Solve 3+4/2*3*4-4/4*5*6+4/6*7*8-4/8*9*10

$$3+ \frac{ 4 }{ 2 \cdot 3 \cdot 4 } - \frac{ 4 }{ 4 \cdot 5 \cdot 6 } + \frac{ 4 }{ 6 \cdot 7 \cdot 8 } - \frac{ 4 }{ 8 \cdot 9 \cdot 10 }$$

Evaluate

$$\frac{989}{315}\approx 3.13968254$$

Solution Steps

Multiply 2 and 3 to get 6.

$$3+\frac{4}{6\times 4}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Multiply 6 and 4 to get 24.

$$3+\frac{4}{24}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

$$3+\frac{1}{6}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{18}{6}+\frac{1}{6}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Since \frac{18}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{18+1}{6}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Add 18 and 1 to get 19.

$$\frac{19}{6}-\frac{4}{4\times 5\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Multiply 4 and 5 to get 20.

$$\frac{19}{6}-\frac{4}{20\times 6}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Multiply 20 and 6 to get 120.

$$\frac{19}{6}-\frac{4}{120}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Reduce the fraction \frac{4}{120} to lowest terms by extracting and canceling out 4.

$$\frac{19}{6}-\frac{1}{30}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Least common multiple of 6 and 30 is 30. Convert \frac{19}{6} and \frac{1}{30} to fractions with denominator 30.

$$\frac{95}{30}-\frac{1}{30}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Since \frac{95}{30} and \frac{1}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-1}{30}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Subtract 1 from 95 to get 94.

$$\frac{94}{30}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Reduce the fraction \frac{94}{30} to lowest terms by extracting and canceling out 2.

$$\frac{47}{15}+\frac{4}{6\times 7\times 8}-\frac{4}{8\times 9\times 10}$$

Multiply 6 and 7 to get 42.

$$\frac{47}{15}+\frac{4}{42\times 8}-\frac{4}{8\times 9\times 10}$$

Multiply 42 and 8 to get 336.

$$\frac{47}{15}+\frac{4}{336}-\frac{4}{8\times 9\times 10}$$

Reduce the fraction \frac{4}{336} to lowest terms by extracting and canceling out 4.

$$\frac{47}{15}+\frac{1}{84}-\frac{4}{8\times 9\times 10}$$

Least common multiple of 15 and 84 is 420. Convert \frac{47}{15} and \frac{1}{84} to fractions with denominator 420.

$$\frac{1316}{420}+\frac{5}{420}-\frac{4}{8\times 9\times 10}$$

Since \frac{1316}{420} and \frac{5}{420} have the same denominator, add them by adding their numerators.

$$\frac{1316+5}{420}-\frac{4}{8\times 9\times 10}$$

Add 1316 and 5 to get 1321.

$$\frac{1321}{420}-\frac{4}{8\times 9\times 10}$$

Multiply 8 and 9 to get 72.

$$\frac{1321}{420}-\frac{4}{72\times 10}$$

Multiply 72 and 10 to get 720.

$$\frac{1321}{420}-\frac{4}{720}$$

Reduce the fraction \frac{4}{720} to lowest terms by extracting and canceling out 4.

$$\frac{1321}{420}-\frac{1}{180}$$

Least common multiple of 420 and 180 is 1260. Convert \frac{1321}{420} and \frac{1}{180} to fractions with denominator 1260.

$$\frac{3963}{1260}-\frac{7}{1260}$$

Since \frac{3963}{1260} and \frac{7}{1260} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3963-7}{1260}$$

Subtract 7 from 3963 to get 3956.

$$\frac{3956}{1260}$$

Reduce the fraction \frac{3956}{1260} to lowest terms by extracting and canceling out 4.

$$\frac{989}{315}$$

Factor

$$\frac{23 \cdot 43}{3 ^ {2} \cdot 5 \cdot 7} = 3\frac{44}{315} = 3.1396825396825396$$