Solve =1/2*5/11/frac{1{2}*3/7+frac{1}{2}*frac{5}{11}}=frac{35}{68}

$$= \frac { \frac { 1 } { 2 } \times \frac { 5 } { 11 } } { \frac { 1 } { 2 } \times \frac { 3 } { 7 } + \frac { 1 } { 2 } \times \frac { 5 } { 11 } } = \frac { 35 } { 68 }$$

Verify

Solution Steps

Multiply \frac{1}{2} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 5}{2\times 11}}{\frac{1}{2}\times \frac{3}{7}+\frac{1}{2}\times \frac{5}{11}}=\frac{35}{68}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 11}.

$$\frac{\frac{5}{22}}{\frac{1}{2}\times \frac{3}{7}+\frac{1}{2}\times \frac{5}{11}}=\frac{35}{68}$$

Multiply \frac{1}{2} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{22}}{\frac{1\times 3}{2\times 7}+\frac{1}{2}\times \frac{5}{11}}=\frac{35}{68}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 7}.

$$\frac{\frac{5}{22}}{\frac{3}{14}+\frac{1}{2}\times \frac{5}{11}}=\frac{35}{68}$$

Multiply \frac{1}{2} times \frac{5}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{22}}{\frac{3}{14}+\frac{1\times 5}{2\times 11}}=\frac{35}{68}$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 11}.

$$\frac{\frac{5}{22}}{\frac{3}{14}+\frac{5}{22}}=\frac{35}{68}$$

Least common multiple of 14 and 22 is 154. Convert \frac{3}{14} and \frac{5}{22} to fractions with denominator 154.

$$\frac{\frac{5}{22}}{\frac{33}{154}+\frac{35}{154}}=\frac{35}{68}$$

Since \frac{33}{154} and \frac{35}{154} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{22}}{\frac{33+35}{154}}=\frac{35}{68}$$

Add 33 and 35 to get 68.

$$\frac{\frac{5}{22}}{\frac{68}{154}}=\frac{35}{68}$$

Reduce the fraction \frac{68}{154} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{22}}{\frac{34}{77}}=\frac{35}{68}$$

Divide \frac{5}{22} by \frac{34}{77} by multiplying \frac{5}{22} by the reciprocal of \frac{34}{77}.

$$\frac{5}{22}\times \frac{77}{34}=\frac{35}{68}$$

Multiply \frac{5}{22} times \frac{77}{34} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 77}{22\times 34}=\frac{35}{68}$$

Do the multiplications in the fraction \frac{5\times 77}{22\times 34}.

$$\frac{385}{748}=\frac{35}{68}$$

Reduce the fraction \frac{385}{748} to lowest terms by extracting and canceling out 11.

$$\frac{35}{68}=\frac{35}{68}$$

Compare \frac{35}{68} and \frac{35}{68}.

$$\text{true}$$