Solve (4/5+4/3-2)*71/2

$$( \frac { 4 } { 5 } + \frac { 4 } { 3 } - 2 ) \times 7 \frac { 1 } { 2 }$$

Evaluate

$$1$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{4}{3} to fractions with denominator 15.

$$\left(\frac{12}{15}+\frac{20}{15}-2\right)\times \frac{7\times 2+1}{2}$$

Since \frac{12}{15} and \frac{20}{15} have the same denominator, add them by adding their numerators.

$$\left(\frac{12+20}{15}-2\right)\times \frac{7\times 2+1}{2}$$

Add 12 and 20 to get 32.

$$\left(\frac{32}{15}-2\right)\times \frac{7\times 2+1}{2}$$

Convert 2 to fraction \frac{30}{15}.

$$\left(\frac{32}{15}-\frac{30}{15}\right)\times \frac{7\times 2+1}{2}$$

Since \frac{32}{15} and \frac{30}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32-30}{15}\times \frac{7\times 2+1}{2}$$

Subtract 30 from 32 to get 2.

$$\frac{2}{15}\times \frac{7\times 2+1}{2}$$

Multiply 7 and 2 to get 14.

$$\frac{2}{15}\times \frac{14+1}{2}$$

Add 14 and 1 to get 15.

$$\frac{2}{15}\times \frac{15}{2}$$

Cancel out \frac{2}{15} and its reciprocal \frac{15}{2}.

$$1$$

Factor

$$1$$