Solve {(3.4-13/8)*22/3-22/3+1}div2.6

$$\{ ( 3.4 - 1 \frac { 3 } { 8 } ) \times 2 \frac { 2 } { 3 } - 2 \frac { 2 } { 3 } + 1 \} \div 2.6$$

Evaluate

$$\frac{56}{39}\approx 1.435897436$$

Solution Steps

Multiply 1 and 8 to get 8.

$$\frac{\left(3.4-\frac{8+3}{8}\right)\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Add 8 and 3 to get 11.

$$\frac{\left(3.4-\frac{11}{8}\right)\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Convert decimal number 3.4 to fraction \frac{34}{10}. Reduce the fraction \frac{34}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\left(\frac{17}{5}-\frac{11}{8}\right)\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Least common multiple of 5 and 8 is 40. Convert \frac{17}{5} and \frac{11}{8} to fractions with denominator 40.

$$\frac{\left(\frac{136}{40}-\frac{55}{40}\right)\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Since \frac{136}{40} and \frac{55}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{136-55}{40}\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Subtract 55 from 136 to get 81.

$$\frac{\frac{81}{40}\times \frac{2\times 3+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{81}{40}\times \frac{6+2}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Add 6 and 2 to get 8.

$$\frac{\frac{81}{40}\times \frac{8}{3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Multiply \frac{81}{40} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{81\times 8}{40\times 3}-\frac{2\times 3+2}{3}+1}{2.6}$$

Do the multiplications in the fraction \frac{81\times 8}{40\times 3}.

$$\frac{\frac{648}{120}-\frac{2\times 3+2}{3}+1}{2.6}$$

Reduce the fraction \frac{648}{120} to lowest terms by extracting and canceling out 24.

$$\frac{\frac{27}{5}-\frac{2\times 3+2}{3}+1}{2.6}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{27}{5}-\frac{6+2}{3}+1}{2.6}$$

Add 6 and 2 to get 8.

$$\frac{\frac{27}{5}-\frac{8}{3}+1}{2.6}$$

Least common multiple of 5 and 3 is 15. Convert \frac{27}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{\frac{81}{15}-\frac{40}{15}+1}{2.6}$$

Since \frac{81}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{81-40}{15}+1}{2.6}$$

Subtract 40 from 81 to get 41.

$$\frac{\frac{41}{15}+1}{2.6}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{\frac{41}{15}+\frac{15}{15}}{2.6}$$

Since \frac{41}{15} and \frac{15}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{41+15}{15}}{2.6}$$

Add 41 and 15 to get 56.

$$\frac{\frac{56}{15}}{2.6}$$

Express \frac{\frac{56}{15}}{2.6} as a single fraction.

$$\frac{56}{15\times 2.6}$$

Multiply 15 and 2.6 to get 39.

$$\frac{56}{39}$$

Factor

$$\frac{7 \cdot 2 ^ {3}}{3 \cdot 13} = 1\frac{17}{39} = 1.435897435897436$$