Solve (1/4+3/5+3/8)*11/7

$$( \frac { 1 } { 4 } + \frac { 3 } { 5 } + \frac { 3 } { 8 } ) \times 1 \frac { 1 } { 7 }$$

Evaluate

$$\frac{7}{5}=1.4$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$\left(\frac{5}{20}+\frac{12}{20}+\frac{3}{8}\right)\times \frac{1\times 7+1}{7}$$

Since \frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\left(\frac{5+12}{20}+\frac{3}{8}\right)\times \frac{1\times 7+1}{7}$$

Add 5 and 12 to get 17.

$$\left(\frac{17}{20}+\frac{3}{8}\right)\times \frac{1\times 7+1}{7}$$

Least common multiple of 20 and 8 is 40. Convert \frac{17}{20} and \frac{3}{8} to fractions with denominator 40.

$$\left(\frac{34}{40}+\frac{15}{40}\right)\times \frac{1\times 7+1}{7}$$

Since \frac{34}{40} and \frac{15}{40} have the same denominator, add them by adding their numerators.

$$\frac{34+15}{40}\times \frac{1\times 7+1}{7}$$

Add 34 and 15 to get 49.

$$\frac{49}{40}\times \frac{1\times 7+1}{7}$$

Multiply 1 and 7 to get 7.

$$\frac{49}{40}\times \frac{7+1}{7}$$

Add 7 and 1 to get 8.

$$\frac{49}{40}\times \frac{8}{7}$$

Multiply \frac{49}{40} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 8}{40\times 7}$$

Do the multiplications in the fraction \frac{49\times 8}{40\times 7}.

$$\frac{392}{280}$$

Reduce the fraction \frac{392}{280} to lowest terms by extracting and canceling out 56.

$$\frac{7}{5}$$

Factor

$$\frac{7}{5} = 1\frac{2}{5} = 1.4$$