Solve 6.437-4/19-27/19-38/19

$$6.437- \frac{ 4 }{ 19 } -2 \frac{ 7 }{ 19 } -3 \frac{ 8 }{ 19 }$$

Evaluate

$$0.437$$

Solution Steps

Convert decimal number 6.437 to fraction \frac{6437}{1000}.

$$\frac{6437}{1000}-\frac{4}{19}-\frac{2\times 19+7}{19}-\frac{3\times 19+8}{19}$$

Least common multiple of 1000 and 19 is 19000. Convert \frac{6437}{1000} and \frac{4}{19} to fractions with denominator 19000.

$$\frac{122303}{19000}-\frac{4000}{19000}-\frac{2\times 19+7}{19}-\frac{3\times 19+8}{19}$$

Since \frac{122303}{19000} and \frac{4000}{19000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{122303-4000}{19000}-\frac{2\times 19+7}{19}-\frac{3\times 19+8}{19}$$

Subtract 4000 from 122303 to get 118303.

$$\frac{118303}{19000}-\frac{2\times 19+7}{19}-\frac{3\times 19+8}{19}$$

Multiply 2 and 19 to get 38.

$$\frac{118303}{19000}-\frac{38+7}{19}-\frac{3\times 19+8}{19}$$

Add 38 and 7 to get 45.

$$\frac{118303}{19000}-\frac{45}{19}-\frac{3\times 19+8}{19}$$

Least common multiple of 19000 and 19 is 19000. Convert \frac{118303}{19000} and \frac{45}{19} to fractions with denominator 19000.

$$\frac{118303}{19000}-\frac{45000}{19000}-\frac{3\times 19+8}{19}$$

Since \frac{118303}{19000} and \frac{45000}{19000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{118303-45000}{19000}-\frac{3\times 19+8}{19}$$

Subtract 45000 from 118303 to get 73303.

$$\frac{73303}{19000}-\frac{3\times 19+8}{19}$$

Multiply 3 and 19 to get 57.

$$\frac{73303}{19000}-\frac{57+8}{19}$$

Add 57 and 8 to get 65.

$$\frac{73303}{19000}-\frac{65}{19}$$

Least common multiple of 19000 and 19 is 19000. Convert \frac{73303}{19000} and \frac{65}{19} to fractions with denominator 19000.

$$\frac{73303}{19000}-\frac{65000}{19000}$$

Since \frac{73303}{19000} and \frac{65000}{19000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{73303-65000}{19000}$$

Subtract 65000 from 73303 to get 8303.

$$\frac{8303}{19000}$$

Reduce the fraction \frac{8303}{19000} to lowest terms by extracting and canceling out 19.

$$\frac{437}{1000}$$

Factor

$$\frac{19 \cdot 23}{2 ^ {3} \cdot 5 ^ {3}} = 0.437$$