Solve 1/1.2+1/2*3+1/3*4*1/99*10^circ

$$\frac { 1 } { 1.2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } \cdot \frac { 1 } { 99 \cdot 10 ^ { \circ } }$$

Evaluate

$$\frac{11881}{11880}\approx 1.000084175$$

Solution Steps

Expand \frac{1}{1.2} by multiplying both numerator and the denominator by 10.

$$\frac{10}{12}+\frac{1}{2\times 3}+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}+\frac{1}{2\times 3}+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Multiply 2 and 3 to get 6.

$$\frac{5}{6}+\frac{1}{6}+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Since \frac{5}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{6}+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Add 5 and 1 to get 6.

$$\frac{6}{6}+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Divide 6 by 6 to get 1.

$$1+\frac{1}{3\times 4}\times \frac{1}{99\times 10}$$

Multiply 3 and 4 to get 12.

$$1+\frac{1}{12}\times \frac{1}{99\times 10}$$

Multiply 99 and 10 to get 990.

$$1+\frac{1}{12}\times \frac{1}{990}$$

Multiply \frac{1}{12} times \frac{1}{990} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\times 1}{12\times 990}$$

Do the multiplications in the fraction \frac{1\times 1}{12\times 990}.

$$1+\frac{1}{11880}$$

Convert 1 to fraction \frac{11880}{11880}.

$$\frac{11880}{11880}+\frac{1}{11880}$$

Since \frac{11880}{11880} and \frac{1}{11880} have the same denominator, add them by adding their numerators.

$$\frac{11880+1}{11880}$$

Add 11880 and 1 to get 11881.

$$\frac{11881}{11880}$$

Factor

$$\frac{109 ^ {2}}{5 \cdot 11 \cdot 2 ^ {3} \cdot 3 ^ {3}} = 1\frac{1}{11880} = 1.0000841750841751$$