Solve 0.214-0.202/441-416*(439-416)+0.202

$$\frac{ 0.214-0.202 }{ 441-416 } \times (439-416)+0.202$$

Evaluate

$$0.21304$$

Solution Steps

Subtract 0.202 from 0.214 to get 0.012.

$$\frac{0.012}{441-416}\left(439-416\right)+0.202$$

Subtract 416 from 441 to get 25.

$$\frac{0.012}{25}\left(439-416\right)+0.202$$

Expand \frac{0.012}{25} by multiplying both numerator and the denominator by 1000.

$$\frac{12}{25000}\left(439-416\right)+0.202$$

Reduce the fraction \frac{12}{25000} to lowest terms by extracting and canceling out 4.

$$\frac{3}{6250}\left(439-416\right)+0.202$$

Subtract 416 from 439 to get 23.

$$\frac{3}{6250}\times 23+0.202$$

Express \frac{3}{6250}\times 23 as a single fraction.

$$\frac{3\times 23}{6250}+0.202$$

Multiply 3 and 23 to get 69.

$$\frac{69}{6250}+0.202$$

Convert decimal number 0.202 to fraction \frac{202}{1000}. Reduce the fraction \frac{202}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{69}{6250}+\frac{101}{500}$$

Least common multiple of 6250 and 500 is 12500. Convert \frac{69}{6250} and \frac{101}{500} to fractions with denominator 12500.

$$\frac{138}{12500}+\frac{2525}{12500}$$

Since \frac{138}{12500} and \frac{2525}{12500} have the same denominator, add them by adding their numerators.

$$\frac{138+2525}{12500}$$

Add 138 and 2525 to get 2663.

$$\frac{2663}{12500}$$

Factor

$$\frac{2663}{2 ^ {2} \cdot 5 ^ {5}} = 0.21304$$