Solve 103/10-(245/10-1/4)

$$10 \frac{ 3 }{ 10 } -(2 \frac{ 45 }{ 10 } - \frac{ 1 }{ 4 } )$$

Evaluate

$$\frac{81}{20}=4.05$$

Solution Steps

Multiply 10 and 10 to get 100.

$$\frac{100+3}{10}-\left(\frac{2\times 10+45}{10}-\frac{1}{4}\right)$$

Add 100 and 3 to get 103.

$$\frac{103}{10}-\left(\frac{2\times 10+45}{10}-\frac{1}{4}\right)$$

Multiply 2 and 10 to get 20.

$$\frac{103}{10}-\left(\frac{20+45}{10}-\frac{1}{4}\right)$$

Add 20 and 45 to get 65.

$$\frac{103}{10}-\left(\frac{65}{10}-\frac{1}{4}\right)$$

Reduce the fraction \frac{65}{10} to lowest terms by extracting and canceling out 5.

$$\frac{103}{10}-\left(\frac{13}{2}-\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{13}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{103}{10}-\left(\frac{26}{4}-\frac{1}{4}\right)$$

Since \frac{26}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103}{10}-\frac{26-1}{4}$$

Subtract 1 from 26 to get 25.

$$\frac{103}{10}-\frac{25}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{103}{10} and \frac{25}{4} to fractions with denominator 20.

$$\frac{206}{20}-\frac{125}{20}$$

Since \frac{206}{20} and \frac{125}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{206-125}{20}$$

Subtract 125 from 206 to get 81.

$$\frac{81}{20}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {2} \cdot 5} = 4\frac{1}{20} = 4.05$$