Solve 131/35:(2-8/9:119/45)

$$1 \frac { 31 } { 35 } : ( 2 - \frac { 8 } { 9 } : 1 \frac { 19 } { 45 } )$$

Evaluate

$$\frac{48}{35}\approx 1.371428571$$

Solution Steps

Multiply 1 and 35 to get 35.

$$\frac{\frac{35+31}{35}}{2-\frac{\frac{8}{9}}{\frac{1\times 45+19}{45}}}$$

Add 35 and 31 to get 66.

$$\frac{\frac{66}{35}}{2-\frac{\frac{8}{9}}{\frac{1\times 45+19}{45}}}$$

Divide \frac{8}{9} by \frac{1\times 45+19}{45} by multiplying \frac{8}{9} by the reciprocal of \frac{1\times 45+19}{45}.

$$\frac{\frac{66}{35}}{2-\frac{8\times 45}{9\left(1\times 45+19\right)}}$$

Cancel out 9 in both numerator and denominator.

$$\frac{\frac{66}{35}}{2-\frac{5\times 8}{19+45}}$$

Multiply 5 and 8 to get 40.

$$\frac{\frac{66}{35}}{2-\frac{40}{19+45}}$$

Add 19 and 45 to get 64.

$$\frac{\frac{66}{35}}{2-\frac{40}{64}}$$

Reduce the fraction \frac{40}{64} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{66}{35}}{2-\frac{5}{8}}$$

Convert 2 to fraction \frac{16}{8}.

$$\frac{\frac{66}{35}}{\frac{16}{8}-\frac{5}{8}}$$

Since \frac{16}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{66}{35}}{\frac{16-5}{8}}$$

Subtract 5 from 16 to get 11.

$$\frac{\frac{66}{35}}{\frac{11}{8}}$$

Divide \frac{66}{35} by \frac{11}{8} by multiplying \frac{66}{35} by the reciprocal of \frac{11}{8}.

$$\frac{66}{35}\times \frac{8}{11}$$

Multiply \frac{66}{35} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{66\times 8}{35\times 11}$$

Do the multiplications in the fraction \frac{66\times 8}{35\times 11}.

$$\frac{528}{385}$$

Reduce the fraction \frac{528}{385} to lowest terms by extracting and canceling out 11.

$$\frac{48}{35}$$

Factor

$$\frac{2 ^ {4} \cdot 3}{5 \cdot 7} = 1\frac{13}{35} = 1.3714285714285714$$