Solve 4/7*54-16*3/5+27*6/7+1/5*3

$$\frac { 4 } { 7 } \times 54 - 16 \times \frac { 3 } { 5 } + 27 \times \frac { 6 } { 7 } + \frac { 1 } { 5 } \times 3$$

Evaluate

$$45$$

Solution Steps

Express \frac{4}{7}\times 54 as a single fraction.

$$\frac{4\times 54}{7}-16\times \frac{3}{5}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Multiply 4 and 54 to get 216.

$$\frac{216}{7}-16\times \frac{3}{5}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Express 16\times \frac{3}{5} as a single fraction.

$$\frac{216}{7}-\frac{16\times 3}{5}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Multiply 16 and 3 to get 48.

$$\frac{216}{7}-\frac{48}{5}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Least common multiple of 7 and 5 is 35. Convert \frac{216}{7} and \frac{48}{5} to fractions with denominator 35.

$$\frac{1080}{35}-\frac{336}{35}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Since \frac{1080}{35} and \frac{336}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1080-336}{35}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Subtract 336 from 1080 to get 744.

$$\frac{744}{35}+27\times \frac{6}{7}+\frac{1}{5}\times 3$$

Express 27\times \frac{6}{7} as a single fraction.

$$\frac{744}{35}+\frac{27\times 6}{7}+\frac{1}{5}\times 3$$

Multiply 27 and 6 to get 162.

$$\frac{744}{35}+\frac{162}{7}+\frac{1}{5}\times 3$$

Least common multiple of 35 and 7 is 35. Convert \frac{744}{35} and \frac{162}{7} to fractions with denominator 35.

$$\frac{744}{35}+\frac{810}{35}+\frac{1}{5}\times 3$$

Since \frac{744}{35} and \frac{810}{35} have the same denominator, add them by adding their numerators.

$$\frac{744+810}{35}+\frac{1}{5}\times 3$$

Add 744 and 810 to get 1554.

$$\frac{1554}{35}+\frac{1}{5}\times 3$$

Reduce the fraction \frac{1554}{35} to lowest terms by extracting and canceling out 7.

$$\frac{222}{5}+\frac{1}{5}\times 3$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

$$\frac{222}{5}+\frac{3}{5}$$

Since \frac{222}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{222+3}{5}$$

Add 222 and 3 to get 225.

$$\frac{225}{5}$$

Divide 225 by 5 to get 45.

$$45$$

Factor

$$3^{2}\times 5$$