Solve 10-(31/2+41/3)

$$10 - ( 3 \frac { 1 } { 2 } + 4 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{13}{6}\approx 2.166666667$$

Solution Steps

Multiply 3 and 2 to get 6.

$$10-\left(\frac{6+1}{2}+\frac{4\times 3+1}{3}\right)$$

Add 6 and 1 to get 7.

$$10-\left(\frac{7}{2}+\frac{4\times 3+1}{3}\right)$$

Multiply 4 and 3 to get 12.

$$10-\left(\frac{7}{2}+\frac{12+1}{3}\right)$$

Add 12 and 1 to get 13.

$$10-\left(\frac{7}{2}+\frac{13}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{13}{3} to fractions with denominator 6.

$$10-\left(\frac{21}{6}+\frac{26}{6}\right)$$

Since \frac{21}{6} and \frac{26}{6} have the same denominator, add them by adding their numerators.

$$10-\frac{21+26}{6}$$

Add 21 and 26 to get 47.

$$10-\frac{47}{6}$$

Convert 10 to fraction \frac{60}{6}.

$$\frac{60}{6}-\frac{47}{6}$$

Since \frac{60}{6} and \frac{47}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60-47}{6}$$

Subtract 47 from 60 to get 13.

$$\frac{13}{6}$$

Factor

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665$$