Solve 34/5+66/15+77/30-83/10=?

$$3 \frac { 4 } { 5 } + 6 \frac { 6 } { 15 } + 7 \frac { 7 } { 30 } - 8 \frac { 3 } { 10 } = ?$$

Evaluate

$$\frac{137}{15}\approx 9.133333333$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{15+4}{5}+\frac{6\times 15+6}{15}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Add 15 and 4 to get 19.

$$\frac{19}{5}+\frac{6\times 15+6}{15}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Multiply 6 and 15 to get 90.

$$\frac{19}{5}+\frac{90+6}{15}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Add 90 and 6 to get 96.

$$\frac{19}{5}+\frac{96}{15}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Reduce the fraction \frac{96}{15} to lowest terms by extracting and canceling out 3.

$$\frac{19}{5}+\frac{32}{5}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Since \frac{19}{5} and \frac{32}{5} have the same denominator, add them by adding their numerators.

$$\frac{19+32}{5}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Add 19 and 32 to get 51.

$$\frac{51}{5}+\frac{7\times 30+7}{30}-\frac{8\times 10+3}{10}$$

Multiply 7 and 30 to get 210.

$$\frac{51}{5}+\frac{210+7}{30}-\frac{8\times 10+3}{10}$$

Add 210 and 7 to get 217.

$$\frac{51}{5}+\frac{217}{30}-\frac{8\times 10+3}{10}$$

Least common multiple of 5 and 30 is 30. Convert \frac{51}{5} and \frac{217}{30} to fractions with denominator 30.

$$\frac{306}{30}+\frac{217}{30}-\frac{8\times 10+3}{10}$$

Since \frac{306}{30} and \frac{217}{30} have the same denominator, add them by adding their numerators.

$$\frac{306+217}{30}-\frac{8\times 10+3}{10}$$

Add 306 and 217 to get 523.

$$\frac{523}{30}-\frac{8\times 10+3}{10}$$

Multiply 8 and 10 to get 80.

$$\frac{523}{30}-\frac{80+3}{10}$$

Add 80 and 3 to get 83.

$$\frac{523}{30}-\frac{83}{10}$$

Least common multiple of 30 and 10 is 30. Convert \frac{523}{30} and \frac{83}{10} to fractions with denominator 30.

$$\frac{523}{30}-\frac{249}{30}$$

Since \frac{523}{30} and \frac{249}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{523-249}{30}$$

Subtract 249 from 523 to get 274.

$$\frac{274}{30}$$

Reduce the fraction \frac{274}{30} to lowest terms by extracting and canceling out 2.

$$\frac{137}{15}$$

Factor

$$\frac{137}{3 \cdot 5} = 9\frac{2}{15} = 9.133333333333333$$