Solve quad41/2+31/2div7/12-1/2div2

$$\quad 4 \frac { 1 } { 2 } + 3 \frac { 1 } { 2 } \div \frac { 7 } { 12 } - \frac { 1 } { 2 } \div 2$$

Evaluate

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

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{8+1}{2}+\frac{\frac{3\times 2+1}{2}}{\frac{7}{12}}-\frac{\frac{1}{2}}{2}$$

Add 8 and 1 to get 9.

$$\frac{9}{2}+\frac{\frac{3\times 2+1}{2}}{\frac{7}{12}}-\frac{\frac{1}{2}}{2}$$

Divide \frac{3\times 2+1}{2} by \frac{7}{12} by multiplying \frac{3\times 2+1}{2} by the reciprocal of \frac{7}{12}.

$$\frac{9}{2}+\frac{\left(3\times 2+1\right)\times 12}{2\times 7}-\frac{\frac{1}{2}}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9}{2}+\frac{6\left(1+2\times 3\right)}{7}-\frac{\frac{1}{2}}{2}$$

Multiply 2 and 3 to get 6.

$$\frac{9}{2}+\frac{6\left(1+6\right)}{7}-\frac{\frac{1}{2}}{2}$$

Add 1 and 6 to get 7.

$$\frac{9}{2}+\frac{6\times 7}{7}-\frac{\frac{1}{2}}{2}$$

Multiply 6 and 7 to get 42.

$$\frac{9}{2}+\frac{42}{7}-\frac{\frac{1}{2}}{2}$$

Divide 42 by 7 to get 6.

$$\frac{9}{2}+6-\frac{\frac{1}{2}}{2}$$

Convert 6 to fraction \frac{12}{2}.

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

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

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

Add 9 and 12 to get 21.

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

Express \frac{\frac{1}{2}}{2} as a single fraction.

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

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

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