Solve 0.002/2.398+0.001/3.301+0.01/4+0.001/4.699+frac{0.023}{6.523}

$$\frac{ 0.002 }{ 2.398 } + \frac{ 0.001 }{ 3.301 } + \frac{ 0.01 }{ 4 } + \frac{ 0.001 }{ 4.699 } + \frac{ 0.023 }{ 6.523 }$$

Evaluate

$$\frac{32538070428793}{4411485307517200}\approx 0.007375763$$

Solution Steps

Expand \frac{0.002}{2.398} by multiplying both numerator and the denominator by 1000.

$$\frac{2}{2398}+\frac{0.001}{3.301}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Reduce the fraction \frac{2}{2398} to lowest terms by extracting and canceling out 2.

$$\frac{1}{1199}+\frac{0.001}{3.301}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Expand \frac{0.001}{3.301} by multiplying both numerator and the denominator by 1000.

$$\frac{1}{1199}+\frac{1}{3301}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Least common multiple of 1199 and 3301 is 3957899. Convert \frac{1}{1199} and \frac{1}{3301} to fractions with denominator 3957899.

$$\frac{3301}{3957899}+\frac{1199}{3957899}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Since \frac{3301}{3957899} and \frac{1199}{3957899} have the same denominator, add them by adding their numerators.

$$\frac{3301+1199}{3957899}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Add 3301 and 1199 to get 4500.

$$\frac{4500}{3957899}+\frac{0.01}{4}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Expand \frac{0.01}{4} by multiplying both numerator and the denominator by 100.

$$\frac{4500}{3957899}+\frac{1}{400}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Least common multiple of 3957899 and 400 is 1583159600. Convert \frac{4500}{3957899} and \frac{1}{400} to fractions with denominator 1583159600.

$$\frac{1800000}{1583159600}+\frac{3957899}{1583159600}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Since \frac{1800000}{1583159600} and \frac{3957899}{1583159600} have the same denominator, add them by adding their numerators.

$$\frac{1800000+3957899}{1583159600}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Add 1800000 and 3957899 to get 5757899.

$$\frac{5757899}{1583159600}+\frac{0.001}{4.699}+\frac{0.023}{6.523}$$

Expand \frac{0.001}{4.699} by multiplying both numerator and the denominator by 1000.

$$\frac{5757899}{1583159600}+\frac{1}{4699}+\frac{0.023}{6.523}$$

Least common multiple of 1583159600 and 4699 is 7439266960400. Convert \frac{5757899}{1583159600} and \frac{1}{4699} to fractions with denominator 7439266960400.

$$\frac{27056367401}{7439266960400}+\frac{1583159600}{7439266960400}+\frac{0.023}{6.523}$$

Since \frac{27056367401}{7439266960400} and \frac{1583159600}{7439266960400} have the same denominator, add them by adding their numerators.

$$\frac{27056367401+1583159600}{7439266960400}+\frac{0.023}{6.523}$$

Add 27056367401 and 1583159600 to get 28639527001.

$$\frac{28639527001}{7439266960400}+\frac{0.023}{6.523}$$

Expand \frac{0.023}{6.523} by multiplying both numerator and the denominator by 1000.

$$\frac{28639527001}{7439266960400}+\frac{23}{6523}$$

Least common multiple of 7439266960400 and 6523 is 4411485307517200. Convert \frac{28639527001}{7439266960400} and \frac{23}{6523} to fractions with denominator 4411485307517200.

$$\frac{16983239511593}{4411485307517200}+\frac{15554830917200}{4411485307517200}$$

Since \frac{16983239511593}{4411485307517200} and \frac{15554830917200}{4411485307517200} have the same denominator, add them by adding their numerators.

$$\frac{16983239511593+15554830917200}{4411485307517200}$$

Add 16983239511593 and 15554830917200 to get 32538070428793.

$$\frac{32538070428793}{4411485307517200}$$

Factor

$$\frac{41 \cdot 495559 \cdot 1601447}{11 \cdot 37 \cdot 109 \cdot 127 \cdot 593 \cdot 3301 \cdot 2 ^ {4} \cdot 5 ^ {2}} = 0.0073757630731191405$$