Solve 29/9-2/10=(1/1-1/3)-(-frac{1}{10})

$$\frac { 29 } { 9 } - \frac { 2 } { 10 } = ( \frac { 1 } { 1 } - \frac { 1 } { 3 } ) - ( - \frac { 1 } { 10 } )$$

Verify

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{29}{9}-\frac{2}{10}=1-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{29}{9}-\frac{1}{5}=1-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Least common multiple of 9 and 5 is 45. Convert \frac{29}{9} and \frac{1}{5} to fractions with denominator 45.

$$\frac{145}{45}-\frac{9}{45}=1-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Since \frac{145}{45} and \frac{9}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{145-9}{45}=1-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Subtract 9 from 145 to get 136.

$$\frac{136}{45}=1-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{136}{45}=\frac{3}{3}-\frac{1}{3}-\left(-\frac{1}{10}\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{136}{45}=\frac{3-1}{3}-\left(-\frac{1}{10}\right)$$

Subtract 1 from 3 to get 2.

$$\frac{136}{45}=\frac{2}{3}-\left(-\frac{1}{10}\right)$$

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$\frac{136}{45}=\frac{2}{3}+\frac{1}{10}$$

Least common multiple of 3 and 10 is 30. Convert \frac{2}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{136}{45}=\frac{20}{30}+\frac{3}{30}$$

Since \frac{20}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{136}{45}=\frac{20+3}{30}$$

Add 20 and 3 to get 23.

$$\frac{136}{45}=\frac{23}{30}$$

Least common multiple of 45 and 30 is 90. Convert \frac{136}{45} and \frac{23}{30} to fractions with denominator 90.

$$\frac{272}{90}=\frac{69}{90}$$

Compare \frac{272}{90} and \frac{69}{90}.

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