Solve 3.1631/13div411/39

$$3.163 \frac { 1 } { 13 } \div 41 \frac { 1 } { 39 }$$

Evaluate

$$0.078973125$$

Solution Steps

Divide \frac{3.163\times 13+1}{13} by \frac{41\times 39+1}{39} by multiplying \frac{3.163\times 13+1}{13} by the reciprocal of \frac{41\times 39+1}{39}.

$$\frac{\left(3.163\times 13+1\right)\times 39}{13\left(41\times 39+1\right)}$$

Cancel out 13 in both numerator and denominator.

$$\frac{3\left(1+3.163\times 13\right)}{1+39\times 41}$$

Multiply 3.163 and 13 to get 41.119.

$$\frac{3\left(1+41.119\right)}{1+39\times 41}$$

Add 1 and 41.119 to get 42.119.

$$\frac{3\times 42.119}{1+39\times 41}$$

Multiply 3 and 42.119 to get 126.357.

$$\frac{126.357}{1+39\times 41}$$

Multiply 39 and 41 to get 1599.

$$\frac{126.357}{1+1599}$$

Add 1 and 1599 to get 1600.

$$\frac{126.357}{1600}$$

Expand \frac{126.357}{1600} by multiplying both numerator and the denominator by 1000.

$$\frac{126357}{1600000}$$

Factor

$$\frac{3 \cdot 7 \cdot 11 \cdot 547}{2 ^ {9} \cdot 5 ^ {5}} = 0.078973125$$