Solve 6-5(4div2)+2^2+1/frac{1{5}+1/4}

$$\frac { 6 - 5 ( 4 \div 2 ) + 2 ^ { 2 } + 1 } { \frac { 1 } { 5 } + \frac { 1 } { 4 } }$$

Evaluate

$$\frac{20}{9}\approx 2.222222222$$

Solution Steps

Divide 4 by 2 to get 2.

$$\frac{6-5\times 2+2^{2}+1}{\frac{1}{5}+\frac{1}{4}}$$

Multiply 5 and 2 to get 10.

$$\frac{6-10+2^{2}+1}{\frac{1}{5}+\frac{1}{4}}$$

Subtract 10 from 6 to get -4.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{-4+4+1}{\frac{1}{5}+\frac{1}{4}}$$

Add -4 and 4 to get 0.

$$\frac{1}{\frac{1}{5}+\frac{1}{4}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{1}{\frac{4}{20}+\frac{5}{20}}$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{4+5}{20}}$$

Add 4 and 5 to get 9.

$$\frac{1}{\frac{9}{20}}$$

Divide 1 by \frac{9}{20} by multiplying 1 by the reciprocal of \frac{9}{20}.

$$1\times \frac{20}{9}$$

Multiply 1 and \frac{20}{9} to get \frac{20}{9}.

$$\frac{20}{9}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3 ^ {2}} = 2\frac{2}{9} = 2.2222222222222223$$