Solve (1/34-1/51)div(1/51-1/68)+(frac{1}{22}-frac{1}{33})div(frac{1}{33}-frac{1}{44})

$$( \frac { 1 } { 34 } - \frac { 1 } { 51 } ) \div ( \frac { 1 } { 51 } - \frac { 1 } { 68 } ) + ( \frac { 1 } { 22 } - \frac { 1 } { 33 } ) \div ( \frac { 1 } { 33 } - \frac { 1 } { 44 } )$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 34 and 51 is 102. Convert \frac{1}{34} and \frac{1}{51} to fractions with denominator 102.

$$\frac{\frac{3}{102}-\frac{2}{102}}{\frac{1}{51}-\frac{1}{68}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Since \frac{3}{102} and \frac{2}{102} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3-2}{102}}{\frac{1}{51}-\frac{1}{68}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{1}{102}}{\frac{1}{51}-\frac{1}{68}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Least common multiple of 51 and 68 is 204. Convert \frac{1}{51} and \frac{1}{68} to fractions with denominator 204.

$$\frac{\frac{1}{102}}{\frac{4}{204}-\frac{3}{204}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Since \frac{4}{204} and \frac{3}{204} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{102}}{\frac{4-3}{204}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Subtract 3 from 4 to get 1.

$$\frac{\frac{1}{102}}{\frac{1}{204}}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Divide \frac{1}{102} by \frac{1}{204} by multiplying \frac{1}{102} by the reciprocal of \frac{1}{204}.

$$\frac{1}{102}\times 204+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Multiply \frac{1}{102} and 204 to get \frac{204}{102}.

$$\frac{204}{102}+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Divide 204 by 102 to get 2.

$$2+\frac{\frac{1}{22}-\frac{1}{33}}{\frac{1}{33}-\frac{1}{44}}$$

Least common multiple of 22 and 33 is 66. Convert \frac{1}{22} and \frac{1}{33} to fractions with denominator 66.

$$2+\frac{\frac{3}{66}-\frac{2}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Since \frac{3}{66} and \frac{2}{66} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{\frac{3-2}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Subtract 2 from 3 to get 1.

$$2+\frac{\frac{1}{66}}{\frac{1}{33}-\frac{1}{44}}$$

Least common multiple of 33 and 44 is 132. Convert \frac{1}{33} and \frac{1}{44} to fractions with denominator 132.

$$2+\frac{\frac{1}{66}}{\frac{4}{132}-\frac{3}{132}}$$

Since \frac{4}{132} and \frac{3}{132} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{\frac{1}{66}}{\frac{4-3}{132}}$$

Subtract 3 from 4 to get 1.

$$2+\frac{\frac{1}{66}}{\frac{1}{132}}$$

Divide \frac{1}{66} by \frac{1}{132} by multiplying \frac{1}{66} by the reciprocal of \frac{1}{132}.

$$2+\frac{1}{66}\times 132$$

Multiply \frac{1}{66} and 132 to get \frac{132}{66}.

$$2+\frac{132}{66}$$

Divide 132 by 66 to get 2.

$$2+2$$

Add 2 and 2 to get 4.

$$4$$

Factor

$$2^{2}$$