Solve (3.6-11/8:13/4)*15

$$( 3.6 - 1 \frac { 1 } { 8 } : 1 \frac { 3 } { 4 } ) \cdot 15$$

Evaluate

$$\frac{621}{14}\approx 44.357142857$$

Solution Steps

Divide \frac{1\times 8+1}{8} by \frac{1\times 4+3}{4} by multiplying \frac{1\times 8+1}{8} by the reciprocal of \frac{1\times 4+3}{4}.

$$\left(3.6-\frac{\left(1\times 8+1\right)\times 4}{8\left(1\times 4+3\right)}\right)\times 15$$

Cancel out 4 in both numerator and denominator.

$$\left(3.6-\frac{1+8}{2\left(3+4\right)}\right)\times 15$$

Add 1 and 8 to get 9.

$$\left(3.6-\frac{9}{2\left(3+4\right)}\right)\times 15$$

Add 3 and 4 to get 7.

$$\left(3.6-\frac{9}{2\times 7}\right)\times 15$$

Multiply 2 and 7 to get 14.

$$\left(3.6-\frac{9}{14}\right)\times 15$$

Convert decimal number 3.6 to fraction \frac{36}{10}. Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\left(\frac{18}{5}-\frac{9}{14}\right)\times 15$$

Least common multiple of 5 and 14 is 70. Convert \frac{18}{5} and \frac{9}{14} to fractions with denominator 70.

$$\left(\frac{252}{70}-\frac{45}{70}\right)\times 15$$

Since \frac{252}{70} and \frac{45}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{252-45}{70}\times 15$$

Subtract 45 from 252 to get 207.

$$\frac{207}{70}\times 15$$

Express \frac{207}{70}\times 15 as a single fraction.

$$\frac{207\times 15}{70}$$

Multiply 207 and 15 to get 3105.

$$\frac{3105}{70}$$

Reduce the fraction \frac{3105}{70} to lowest terms by extracting and canceling out 5.

$$\frac{621}{14}$$

Factor

$$\frac{23 \cdot 3 ^ {3}}{2 \cdot 7} = 44\frac{5}{14} = 44.357142857142854$$