Solve 9.9/7+3/2/frac{11{7}}

$$\frac { \frac { 9.9 } { 7 } + \frac { 3 } { 2 } } { \frac { 11 } { 7 } }$$

Evaluate

$$\frac{102}{55}\approx 1.854545455$$

Solution Steps

Expand \frac{9.9}{7} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{99}{70}+\frac{3}{2}}{\frac{11}{7}}$$

Least common multiple of 70 and 2 is 70. Convert \frac{99}{70} and \frac{3}{2} to fractions with denominator 70.

$$\frac{\frac{99}{70}+\frac{105}{70}}{\frac{11}{7}}$$

Since \frac{99}{70} and \frac{105}{70} have the same denominator, add them by adding their numerators.

$$\frac{\frac{99+105}{70}}{\frac{11}{7}}$$

Add 99 and 105 to get 204.

$$\frac{\frac{204}{70}}{\frac{11}{7}}$$

Reduce the fraction \frac{204}{70} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{102}{35}}{\frac{11}{7}}$$

Divide \frac{102}{35} by \frac{11}{7} by multiplying \frac{102}{35} by the reciprocal of \frac{11}{7}.

$$\frac{102}{35}\times \frac{7}{11}$$

Multiply \frac{102}{35} times \frac{7}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{102\times 7}{35\times 11}$$

Do the multiplications in the fraction \frac{102\times 7}{35\times 11}.

$$\frac{714}{385}$$

Reduce the fraction \frac{714}{385} to lowest terms by extracting and canceling out 7.

$$\frac{102}{55}$$

Factor

$$\frac{2 \cdot 3 \cdot 17}{5 \cdot 11} = 1\frac{47}{55} = 1.8545454545454545$$