Solve 2-13/4*(11/5-11/4)

$$2 - 1 \frac { 3 } { 4 } \times ( 1 \frac { 1 } { 5 } - 1 \frac { 1 } { 4 } )$$

Evaluate

$$\frac{167}{80}=2.0875$$

Solution Steps

Multiply 1 and 4 to get 4.

$$2-\frac{4+3}{4}\left(\frac{1\times 5+1}{5}-\frac{1\times 4+1}{4}\right)$$

Add 4 and 3 to get 7.

$$2-\frac{7}{4}\left(\frac{1\times 5+1}{5}-\frac{1\times 4+1}{4}\right)$$

Multiply 1 and 5 to get 5.

$$2-\frac{7}{4}\left(\frac{5+1}{5}-\frac{1\times 4+1}{4}\right)$$

Add 5 and 1 to get 6.

$$2-\frac{7}{4}\left(\frac{6}{5}-\frac{1\times 4+1}{4}\right)$$

Multiply 1 and 4 to get 4.

$$2-\frac{7}{4}\left(\frac{6}{5}-\frac{4+1}{4}\right)$$

Add 4 and 1 to get 5.

$$2-\frac{7}{4}\left(\frac{6}{5}-\frac{5}{4}\right)$$

Least common multiple of 5 and 4 is 20. Convert \frac{6}{5} and \frac{5}{4} to fractions with denominator 20.

$$2-\frac{7}{4}\left(\frac{24}{20}-\frac{25}{20}\right)$$

Since \frac{24}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{7}{4}\times \frac{24-25}{20}$$

Subtract 25 from 24 to get -1.

$$2-\frac{7}{4}\left(-\frac{1}{20}\right)$$

Multiply \frac{7}{4} times -\frac{1}{20} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{7\left(-1\right)}{4\times 20}$$

Do the multiplications in the fraction \frac{7\left(-1\right)}{4\times 20}.

$$2-\frac{-7}{80}$$

Fraction \frac{-7}{80} can be rewritten as -\frac{7}{80} by extracting the negative sign.

$$2-\left(-\frac{7}{80}\right)$$

The opposite of -\frac{7}{80} is \frac{7}{80}.

$$2+\frac{7}{80}$$

Convert 2 to fraction \frac{160}{80}.

$$\frac{160}{80}+\frac{7}{80}$$

Since \frac{160}{80} and \frac{7}{80} have the same denominator, add them by adding their numerators.

$$\frac{160+7}{80}$$

Add 160 and 7 to get 167.

$$\frac{167}{80}$$

Factor

$$\frac{167}{2 ^ {4} \cdot 5} = 2\frac{7}{80} = 2.0875$$