Solve 4/15*(22/3-3/4)+11/2divfrac{15}{9}

$$\frac { 4 } { 15 } \times ( 2 \frac { 2 } { 3 } - \frac { 3 } { 4 } ) + 1 \frac { 1 } { 2 } \div \frac { 15 } { 9 }$$

Evaluate

$$\frac{127}{90}\approx 1.411111111$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{4}{15}\left(\frac{6+2}{3}-\frac{3}{4}\right)+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Add 6 and 2 to get 8.

$$\frac{4}{15}\left(\frac{8}{3}-\frac{3}{4}\right)+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{8}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{4}{15}\left(\frac{32}{12}-\frac{9}{12}\right)+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Since \frac{32}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}\times \frac{32-9}{12}+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Subtract 9 from 32 to get 23.

$$\frac{4}{15}\times \frac{23}{12}+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Multiply \frac{4}{15} times \frac{23}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 23}{15\times 12}+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Do the multiplications in the fraction \frac{4\times 23}{15\times 12}.

$$\frac{92}{180}+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Reduce the fraction \frac{92}{180} to lowest terms by extracting and canceling out 4.

$$\frac{23}{45}+\frac{\frac{1\times 2+1}{2}}{\frac{15}{9}}$$

Divide \frac{1\times 2+1}{2} by \frac{15}{9} by multiplying \frac{1\times 2+1}{2} by the reciprocal of \frac{15}{9}.

$$\frac{23}{45}+\frac{\left(1\times 2+1\right)\times 9}{2\times 15}$$

Cancel out 3 in both numerator and denominator.

$$\frac{23}{45}+\frac{3\left(1+2\right)}{2\times 5}$$

Add 1 and 2 to get 3.

$$\frac{23}{45}+\frac{3\times 3}{2\times 5}$$

Multiply 3 and 3 to get 9.

$$\frac{23}{45}+\frac{9}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{23}{45}+\frac{9}{10}$$

Least common multiple of 45 and 10 is 90. Convert \frac{23}{45} and \frac{9}{10} to fractions with denominator 90.

$$\frac{46}{90}+\frac{81}{90}$$

Since \frac{46}{90} and \frac{81}{90} have the same denominator, add them by adding their numerators.

$$\frac{46+81}{90}$$

Add 46 and 81 to get 127.

$$\frac{127}{90}$$

Factor

$$\frac{127}{2 \cdot 3 ^ {2} \cdot 5} = 1\frac{37}{90} = 1.4111111111111112$$