Solve 3+(5-1/2)div(5/26div5/13)

$$3 + ( 5 - \frac { 1 } { 2 } ) \div ( \frac { 5 } { 26 } \div \frac { 5 } { 13 } )$$

Evaluate

$$12$$

Solution Steps

Convert 5 to fraction \frac{10}{2}.

$$3+\frac{\frac{10}{2}-\frac{1}{2}}{\frac{\frac{5}{26}}{\frac{5}{13}}}$$

Since \frac{10}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$3+\frac{\frac{10-1}{2}}{\frac{\frac{5}{26}}{\frac{5}{13}}}$$

Subtract 1 from 10 to get 9.

$$3+\frac{\frac{9}{2}}{\frac{\frac{5}{26}}{\frac{5}{13}}}$$

Divide \frac{5}{26} by \frac{5}{13} by multiplying \frac{5}{26} by the reciprocal of \frac{5}{13}.

$$3+\frac{\frac{9}{2}}{\frac{5}{26}\times \frac{13}{5}}$$

Multiply \frac{5}{26} times \frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{\frac{9}{2}}{\frac{5\times 13}{26\times 5}}$$

Cancel out 5 in both numerator and denominator.

$$3+\frac{\frac{9}{2}}{\frac{13}{26}}$$

Reduce the fraction \frac{13}{26} to lowest terms by extracting and canceling out 13.

$$3+\frac{\frac{9}{2}}{\frac{1}{2}}$$

Divide \frac{9}{2} by \frac{1}{2} by multiplying \frac{9}{2} by the reciprocal of \frac{1}{2}.

$$3+\frac{9}{2}\times 2$$

Cancel out 2 and 2.

$$3+9$$

Add 3 and 9 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$