Solve 5/13+3/4-5/13+1/4

$$\frac { 5 } { 13 } + \frac { 3 } { 4 } - \frac { 5 } { 13 } + \frac { 1 } { 4 }$$

Evaluate

$$1$$

Solution Steps

Least common multiple of 13 and 4 is 52. Convert \frac{5}{13} and \frac{3}{4} to fractions with denominator 52.

$$\frac{20}{52}+\frac{39}{52}-\frac{5}{13}+\frac{1}{4}$$

Since \frac{20}{52} and \frac{39}{52} have the same denominator, add them by adding their numerators.

$$\frac{20+39}{52}-\frac{5}{13}+\frac{1}{4}$$

Add 20 and 39 to get 59.

$$\frac{59}{52}-\frac{5}{13}+\frac{1}{4}$$

Least common multiple of 52 and 13 is 52. Convert \frac{59}{52} and \frac{5}{13} to fractions with denominator 52.

$$\frac{59}{52}-\frac{20}{52}+\frac{1}{4}$$

Since \frac{59}{52} and \frac{20}{52} have the same denominator, subtract them by subtracting their numerators.

$$\frac{59-20}{52}+\frac{1}{4}$$

Subtract 20 from 59 to get 39.

$$\frac{39}{52}+\frac{1}{4}$$

Reduce the fraction \frac{39}{52} to lowest terms by extracting and canceling out 13.

$$\frac{3}{4}+\frac{1}{4}$$

Since \frac{3}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{4}$$

Add 3 and 1 to get 4.

$$\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$1$$

Factor

$$1$$