Solve max(5/6+11/10)*24

$$\max ( \frac { 5 } { 6 } + 1 \frac { 1 } { 10 } ) \cdot 24$$

Evaluate

$$\frac{232}{5}=46.4$$

Solution Steps

Multiply 1 and 10 to get 10.

$$max(\frac{5}{6}+\frac{10+1}{10})\times 24$$

Add 10 and 1 to get 11.

$$max(\frac{5}{6}+\frac{11}{10})\times 24$$

Least common multiple of 6 and 10 is 30. Convert \frac{5}{6} and \frac{11}{10} to fractions with denominator 30.

$$max(\frac{25}{30}+\frac{33}{30})\times 24$$

Since \frac{25}{30} and \frac{33}{30} have the same denominator, add them by adding their numerators.

$$max(\frac{25+33}{30})\times 24$$

Add 25 and 33 to get 58.

$$max(\frac{58}{30})\times 24$$

Reduce the fraction \frac{58}{30} to lowest terms by extracting and canceling out 2.

$$max(\frac{29}{15})\times 24$$

To find the maximum of \frac{29}{15}, first put the numbers in order from least to greatest. This set is already in order.

$$\frac{29}{15}$$

The maximum is \frac{29}{15}, the rightmost value in the set ordered from least to greatest.

$$\frac{29}{15}\times 24$$

Express \frac{29}{15}\times 24 as a single fraction.

$$\frac{29\times 24}{15}$$

Multiply 29 and 24 to get 696.

$$\frac{696}{15}$$

Reduce the fraction \frac{696}{15} to lowest terms by extracting and canceling out 3.

$$\frac{232}{5}$$

Factor

$$\frac{2 ^ {3} \cdot 29}{5} = 46\frac{2}{5} = 46.4$$