Evaluate -1/5(3/8-5/6)

$- \frac{1}{5} (\frac{3}{8} - \frac{5}{6})$

Step 1

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{1}{5} \cdot (\frac{3}{8} \cdot \frac{3}{3} - \frac{5}{6})$

Step 2

To write $- \frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{1}{5} \cdot (\frac{3}{8} \cdot \frac{3}{3} - \frac{5}{6} \cdot \frac{4}{4})$

Step 3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$- \frac{1}{5} \cdot (\frac{3 \cdot 3}{8 \cdot 3} - \frac{5}{6} \cdot \frac{4}{4})$

Multiply $8$ by $3$ .

$- \frac{1}{5} \cdot (\frac{3 \cdot 3}{24} - \frac{5}{6} \cdot \frac{4}{4})$

Multiply $\frac{5}{6}$ by $\frac{4}{4}$ .

$- \frac{1}{5} \cdot (\frac{3 \cdot 3}{24} - \frac{5 \cdot 4}{6 \cdot 4})$

Multiply $6$ by $4$ .

$- \frac{1}{5} \cdot (\frac{3 \cdot 3}{24} - \frac{5 \cdot 4}{24})$

Step 4

Combine the numerators over the common denominator.

$- \frac{1}{5} \cdot \frac{3 \cdot 3 - 5 \cdot 4}{24}$

Step 5

Simplify the numerator.

Multiply $3$ by $3$ .

$- \frac{1}{5} \cdot \frac{9 - 5 \cdot 4}{24}$

Multiply $- 5$ by $4$ .

$- \frac{1}{5} \cdot \frac{9 - 20}{24}$

Subtract $20$ from $9$ .

$- \frac{1}{5} \cdot \frac{- 11}{24}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{5} \cdot (- \frac{11}{24})$

Step 7

Multiply $- \frac{1}{5} (- \frac{11}{24})$ .

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{5}) \frac{11}{24}$

Multiply $\frac{1}{5}$ by $1$ .

$\frac{1}{5} \cdot \frac{11}{24}$

Multiply $\frac{1}{5}$ by $\frac{11}{24}$ .

$\frac{11}{5 \cdot 24}$

Multiply $5$ by $24$ .

$\frac{11}{120}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{120}$

Decimal Form:

$0.091\overline{6}$

Evaluate -1/5(3/8-5/6)

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