Solve 1+0.5left(75/201-0.18right)

$$1+0.5 \left( \frac{ 75 }{ 201 } -0.18 \right)$$

Evaluate

$$\frac{7347}{6700}\approx 1.096567164$$

Solution Steps

Reduce the fraction \frac{75}{201} to lowest terms by extracting and canceling out 3.

$$1+0.5\left(\frac{25}{67}-0.18\right)$$

Convert decimal number 0.18 to fraction \frac{18}{100}. Reduce the fraction \frac{18}{100} to lowest terms by extracting and canceling out 2.

$$1+0.5\left(\frac{25}{67}-\frac{9}{50}\right)$$

Least common multiple of 67 and 50 is 3350. Convert \frac{25}{67} and \frac{9}{50} to fractions with denominator 3350.

$$1+0.5\left(\frac{1250}{3350}-\frac{603}{3350}\right)$$

Since \frac{1250}{3350} and \frac{603}{3350} have the same denominator, subtract them by subtracting their numerators.

$$1+0.5\times \frac{1250-603}{3350}$$

Subtract 603 from 1250 to get 647.

$$1+0.5\times \frac{647}{3350}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$1+\frac{1}{2}\times \frac{647}{3350}$$

Multiply \frac{1}{2} times \frac{647}{3350} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\times 647}{2\times 3350}$$

Do the multiplications in the fraction \frac{1\times 647}{2\times 3350}.

$$1+\frac{647}{6700}$$

Convert 1 to fraction \frac{6700}{6700}.

$$\frac{6700}{6700}+\frac{647}{6700}$$

Since \frac{6700}{6700} and \frac{647}{6700} have the same denominator, add them by adding their numerators.

$$\frac{6700+647}{6700}$$

Add 6700 and 647 to get 7347.

$$\frac{7347}{6700}$$

Factor

$$\frac{3 \cdot 31 \cdot 79}{67 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 1\frac{647}{6700} = 1.0965671641791044$$