Solve 31/2-(1.25-21/3)

$$3 \frac { 1 } { 2 } - ( 1.25 - 2 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{55}{12}\approx 4.583333333$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-\left(1.25-\frac{2\times 3+1}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\left(1.25-\frac{2\times 3+1}{3}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{7}{2}-\left(1.25-\frac{6+1}{3}\right)$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\left(1.25-\frac{7}{3}\right)$$

Convert decimal number 1.25 to fraction \frac{125}{100}. Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{7}{2}-\left(\frac{5}{4}-\frac{7}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{7}{2}-\left(\frac{15}{12}-\frac{28}{12}\right)$$

Since \frac{15}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\frac{15-28}{12}$$

Subtract 28 from 15 to get -13.

$$\frac{7}{2}-\left(-\frac{13}{12}\right)$$

The opposite of -\frac{13}{12} is \frac{13}{12}.

$$\frac{7}{2}+\frac{13}{12}$$

Least common multiple of 2 and 12 is 12. Convert \frac{7}{2} and \frac{13}{12} to fractions with denominator 12.

$$\frac{42}{12}+\frac{13}{12}$$

Since \frac{42}{12} and \frac{13}{12} have the same denominator, add them by adding their numerators.

$$\frac{42+13}{12}$$

Add 42 and 13 to get 55.

$$\frac{55}{12}$$

Factor

$$\frac{5 \cdot 11}{3 \cdot 2 ^ {2}} = 4\frac{7}{12} = 4.583333333333333$$