Solve 37/10-2/57/10=frac{7/10}{10}-frac{7}{4}

$$3 \frac{ 7 }{ 10 } - \frac{ 2 }{ 5 } \frac{ 7 }{ 10 } = \frac{ \frac{ 7 }{ 10 } }{ 10 } - \frac{ 7 }{ 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 10,5,4.

$$2\left(3\times 10+7\right)-8\times \frac{7}{10}=2\times \frac{7}{10}-35$$

Multiply 3 and 10 to get 30.

$$2\left(30+7\right)-8\times \frac{7}{10}=2\times \frac{7}{10}-35$$

Add 30 and 7 to get 37.

$$2\times 37-8\times \frac{7}{10}=2\times \frac{7}{10}-35$$

Multiply 2 and 37 to get 74.

$$74-8\times \frac{7}{10}=2\times \frac{7}{10}-35$$

Express 8\times \frac{7}{10} as a single fraction.

$$74-\frac{8\times 7}{10}=2\times \frac{7}{10}-35$$

Multiply 8 and 7 to get 56.

$$74-\frac{56}{10}=2\times \frac{7}{10}-35$$

Reduce the fraction \frac{56}{10} to lowest terms by extracting and canceling out 2.

$$74-\frac{28}{5}=2\times \frac{7}{10}-35$$

Convert 74 to fraction \frac{370}{5}.

$$\frac{370}{5}-\frac{28}{5}=2\times \frac{7}{10}-35$$

Since \frac{370}{5} and \frac{28}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{370-28}{5}=2\times \frac{7}{10}-35$$

Subtract 28 from 370 to get 342.

$$\frac{342}{5}=2\times \frac{7}{10}-35$$

Express 2\times \frac{7}{10} as a single fraction.

$$\frac{342}{5}=\frac{2\times 7}{10}-35$$

Multiply 2 and 7 to get 14.

$$\frac{342}{5}=\frac{14}{10}-35$$

Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{342}{5}=\frac{7}{5}-35$$

Convert 35 to fraction \frac{175}{5}.

$$\frac{342}{5}=\frac{7}{5}-\frac{175}{5}$$

Since \frac{7}{5} and \frac{175}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{342}{5}=\frac{7-175}{5}$$

Subtract 175 from 7 to get -168.

$$\frac{342}{5}=-\frac{168}{5}$$

Compare \frac{342}{5} and -\frac{168}{5}.

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