Solve 22/3*33/4-51/8/1frac{8{13}*frac{13}{42}:frac{1}{3}}

$$\frac { 2 \frac { 2 } { 3 } \cdot 3 \frac { 3 } { 4 } - 5 \frac { 1 } { 8 } } { 1 \frac { 8 } { 13 } \cdot \frac { 13 } { 42 } : \frac { 1 } { 3 } }$$

Evaluate

$$\frac{13}{4}=3.25$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{\frac{6+2}{3}\times \frac{3\times 4+3}{4}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Add 6 and 2 to get 8.

$$\frac{\frac{8}{3}\times \frac{3\times 4+3}{4}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{8}{3}\times \frac{12+3}{4}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Add 12 and 3 to get 15.

$$\frac{\frac{8}{3}\times \frac{15}{4}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Multiply \frac{8}{3} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8\times 15}{3\times 4}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Do the multiplications in the fraction \frac{8\times 15}{3\times 4}.

$$\frac{\frac{120}{12}-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Divide 120 by 12 to get 10.

$$\frac{10-\frac{5\times 8+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Multiply 5 and 8 to get 40.

$$\frac{10-\frac{40+1}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Add 40 and 1 to get 41.

$$\frac{10-\frac{41}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Convert 10 to fraction \frac{80}{8}.

$$\frac{\frac{80}{8}-\frac{41}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Since \frac{80}{8} and \frac{41}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{80-41}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Subtract 41 from 80 to get 39.

$$\frac{\frac{39}{8}}{\frac{\frac{1\times 13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Multiply 1 and 13 to get 13.

$$\frac{\frac{39}{8}}{\frac{\frac{13+8}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Add 13 and 8 to get 21.

$$\frac{\frac{39}{8}}{\frac{\frac{21}{13}\times \frac{13}{42}}{\frac{1}{3}}}$$

Multiply \frac{21}{13} times \frac{13}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{39}{8}}{\frac{\frac{21\times 13}{13\times 42}}{\frac{1}{3}}}$$

Cancel out 13 in both numerator and denominator.

$$\frac{\frac{39}{8}}{\frac{\frac{21}{42}}{\frac{1}{3}}}$$

Reduce the fraction \frac{21}{42} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{39}{8}}{\frac{\frac{1}{2}}{\frac{1}{3}}}$$

Divide \frac{1}{2} by \frac{1}{3} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{3}.

$$\frac{\frac{39}{8}}{\frac{1}{2}\times 3}$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{\frac{39}{8}}{\frac{3}{2}}$$

Divide \frac{39}{8} by \frac{3}{2} by multiplying \frac{39}{8} by the reciprocal of \frac{3}{2}.

$$\frac{39}{8}\times \frac{2}{3}$$

Multiply \frac{39}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 2}{8\times 3}$$

Do the multiplications in the fraction \frac{39\times 2}{8\times 3}.

$$\frac{78}{24}$$

Reduce the fraction \frac{78}{24} to lowest terms by extracting and canceling out 6.

$$\frac{13}{4}$$

Factor

$$\frac{13}{2 ^ {2}} = 3\frac{1}{4} = 3.25$$