Solve 5/7+8/9-3/10+9/5=

$$\frac { 5 } { 7 } + \frac { 8 } { 9 } - \frac { 3 } { 10 } + \frac { 9 } { 5 } =$$

Evaluate

$$\frac{391}{126}\approx 3.103174603$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{5}{7} and \frac{8}{9} to fractions with denominator 63.

$$\frac{45}{63}+\frac{56}{63}-\frac{3}{10}+\frac{9}{5}$$

Since \frac{45}{63} and \frac{56}{63} have the same denominator, add them by adding their numerators.

$$\frac{45+56}{63}-\frac{3}{10}+\frac{9}{5}$$

Add 45 and 56 to get 101.

$$\frac{101}{63}-\frac{3}{10}+\frac{9}{5}$$

Least common multiple of 63 and 10 is 630. Convert \frac{101}{63} and \frac{3}{10} to fractions with denominator 630.

$$\frac{1010}{630}-\frac{189}{630}+\frac{9}{5}$$

Since \frac{1010}{630} and \frac{189}{630} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1010-189}{630}+\frac{9}{5}$$

Subtract 189 from 1010 to get 821.

$$\frac{821}{630}+\frac{9}{5}$$

Least common multiple of 630 and 5 is 630. Convert \frac{821}{630} and \frac{9}{5} to fractions with denominator 630.

$$\frac{821}{630}+\frac{1134}{630}$$

Since \frac{821}{630} and \frac{1134}{630} have the same denominator, add them by adding their numerators.

$$\frac{821+1134}{630}$$

Add 821 and 1134 to get 1955.

$$\frac{1955}{630}$$

Reduce the fraction \frac{1955}{630} to lowest terms by extracting and canceling out 5.

$$\frac{391}{126}$$

Factor

$$\frac{17 \cdot 23}{2 \cdot 3 ^ {2} \cdot 7} = 3\frac{13}{126} = 3.1031746031746033$$