Solve 121/3-(81/4-32/3)

$$12 \frac { 1 } { 3 } - ( 8 \frac { 1 } { 4 } - 3 \frac { 2 } { 3 } )$$

Evaluate

$$\frac{31}{4}=7.75$$

Solution Steps

Multiply 12 and 3 to get 36.

$$\frac{36+1}{3}-\left(\frac{8\times 4+1}{4}-\frac{3\times 3+2}{3}\right)$$

Add 36 and 1 to get 37.

$$\frac{37}{3}-\left(\frac{8\times 4+1}{4}-\frac{3\times 3+2}{3}\right)$$

Multiply 8 and 4 to get 32.

$$\frac{37}{3}-\left(\frac{32+1}{4}-\frac{3\times 3+2}{3}\right)$$

Add 32 and 1 to get 33.

$$\frac{37}{3}-\left(\frac{33}{4}-\frac{3\times 3+2}{3}\right)$$

Multiply 3 and 3 to get 9.

$$\frac{37}{3}-\left(\frac{33}{4}-\frac{9+2}{3}\right)$$

Add 9 and 2 to get 11.

$$\frac{37}{3}-\left(\frac{33}{4}-\frac{11}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{33}{4} and \frac{11}{3} to fractions with denominator 12.

$$\frac{37}{3}-\left(\frac{99}{12}-\frac{44}{12}\right)$$

Since \frac{99}{12} and \frac{44}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37}{3}-\frac{99-44}{12}$$

Subtract 44 from 99 to get 55.

$$\frac{37}{3}-\frac{55}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{37}{3} and \frac{55}{12} to fractions with denominator 12.

$$\frac{148}{12}-\frac{55}{12}$$

Since \frac{148}{12} and \frac{55}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{148-55}{12}$$

Subtract 55 from 148 to get 93.

$$\frac{93}{12}$$

Reduce the fraction \frac{93}{12} to lowest terms by extracting and canceling out 3.

$$\frac{31}{4}$$

Factor

$$\frac{31}{2 ^ {2}} = 7\frac{3}{4} = 7.75$$