Solve 4/9*10+15*3/8-4*1/9-1/8*5

$$\frac { 4 } { 9 } \times 10 + 15 \times \frac { 3 } { 8 } - 4 \times \frac { 1 } { 9 } - \frac { 1 } { 8 } \times 5$$

Evaluate

$$9$$

Solution Steps

Express \frac{4}{9}\times 10 as a single fraction.

$$\frac{4\times 10}{9}+15\times \frac{3}{8}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Multiply 4 and 10 to get 40.

$$\frac{40}{9}+15\times \frac{3}{8}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Express 15\times \frac{3}{8} as a single fraction.

$$\frac{40}{9}+\frac{15\times 3}{8}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Multiply 15 and 3 to get 45.

$$\frac{40}{9}+\frac{45}{8}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Least common multiple of 9 and 8 is 72. Convert \frac{40}{9} and \frac{45}{8} to fractions with denominator 72.

$$\frac{320}{72}+\frac{405}{72}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Since \frac{320}{72} and \frac{405}{72} have the same denominator, add them by adding their numerators.

$$\frac{320+405}{72}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Add 320 and 405 to get 725.

$$\frac{725}{72}-4\times \frac{1}{9}-\frac{1}{8}\times 5$$

Multiply 4 and \frac{1}{9} to get \frac{4}{9}.

$$\frac{725}{72}-\frac{4}{9}-\frac{1}{8}\times 5$$

Least common multiple of 72 and 9 is 72. Convert \frac{725}{72} and \frac{4}{9} to fractions with denominator 72.

$$\frac{725}{72}-\frac{32}{72}-\frac{1}{8}\times 5$$

Since \frac{725}{72} and \frac{32}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{725-32}{72}-\frac{1}{8}\times 5$$

Subtract 32 from 725 to get 693.

$$\frac{693}{72}-\frac{1}{8}\times 5$$

Reduce the fraction \frac{693}{72} to lowest terms by extracting and canceling out 9.

$$\frac{77}{8}-\frac{1}{8}\times 5$$

Multiply \frac{1}{8} and 5 to get \frac{5}{8}.

$$\frac{77}{8}-\frac{5}{8}$$

Since \frac{77}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{77-5}{8}$$

Subtract 5 from 77 to get 72.

$$\frac{72}{8}$$

Divide 72 by 8 to get 9.

$$9$$

Factor

$$3^{2}$$