Solve 1/0.14*frac{16{18}+0.26*2/18}

$$\frac { 1 } { 0.14 \times \frac { 16 } { 18 } + 0.26 \times \frac { 2 } { 18 } }$$

Evaluate

$$\frac{150}{23}\approx 6.52173913$$

Solution Steps

Reduce the fraction \frac{16}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1}{0.14\times \frac{8}{9}+0.26\times \frac{2}{18}}$$

Convert decimal number 0.14 to fraction \frac{14}{100}. Reduce the fraction \frac{14}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{7}{50}\times \frac{8}{9}+0.26\times \frac{2}{18}}$$

Multiply \frac{7}{50} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{\frac{7\times 8}{50\times 9}+0.26\times \frac{2}{18}}$$

Do the multiplications in the fraction \frac{7\times 8}{50\times 9}.

$$\frac{1}{\frac{56}{450}+0.26\times \frac{2}{18}}$$

Reduce the fraction \frac{56}{450} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{28}{225}+0.26\times \frac{2}{18}}$$

Reduce the fraction \frac{2}{18} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{28}{225}+0.26\times \frac{1}{9}}$$

Convert decimal number 0.26 to fraction \frac{26}{100}. Reduce the fraction \frac{26}{100} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\frac{28}{225}+\frac{13}{50}\times \frac{1}{9}}$$

Multiply \frac{13}{50} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{\frac{28}{225}+\frac{13\times 1}{50\times 9}}$$

Do the multiplications in the fraction \frac{13\times 1}{50\times 9}.

$$\frac{1}{\frac{28}{225}+\frac{13}{450}}$$

Least common multiple of 225 and 450 is 450. Convert \frac{28}{225} and \frac{13}{450} to fractions with denominator 450.

$$\frac{1}{\frac{56}{450}+\frac{13}{450}}$$

Since \frac{56}{450} and \frac{13}{450} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{56+13}{450}}$$

Add 56 and 13 to get 69.

$$\frac{1}{\frac{69}{450}}$$

Reduce the fraction \frac{69}{450} to lowest terms by extracting and canceling out 3.

$$\frac{1}{\frac{23}{150}}$$

Divide 1 by \frac{23}{150} by multiplying 1 by the reciprocal of \frac{23}{150}.

$$1\times \frac{150}{23}$$

Multiply 1 and \frac{150}{23} to get \frac{150}{23}.

$$\frac{150}{23}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 ^ {2}}{23} = 6\frac{12}{23} = 6.521739130434782$$