Solve 3/4*12/5+1/5div4/3-frac{5}{4}*frac{3}{5}

$$\frac { 3 } { 4 } \times \frac { 12 } { 5 } + \frac { 1 } { 5 } \div \frac { 4 } { 3 } - \frac { 5 } { 4 } \times \frac { 3 } { 5 }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Multiply \frac{3}{4} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 12}{4\times 5}+\frac{\frac{1}{5}}{\frac{4}{3}}-\frac{5}{4}\times \frac{3}{5}$$

Do the multiplications in the fraction \frac{3\times 12}{4\times 5}.

$$\frac{36}{20}+\frac{\frac{1}{5}}{\frac{4}{3}}-\frac{5}{4}\times \frac{3}{5}$$

Reduce the fraction \frac{36}{20} to lowest terms by extracting and canceling out 4.

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

Divide \frac{1}{5} by \frac{4}{3} by multiplying \frac{1}{5} by the reciprocal of \frac{4}{3}.

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

Multiply \frac{1}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 3}{5\times 4}.

$$\frac{9}{5}+\frac{3}{20}-\frac{5}{4}\times \frac{3}{5}$$

Least common multiple of 5 and 20 is 20. Convert \frac{9}{5} and \frac{3}{20} to fractions with denominator 20.

$$\frac{36}{20}+\frac{3}{20}-\frac{5}{4}\times \frac{3}{5}$$

Since \frac{36}{20} and \frac{3}{20} have the same denominator, add them by adding their numerators.

$$\frac{36+3}{20}-\frac{5}{4}\times \frac{3}{5}$$

Add 36 and 3 to get 39.

$$\frac{39}{20}-\frac{5}{4}\times \frac{3}{5}$$

Multiply \frac{5}{4} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39}{20}-\frac{5\times 3}{4\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{39}{20}-\frac{3}{4}$$

Least common multiple of 20 and 4 is 20. Convert \frac{39}{20} and \frac{3}{4} to fractions with denominator 20.

$$\frac{39}{20}-\frac{15}{20}$$

Since \frac{39}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-15}{20}$$

Subtract 15 from 39 to get 24.

$$\frac{24}{20}$$

Reduce the fraction \frac{24}{20} to lowest terms by extracting and canceling out 4.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$