Solve 6+3/4+2/9+3/32+6/125

$$6+ \frac{ 3 }{ 4 } + \frac{ 2 }{ 9 } + \frac{ 3 }{ 32 } + \frac{ 6 }{ 125 }$$

Evaluate

$$\frac{256103}{36000}\approx 7.113972222$$

Solution Steps

Convert 6 to fraction \frac{24}{4}.

$$\frac{24}{4}+\frac{3}{4}+\frac{2}{9}+\frac{3}{32}+\frac{6}{125}$$

Since \frac{24}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{24+3}{4}+\frac{2}{9}+\frac{3}{32}+\frac{6}{125}$$

Add 24 and 3 to get 27.

$$\frac{27}{4}+\frac{2}{9}+\frac{3}{32}+\frac{6}{125}$$

Least common multiple of 4 and 9 is 36. Convert \frac{27}{4} and \frac{2}{9} to fractions with denominator 36.

$$\frac{243}{36}+\frac{8}{36}+\frac{3}{32}+\frac{6}{125}$$

Since \frac{243}{36} and \frac{8}{36} have the same denominator, add them by adding their numerators.

$$\frac{243+8}{36}+\frac{3}{32}+\frac{6}{125}$$

Add 243 and 8 to get 251.

$$\frac{251}{36}+\frac{3}{32}+\frac{6}{125}$$

Least common multiple of 36 and 32 is 288. Convert \frac{251}{36} and \frac{3}{32} to fractions with denominator 288.

$$\frac{2008}{288}+\frac{27}{288}+\frac{6}{125}$$

Since \frac{2008}{288} and \frac{27}{288} have the same denominator, add them by adding their numerators.

$$\frac{2008+27}{288}+\frac{6}{125}$$

Add 2008 and 27 to get 2035.

$$\frac{2035}{288}+\frac{6}{125}$$

Least common multiple of 288 and 125 is 36000. Convert \frac{2035}{288} and \frac{6}{125} to fractions with denominator 36000.

$$\frac{254375}{36000}+\frac{1728}{36000}$$

Since \frac{254375}{36000} and \frac{1728}{36000} have the same denominator, add them by adding their numerators.

$$\frac{254375+1728}{36000}$$

Add 254375 and 1728 to get 256103.

$$\frac{256103}{36000}$$

Factor

$$\frac{47 \cdot 5449}{2 ^ {5} \cdot 3 ^ {2} \cdot 5 ^ {3}} = 7\frac{4103}{36000} = 7.113972222222222$$