Solve 59/10+46/13-39/10

$$5 \frac { 9 } { 10 } + 4 \frac { 6 } { 13 } - 3 \frac { 9 } { 10 }$$

Evaluate

$$\frac{84}{13}\approx 6.461538462$$

Solution Steps

Multiply 5 and 10 to get 50.

$$\frac{50+9}{10}+\frac{4\times 13+6}{13}-\frac{3\times 10+9}{10}$$

Add 50 and 9 to get 59.

$$\frac{59}{10}+\frac{4\times 13+6}{13}-\frac{3\times 10+9}{10}$$

Multiply 4 and 13 to get 52.

$$\frac{59}{10}+\frac{52+6}{13}-\frac{3\times 10+9}{10}$$

Add 52 and 6 to get 58.

$$\frac{59}{10}+\frac{58}{13}-\frac{3\times 10+9}{10}$$

Least common multiple of 10 and 13 is 130. Convert \frac{59}{10} and \frac{58}{13} to fractions with denominator 130.

$$\frac{767}{130}+\frac{580}{130}-\frac{3\times 10+9}{10}$$

Since \frac{767}{130} and \frac{580}{130} have the same denominator, add them by adding their numerators.

$$\frac{767+580}{130}-\frac{3\times 10+9}{10}$$

Add 767 and 580 to get 1347.

$$\frac{1347}{130}-\frac{3\times 10+9}{10}$$

Multiply 3 and 10 to get 30.

$$\frac{1347}{130}-\frac{30+9}{10}$$

Add 30 and 9 to get 39.

$$\frac{1347}{130}-\frac{39}{10}$$

Least common multiple of 130 and 10 is 130. Convert \frac{1347}{130} and \frac{39}{10} to fractions with denominator 130.

$$\frac{1347}{130}-\frac{507}{130}$$

Since \frac{1347}{130} and \frac{507}{130} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1347-507}{130}$$

Subtract 507 from 1347 to get 840.

$$\frac{840}{130}$$

Reduce the fraction \frac{840}{130} to lowest terms by extracting and canceling out 10.

$$\frac{84}{13}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 7}{13} = 6\frac{6}{13} = 6.461538461538462$$