-1$$

Reduce the fraction \frac{-12}{72} to lowest terms by extracting and canceling out 12.

$$\frac{7}{2}=\frac{6}{5}-\frac{1}{6}-1$$

Least common multiple of 5 and 6 is 30. Convert \frac{6}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{7}{2}=\frac{36}{30}-\frac{5}{30}-1$$

Since \frac{36}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}=\frac{36-5}{30}-1$$

Subtract 5 from 36 to get 31.

$$\frac{7}{2}=\frac{31}{30}-1$$

Convert 1 to fraction \frac{30}{30}.

$$\frac{7}{2}=\frac{31}{30}-\frac{30}{30}$$

Since \frac{31}{30} and \frac{30}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}=\frac{31-30}{30}$$

Subtract 30 from 31 to get 1.

$$\frac{7}{2}=\frac{1}{30}$$

Least common multiple of 2 and 30 is 30. Convert \frac{7}{2} and \frac{1}{30} to fractions with denominator 30.

$$\frac{105}{30}=\frac{1}{30}$$

Compare \frac{105}{30} and \frac{1}{30}.

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