Solve 9/13+15/16-(5/13-3/10)

$$\frac { 9 } { 13 } + \frac { 15 } { 16 } - ( \frac { 5 } { 13 } - \frac { 3 } { 10 } )$$

Evaluate

$$\frac{1607}{1040}\approx 1.545192308$$

Solution Steps

Least common multiple of 13 and 16 is 208. Convert \frac{9}{13} and \frac{15}{16} to fractions with denominator 208.

$$\frac{144}{208}+\frac{195}{208}-\left(\frac{5}{13}-\frac{3}{10}\right)$$

Since \frac{144}{208} and \frac{195}{208} have the same denominator, add them by adding their numerators.

$$\frac{144+195}{208}-\left(\frac{5}{13}-\frac{3}{10}\right)$$

Add 144 and 195 to get 339.

$$\frac{339}{208}-\left(\frac{5}{13}-\frac{3}{10}\right)$$

Least common multiple of 13 and 10 is 130. Convert \frac{5}{13} and \frac{3}{10} to fractions with denominator 130.

$$\frac{339}{208}-\left(\frac{50}{130}-\frac{39}{130}\right)$$

Since \frac{50}{130} and \frac{39}{130} have the same denominator, subtract them by subtracting their numerators.

$$\frac{339}{208}-\frac{50-39}{130}$$

Subtract 39 from 50 to get 11.

$$\frac{339}{208}-\frac{11}{130}$$

Least common multiple of 208 and 130 is 1040. Convert \frac{339}{208} and \frac{11}{130} to fractions with denominator 1040.

$$\frac{1695}{1040}-\frac{88}{1040}$$

Since \frac{1695}{1040} and \frac{88}{1040} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1695-88}{1040}$$

Subtract 88 from 1695 to get 1607.

$$\frac{1607}{1040}$$

Factor

$$\frac{1607}{2 ^ {4} \cdot 5 \cdot 13} = 1\frac{567}{1040} = 1.5451923076923078$$