Solve 412/9-671/100+38/9-45/100

$$\frac{ 412 }{ 9 } - \frac{ 671 }{ 100 } + \frac{ 38 }{ 9 } - \frac{ 45 }{ 100 }$$

Evaluate

$$\frac{1071}{25}=42.84$$

Solution Steps

Least common multiple of 9 and 100 is 900. Convert \frac{412}{9} and \frac{671}{100} to fractions with denominator 900.

$$\frac{41200}{900}-\frac{6039}{900}+\frac{38}{9}-\frac{45}{100}$$

Since \frac{41200}{900} and \frac{6039}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{41200-6039}{900}+\frac{38}{9}-\frac{45}{100}$$

Subtract 6039 from 41200 to get 35161.

$$\frac{35161}{900}+\frac{38}{9}-\frac{45}{100}$$

Least common multiple of 900 and 9 is 900. Convert \frac{35161}{900} and \frac{38}{9} to fractions with denominator 900.

$$\frac{35161}{900}+\frac{3800}{900}-\frac{45}{100}$$

Since \frac{35161}{900} and \frac{3800}{900} have the same denominator, add them by adding their numerators.

$$\frac{35161+3800}{900}-\frac{45}{100}$$

Add 35161 and 3800 to get 38961.

$$\frac{38961}{900}-\frac{45}{100}$$

Reduce the fraction \frac{38961}{900} to lowest terms by extracting and canceling out 9.

$$\frac{4329}{100}-\frac{45}{100}$$

Since \frac{4329}{100} and \frac{45}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4329-45}{100}$$

Subtract 45 from 4329 to get 4284.

$$\frac{4284}{100}$$

Reduce the fraction \frac{4284}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1071}{25}$$

Factor

$$\frac{3 ^ {2} \cdot 7 \cdot 17}{5 ^ {2}} = 42\frac{21}{25} = 42.84$$