Solve 3/4+5/6div2/7-1/4-3*(-frac{1}{3})

$$\frac { 3 } { 4 } + \frac { 5 } { 6 } \div \frac { 2 } { 7 } - \frac { 1 } { 4 } - 3 \times ( - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{53}{12}\approx 4.416666667$$

Solution Steps

Divide \frac{5}{6} by \frac{2}{7} by multiplying \frac{5}{6} by the reciprocal of \frac{2}{7}.

$$\frac{3}{4}+\frac{5}{6}\times \frac{7}{2}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Multiply \frac{5}{6} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}+\frac{5\times 7}{6\times 2}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 2}.

$$\frac{3}{4}+\frac{35}{12}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{35}{12} to fractions with denominator 12.

$$\frac{9}{12}+\frac{35}{12}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Since \frac{9}{12} and \frac{35}{12} have the same denominator, add them by adding their numerators.

$$\frac{9+35}{12}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Add 9 and 35 to get 44.

$$\frac{44}{12}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Reduce the fraction \frac{44}{12} to lowest terms by extracting and canceling out 4.

$$\frac{11}{3}-\frac{1}{4}-3\left(-\frac{1}{3}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{11}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{44}{12}-\frac{3}{12}-3\left(-\frac{1}{3}\right)$$

Since \frac{44}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-3}{12}-3\left(-\frac{1}{3}\right)$$

Subtract 3 from 44 to get 41.

$$\frac{41}{12}-3\left(-\frac{1}{3}\right)$$

Cancel out 3 and 3.

$$\frac{41}{12}-\left(-1\right)$$

The opposite of -1 is 1.

$$\frac{41}{12}+1$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{41}{12}+\frac{12}{12}$$

Since \frac{41}{12} and \frac{12}{12} have the same denominator, add them by adding their numerators.

$$\frac{41+12}{12}$$

Add 41 and 12 to get 53.

$$\frac{53}{12}$$

Factor

$$\frac{53}{2 ^ {2} \cdot 3} = 4\frac{5}{12} = 4.416666666666667$$