Solve 5/44-1/22/frac{5{44}+4/11}

$$\frac { \frac { 5 } { 44 } - \frac { 1 } { 22 } } { \frac { 5 } { 44 } + \frac { 4 } { 11 } }$$

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Solution Steps

Least common multiple of 44 and 22 is 44. Convert \frac{5}{44} and \frac{1}{22} to fractions with denominator 44.

$$\frac{\frac{5}{44}-\frac{2}{44}}{\frac{5}{44}+\frac{4}{11}}$$

Since \frac{5}{44} and \frac{2}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-2}{44}}{\frac{5}{44}+\frac{4}{11}}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{3}{44}}{\frac{5}{44}+\frac{4}{11}}$$

Least common multiple of 44 and 11 is 44. Convert \frac{5}{44} and \frac{4}{11} to fractions with denominator 44.

$$\frac{\frac{3}{44}}{\frac{5}{44}+\frac{16}{44}}$$

Since \frac{5}{44} and \frac{16}{44} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{44}}{\frac{5+16}{44}}$$

Add 5 and 16 to get 21.

$$\frac{\frac{3}{44}}{\frac{21}{44}}$$

Divide \frac{3}{44} by \frac{21}{44} by multiplying \frac{3}{44} by the reciprocal of \frac{21}{44}.

$$\frac{3}{44}\times \frac{44}{21}$$

Multiply \frac{3}{44} times \frac{44}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 44}{44\times 21}$$

Cancel out 44 in both numerator and denominator.

$$\frac{3}{21}$$

Reduce the fraction \frac{3}{21} to lowest terms by extracting and canceling out 3.

$$\frac{1}{7}$$

Factor

$$\frac{1}{7} = 0.14285714285714285$$