Solve 9/2+7/2div7/12-1/2divfrac{2}{1}

$$\frac{ 9 }{ 2 } + \frac{ 7 }{ 2 } \div \frac{ 7 }{ 12 } - \frac{ 1 }{ 2 } \div \frac{ 2 }{ 1 }$$

Evaluate

$$\frac{41}{4}=10.25$$

Solution Steps

Divide \frac{7}{2} by \frac{7}{12} by multiplying \frac{7}{2} by the reciprocal of \frac{7}{12}.

$$\frac{9}{2}+\frac{7}{2}\times \frac{12}{7}-\frac{\frac{1}{2}}{\frac{2}{1}}$$

Multiply \frac{7}{2} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{2}+\frac{7\times 12}{2\times 7}-\frac{\frac{1}{2}}{\frac{2}{1}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{9}{2}+\frac{12}{2}-\frac{\frac{1}{2}}{\frac{2}{1}}$$

Since \frac{9}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$\frac{9+12}{2}-\frac{\frac{1}{2}}{\frac{2}{1}}$$

Add 9 and 12 to get 21.

$$\frac{21}{2}-\frac{\frac{1}{2}}{\frac{2}{1}}$$

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

$$\frac{21}{2}-\frac{1}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{21}{2}-\frac{1}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{21}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{42}{4}-\frac{1}{4}$$

Since \frac{42}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{42-1}{4}$$

Subtract 1 from 42 to get 41.

$$\frac{41}{4}$$

Factor

$$\frac{41}{2 ^ {2}} = 10\frac{1}{4} = 10.25$$