Solve 2*+3/23+1/5=-3/10left(3/23-1right)+0.2

$$2 \times + \frac{ 3 }{ 23 } + \frac{ 1 }{ 5 } = - \frac{ 3 }{ 10 } \left( \frac{ 3 }{ 23 } -1 \right) +0.2$$

Verify

Solution Steps

Express 2\times \frac{3}{23} as a single fraction.

$$\frac{2\times 3}{23}+\frac{1}{5}=-\frac{3}{10}\left(\frac{3}{23}-1\right)+0.2$$

Multiply 2 and 3 to get 6.

$$\frac{6}{23}+\frac{1}{5}=-\frac{3}{10}\left(\frac{3}{23}-1\right)+0.2$$

Least common multiple of 23 and 5 is 115. Convert \frac{6}{23} and \frac{1}{5} to fractions with denominator 115.

$$\frac{30}{115}+\frac{23}{115}=-\frac{3}{10}\left(\frac{3}{23}-1\right)+0.2$$

Since \frac{30}{115} and \frac{23}{115} have the same denominator, add them by adding their numerators.

$$\frac{30+23}{115}=-\frac{3}{10}\left(\frac{3}{23}-1\right)+0.2$$

Add 30 and 23 to get 53.

$$\frac{53}{115}=-\frac{3}{10}\left(\frac{3}{23}-1\right)+0.2$$

Convert 1 to fraction \frac{23}{23}.

$$\frac{53}{115}=-\frac{3}{10}\left(\frac{3}{23}-\frac{23}{23}\right)+0.2$$

Since \frac{3}{23} and \frac{23}{23} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53}{115}=-\frac{3}{10}\times \frac{3-23}{23}+0.2$$

Subtract 23 from 3 to get -20.

$$\frac{53}{115}=-\frac{3}{10}\left(-\frac{20}{23}\right)+0.2$$

Multiply -\frac{3}{10} times -\frac{20}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{53}{115}=\frac{-3\left(-20\right)}{10\times 23}+0.2$$

Do the multiplications in the fraction \frac{-3\left(-20\right)}{10\times 23}.

$$\frac{53}{115}=\frac{60}{230}+0.2$$

Reduce the fraction \frac{60}{230} to lowest terms by extracting and canceling out 10.

$$\frac{53}{115}=\frac{6}{23}+0.2$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{53}{115}=\frac{6}{23}+\frac{1}{5}$$

Least common multiple of 23 and 5 is 115. Convert \frac{6}{23} and \frac{1}{5} to fractions with denominator 115.

$$\frac{53}{115}=\frac{30}{115}+\frac{23}{115}$$

Since \frac{30}{115} and \frac{23}{115} have the same denominator, add them by adding their numerators.

$$\frac{53}{115}=\frac{30+23}{115}$$

Add 30 and 23 to get 53.

$$\frac{53}{115}=\frac{53}{115}$$

Compare \frac{53}{115} and \frac{53}{115}.

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