Evaluate 31 3/4-11.82

$31 \frac{3}{4} - 11.82$

Step 1

Convert $31 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$31 + \frac{3}{4} - 11.82$

Add $31$ and $\frac{3}{4}$ .

To write $31$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$31 \cdot \frac{4}{4} + \frac{3}{4} - 11.82$

Combine $31$ and $\frac{4}{4}$ .

$\frac{31 \cdot 4}{4} + \frac{3}{4} - 11.82$

Combine the numerators over the common denominator.

$\frac{31 \cdot 4 + 3}{4} - 11.82$

Simplify the numerator.

Multiply $31$ by $4$ .

$\frac{124 + 3}{4} - 11.82$

Add $124$ and $3$ .

$\frac{127}{4} - 11.82$

Step 2

To write $- 11.82$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{127}{4} - 11.82 \cdot \frac{4}{4}$

Step 3

Combine fractions.

Combine $- 11.82$ and $\frac{4}{4}$ .

$\frac{127}{4} + \frac{- 11.82 \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{127 - 11.82 \cdot 4}{4}$

Step 4

Simplify the numerator.

Multiply $- 11.82$ by $4$ .

$\frac{127 - 47.28}{4}$

Subtract $47.28$ from $127$ .

$\frac{79.72}{4}$

Step 5

Divide $79.72$ by $4$ .

$19.93$