Solve (1.2+6)-(3/4:0.5+11/3)

$$( 1.2 + 6 ) - ( \frac { 3 } { 4 } : 0.5 + 1 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{131}{30}\approx 4.366666667$$

Solution Steps

Add 1.2 and 6 to get 7.2.

$$7.2-\left(\frac{\frac{3}{4}}{0.5}+\frac{1\times 3+1}{3}\right)$$

Express \frac{\frac{3}{4}}{0.5} as a single fraction.

$$7.2-\left(\frac{3}{4\times 0.5}+\frac{1\times 3+1}{3}\right)$$

Multiply 4 and 0.5 to get 2.

$$7.2-\left(\frac{3}{2}+\frac{1\times 3+1}{3}\right)$$

Multiply 1 and 3 to get 3.

$$7.2-\left(\frac{3}{2}+\frac{3+1}{3}\right)$$

Add 3 and 1 to get 4.

$$7.2-\left(\frac{3}{2}+\frac{4}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$7.2-\left(\frac{9}{6}+\frac{8}{6}\right)$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$7.2-\frac{9+8}{6}$$

Add 9 and 8 to get 17.

$$7.2-\frac{17}{6}$$

Convert decimal number 7.2 to fraction \frac{72}{10}. Reduce the fraction \frac{72}{10} to lowest terms by extracting and canceling out 2.

$$\frac{36}{5}-\frac{17}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{36}{5} and \frac{17}{6} to fractions with denominator 30.

$$\frac{216}{30}-\frac{85}{30}$$

Since \frac{216}{30} and \frac{85}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{216-85}{30}$$

Subtract 85 from 216 to get 131.

$$\frac{131}{30}$$

Factor

$$\frac{131}{2 \cdot 3 \cdot 5} = 4\frac{11}{30} = 4.366666666666666$$