Solve 55/6div53/4

$$5 \frac { 5 } { 6 } \div 5 \frac { 3 } { 4 }$$

Evaluate

$$\frac{70}{69}\approx 1.014492754$$

Solution Steps

Divide \frac{5\times 6+5}{6} by \frac{5\times 4+3}{4} by multiplying \frac{5\times 6+5}{6} by the reciprocal of \frac{5\times 4+3}{4}.

$$\frac{\left(5\times 6+5\right)\times 4}{6\left(5\times 4+3\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\left(5+5\times 6\right)}{3\left(3+4\times 5\right)}$$

Multiply 5 and 6 to get 30.

$$\frac{2\left(5+30\right)}{3\left(3+4\times 5\right)}$$

Add 5 and 30 to get 35.

$$\frac{2\times 35}{3\left(3+4\times 5\right)}$$

Multiply 2 and 35 to get 70.

$$\frac{70}{3\left(3+4\times 5\right)}$$

Multiply 4 and 5 to get 20.

$$\frac{70}{3\left(3+20\right)}$$

Add 3 and 20 to get 23.

$$\frac{70}{3\times 23}$$

Multiply 3 and 23 to get 69.

$$\frac{70}{69}$$

Factor

$$\frac{2 \cdot 5 \cdot 7}{3 \cdot 23} = 1\frac{1}{69} = 1.0144927536231885$$