Solve 100*0.2^3+0.3^2:(17/52+8/65)=

$$100 \cdot 0.2 ^ { 3 } + 0.3 ^ { 2 } : ( \frac { 17 } { 52 } + \frac { 8 } { 65 } ) =$$

Evaluate

$$1$$

Solution Steps

Calculate 0.2 to the power of 3 and get 0.008.

$$100\times 0.008+\frac{0.3^{2}}{\frac{17}{52}+\frac{8}{65}}$$

Multiply 100 and 0.008 to get 0.8.

$$0.8+\frac{0.3^{2}}{\frac{17}{52}+\frac{8}{65}}$$

Calculate 0.3 to the power of 2 and get 0.09.

$$0.8+\frac{0.09}{\frac{17}{52}+\frac{8}{65}}$$

Least common multiple of 52 and 65 is 260. Convert \frac{17}{52} and \frac{8}{65} to fractions with denominator 260.

$$0.8+\frac{0.09}{\frac{85}{260}+\frac{32}{260}}$$

Since \frac{85}{260} and \frac{32}{260} have the same denominator, add them by adding their numerators.

$$0.8+\frac{0.09}{\frac{85+32}{260}}$$

Add 85 and 32 to get 117.

$$0.8+\frac{0.09}{\frac{117}{260}}$$

Reduce the fraction \frac{117}{260} to lowest terms by extracting and canceling out 13.

$$0.8+\frac{0.09}{\frac{9}{20}}$$

Divide 0.09 by \frac{9}{20} by multiplying 0.09 by the reciprocal of \frac{9}{20}.

$$0.8+0.09\times \frac{20}{9}$$

Convert decimal number 0.09 to fraction \frac{9}{100}.

$$0.8+\frac{9}{100}\times \frac{20}{9}$$

Multiply \frac{9}{100} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$0.8+\frac{9\times 20}{100\times 9}$$

Cancel out 9 in both numerator and denominator.

$$0.8+\frac{20}{100}$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$0.8+\frac{1}{5}$$

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

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

Since \frac{4}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

$$\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$1$$

Factor

$$1$$