Solve 1.1*2.5+1.1^2div111.1*(2.5+1.1^2)div11

$$1.1 \times 2.5+ { 1.1 }^{ 2 } \div 111.1 \times (2.5+ { 1.1 }^{ 2 } ) \div 11$$

Evaluate

$$\frac{278121}{101000}\approx 2.753673267$$

Solution Steps

Multiply 1.1 and 2.5 to get 2.75.

$$2.75+\frac{\frac{1.1^{2}}{111.1}\left(2.5+1.1^{2}\right)}{11}$$

Calculate 1.1 to the power of 2 and get 1.21.

$$2.75+\frac{\frac{1.21}{111.1}\left(2.5+1.1^{2}\right)}{11}$$

Expand \frac{1.21}{111.1} by multiplying both numerator and the denominator by 100.

$$2.75+\frac{\frac{121}{11110}\left(2.5+1.1^{2}\right)}{11}$$

Reduce the fraction \frac{121}{11110} to lowest terms by extracting and canceling out 11.

$$2.75+\frac{\frac{11}{1010}\left(2.5+1.1^{2}\right)}{11}$$

Calculate 1.1 to the power of 2 and get 1.21.

$$2.75+\frac{\frac{11}{1010}\left(2.5+1.21\right)}{11}$$

Add 2.5 and 1.21 to get 3.71.

$$2.75+\frac{\frac{11}{1010}\times 3.71}{11}$$

Convert decimal number 3.71 to fraction \frac{371}{100}.

$$2.75+\frac{\frac{11}{1010}\times \frac{371}{100}}{11}$$

Multiply \frac{11}{1010} times \frac{371}{100} by multiplying numerator times numerator and denominator times denominator.

$$2.75+\frac{\frac{11\times 371}{1010\times 100}}{11}$$

Do the multiplications in the fraction \frac{11\times 371}{1010\times 100}.

$$2.75+\frac{\frac{4081}{101000}}{11}$$

Express \frac{\frac{4081}{101000}}{11} as a single fraction.

$$2.75+\frac{4081}{101000\times 11}$$

Multiply 101000 and 11 to get 1111000.

$$2.75+\frac{4081}{1111000}$$

Reduce the fraction \frac{4081}{1111000} to lowest terms by extracting and canceling out 11.

$$2.75+\frac{371}{101000}$$

Convert decimal number 2.75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\frac{11}{4}+\frac{371}{101000}$$

Least common multiple of 4 and 101000 is 101000. Convert \frac{11}{4} and \frac{371}{101000} to fractions with denominator 101000.

$$\frac{277750}{101000}+\frac{371}{101000}$$

Since \frac{277750}{101000} and \frac{371}{101000} have the same denominator, add them by adding their numerators.

$$\frac{277750+371}{101000}$$

Add 277750 and 371 to get 278121.

$$\frac{278121}{101000}$$

Factor

$$\frac{3 \cdot 92707}{101 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 2\frac{76121}{101000} = 2.753673267326733$$