Solve 31/3div31/5=

$$3 \frac { 1 } { 3 } \div 3 \frac { 1 } { 5 } =$$

Evaluate

$$\frac{25}{24}\approx 1.041666667$$

Solution Steps

Divide \frac{3\times 3+1}{3} by \frac{3\times 5+1}{5} by multiplying \frac{3\times 3+1}{3} by the reciprocal of \frac{3\times 5+1}{5}.

$$\frac{\left(3\times 3+1\right)\times 5}{3\left(3\times 5+1\right)}$$

Multiply 3 and 3 to get 9.

$$\frac{\left(9+1\right)\times 5}{3\left(3\times 5+1\right)}$$

Add 9 and 1 to get 10.

$$\frac{10\times 5}{3\left(3\times 5+1\right)}$$

Multiply 10 and 5 to get 50.

$$\frac{50}{3\left(3\times 5+1\right)}$$

Multiply 3 and 5 to get 15.

$$\frac{50}{3\left(15+1\right)}$$

Add 15 and 1 to get 16.

$$\frac{50}{3\times 16}$$

Multiply 3 and 16 to get 48.

$$\frac{50}{48}$$

Reduce the fraction \frac{50}{48} to lowest terms by extracting and canceling out 2.

$$\frac{25}{24}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 3} = 1\frac{1}{24} = 1.0416666666666667$$