Solve 11/10409/97+4.09190/97-4.099/97

$$\frac{ 11 }{ 10 } \frac{ 409 }{ 97 } +4.09 \frac{ 190 }{ 97 } -4.09 \frac{ 9 }{ 97 }$$

Evaluate

$$\frac{6309}{970}\approx 6.504123711$$

Solution Steps

Multiply \frac{11}{10} times \frac{409}{97} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 409}{10\times 97}+\frac{4.09\times 97+190}{97}-\frac{4.09\times 97+9}{97}$$

Do the multiplications in the fraction \frac{11\times 409}{10\times 97}.

$$\frac{4499}{970}+\frac{4.09\times 97+190}{97}-\frac{4.09\times 97+9}{97}$$

Multiply 4.09 and 97 to get 396.73.

$$\frac{4499}{970}+\frac{396.73+190}{97}-\frac{4.09\times 97+9}{97}$$

Add 396.73 and 190 to get 586.73.

$$\frac{4499}{970}+\frac{586.73}{97}-\frac{4.09\times 97+9}{97}$$

Expand \frac{586.73}{97} by multiplying both numerator and the denominator by 100.

$$\frac{4499}{970}+\frac{58673}{9700}-\frac{4.09\times 97+9}{97}$$

Least common multiple of 970 and 9700 is 9700. Convert \frac{4499}{970} and \frac{58673}{9700} to fractions with denominator 9700.

$$\frac{44990}{9700}+\frac{58673}{9700}-\frac{4.09\times 97+9}{97}$$

Since \frac{44990}{9700} and \frac{58673}{9700} have the same denominator, add them by adding their numerators.

$$\frac{44990+58673}{9700}-\frac{4.09\times 97+9}{97}$$

Add 44990 and 58673 to get 103663.

$$\frac{103663}{9700}-\frac{4.09\times 97+9}{97}$$

Multiply 4.09 and 97 to get 396.73.

$$\frac{103663}{9700}-\frac{396.73+9}{97}$$

Add 396.73 and 9 to get 405.73.

$$\frac{103663}{9700}-\frac{405.73}{97}$$

Expand \frac{405.73}{97} by multiplying both numerator and the denominator by 100.

$$\frac{103663}{9700}-\frac{40573}{9700}$$

Since \frac{103663}{9700} and \frac{40573}{9700} have the same denominator, subtract them by subtracting their numerators.

$$\frac{103663-40573}{9700}$$

Subtract 40573 from 103663 to get 63090.

$$\frac{63090}{9700}$$

Reduce the fraction \frac{63090}{9700} to lowest terms by extracting and canceling out 10.

$$\frac{6309}{970}$$

Factor

$$\frac{701 \cdot 3 ^ {2}}{2 \cdot 5 \cdot 97} = 6\frac{489}{970} = 6.504123711340206$$