Solve 0.1*3^2+1^2/2^-4/5+1/2+1=0.55

$$0.1 \times { 3 }^{ 2 } + \frac{ { 1 }^{ 2 } }{ { 2 }^{ } } - \frac{ 4 }{ 5 } + \frac{ 1 }{ 2 } +1=0.55$$

Verify

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$0.1\times 9+\frac{1^{2}}{2^{1}}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Multiply 0.1 and 9 to get 0.9.

$$0.9+\frac{1^{2}}{2^{1}}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Calculate 1 to the power of 2 and get 1.

$$0.9+\frac{1}{2^{1}}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Calculate 2 to the power of 1 and get 2.

$$0.9+\frac{1}{2}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$\frac{9}{10}+\frac{1}{2}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Least common multiple of 10 and 2 is 10. Convert \frac{9}{10} and \frac{1}{2} to fractions with denominator 10.

$$\frac{9}{10}+\frac{5}{10}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Since \frac{9}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{9+5}{10}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Add 9 and 5 to get 14.

$$\frac{14}{10}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

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

$$\frac{7}{5}-\frac{4}{5}+\frac{1}{2}+1=0.55$$

Since \frac{7}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-4}{5}+\frac{1}{2}+1=0.55$$

Subtract 4 from 7 to get 3.

$$\frac{3}{5}+\frac{1}{2}+1=0.55$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{6}{10}+\frac{5}{10}+1=0.55$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{6+5}{10}+1=0.55$$

Add 6 and 5 to get 11.

$$\frac{11}{10}+1=0.55$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{11}{10}+\frac{10}{10}=0.55$$

Since \frac{11}{10} and \frac{10}{10} have the same denominator, add them by adding their numerators.

$$\frac{11+10}{10}=0.55$$

Add 11 and 10 to get 21.

$$\frac{21}{10}=0.55$$

Convert decimal number 0.55 to fraction \frac{55}{100}. Reduce the fraction \frac{55}{100} to lowest terms by extracting and canceling out 5.

$$\frac{21}{10}=\frac{11}{20}$$

Least common multiple of 10 and 20 is 20. Convert \frac{21}{10} and \frac{11}{20} to fractions with denominator 20.

$$\frac{42}{20}=\frac{11}{20}$$

Compare \frac{42}{20} and \frac{11}{20}.

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