Solve 61/4div5/6

$$6 \frac { 1 } { 4 } \div \frac { 5 } { 6 }$$

Evaluate

$$\frac{15}{2}=7.5$$

Solution Steps

Divide \frac{6\times 4+1}{4} by \frac{5}{6} by multiplying \frac{6\times 4+1}{4} by the reciprocal of \frac{5}{6}.

$$\frac{\left(6\times 4+1\right)\times 6}{4\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\left(1+4\times 6\right)}{2\times 5}$$

Multiply 4 and 6 to get 24.

$$\frac{3\left(1+24\right)}{2\times 5}$$

Add 1 and 24 to get 25.

$$\frac{3\times 25}{2\times 5}$$

Multiply 3 and 25 to get 75.

$$\frac{75}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{75}{10}$$

Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$