Solve 11*25+11^2div1111*(25+11^2)div11

$$11 \times 25+ { 11 }^{ 2 } \div 1111 \times (25+ { 11 }^{ 2 } ) \div 11$$

Evaluate

$$\frac{27921}{101}\approx 276.445544554$$

Solution Steps

Multiply 11 and 25 to get 275.

$$275+\frac{\frac{11^{2}}{1111}\left(25+11^{2}\right)}{11}$$

Calculate 11 to the power of 2 and get 121.

$$275+\frac{\frac{121}{1111}\left(25+11^{2}\right)}{11}$$

Reduce the fraction \frac{121}{1111} to lowest terms by extracting and canceling out 11.

$$275+\frac{\frac{11}{101}\left(25+11^{2}\right)}{11}$$

Calculate 11 to the power of 2 and get 121.

$$275+\frac{\frac{11}{101}\left(25+121\right)}{11}$$

Add 25 and 121 to get 146.

$$275+\frac{\frac{11}{101}\times 146}{11}$$

Express \frac{11}{101}\times 146 as a single fraction.

$$275+\frac{\frac{11\times 146}{101}}{11}$$

Multiply 11 and 146 to get 1606.

$$275+\frac{\frac{1606}{101}}{11}$$

Express \frac{\frac{1606}{101}}{11} as a single fraction.

$$275+\frac{1606}{101\times 11}$$

Multiply 101 and 11 to get 1111.

$$275+\frac{1606}{1111}$$

Reduce the fraction \frac{1606}{1111} to lowest terms by extracting and canceling out 11.

$$275+\frac{146}{101}$$

Convert 275 to fraction \frac{27775}{101}.

$$\frac{27775}{101}+\frac{146}{101}$$

Since \frac{27775}{101} and \frac{146}{101} have the same denominator, add them by adding their numerators.

$$\frac{27775+146}{101}$$

Add 27775 and 146 to get 27921.

$$\frac{27921}{101}$$

Factor

$$\frac{3 \cdot 41 \cdot 227}{101} = 276\frac{45}{101} = 276.44554455445547$$