Evaluate 5/12-4/9

$\frac{5}{12} - \frac{4}{9}$

Step 1

To write $\frac{5}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{12} \cdot \frac{3}{3} - \frac{4}{9}$

Step 2

To write $- \frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{12} \cdot \frac{3}{3} - \frac{4}{9} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{12}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{12 \cdot 3} - \frac{4}{9} \cdot \frac{4}{4}$

Multiply $12$ by $3$ .

$\frac{5 \cdot 3}{36} - \frac{4}{9} \cdot \frac{4}{4}$

Multiply $\frac{4}{9}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 3}{36} - \frac{4 \cdot 4}{9 \cdot 4}$

Multiply $9$ by $4$ .

$\frac{5 \cdot 3}{36} - \frac{4 \cdot 4}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 4 \cdot 4}{36}$

Step 5

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 - 4 \cdot 4}{36}$

Multiply $- 4$ by $4$ .

$\frac{15 - 16}{36}$

Subtract $16$ from $15$ .

$\frac{- 1}{36}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{36}$

Decimal Form:

$- 0.02\overline{7}$