Solve [1-(1/4+5/12)]div1/9

$$[ 1 - ( \frac { 1 } { 4 } + \frac { 5 } { 12 } ) ] \div \frac { 1 } { 9 }$$

Evaluate

$$3$$

Solution Steps

Least common multiple of 4 and 12 is 12. Convert \frac{1}{4} and \frac{5}{12} to fractions with denominator 12.

$$\frac{1-\left(\frac{3}{12}+\frac{5}{12}\right)}{\frac{1}{9}}$$

Since \frac{3}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\frac{1-\frac{3+5}{12}}{\frac{1}{9}}$$

Add 3 and 5 to get 8.

$$\frac{1-\frac{8}{12}}{\frac{1}{9}}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

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

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 3 to get 1.

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

Divide \frac{1}{3} by \frac{1}{9} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{9}.

$$\frac{1}{3}\times 9$$

Multiply \frac{1}{3} and 9 to get \frac{9}{3}.

$$\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$3$$

Factor

$$3$$