Evaluate (1-3/4*2/5)÷(0.2+1/2)

$(1 - \frac{3}{4} \cdot \frac{2}{5}) \div (0.2 + \frac{1}{2})$

Step 1

Rewrite the division as a fraction.

$\frac{1 - \frac{3}{4} \cdot \frac{2}{5}}{0.2 + \frac{1}{2}}$

Step 2

Multiply the numerator and denominator of the complex fraction by $2$ .

Multiply $\frac{1 - \frac{3}{4} \cdot \frac{2}{5}}{0.2 + \frac{1}{2}}$ by $\frac{2}{2}$ .

$\frac{2}{2} \cdot \frac{1 - \frac{3}{4} \cdot \frac{2}{5}}{0.2 + \frac{1}{2}}$

Combine.

$\frac{2 (1 - \frac{3}{4} \cdot \frac{2}{5})}{2 (0.2 + \frac{1}{2})}$

Step 3

Apply the distributive property.

$\frac{2 \cdot 1 + 2 (- \frac{3}{4} \cdot \frac{2}{5})}{2 \cdot 0.2 + 2 (\frac{1}{2})}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \cdot 1 + 2 (- \frac{3}{4} \cdot \frac{2}{5})}{2 \cdot 0.2 + 2 (\frac{1}{2})}$

Rewrite the expression.

$\frac{2 \cdot 1 + 2 (- \frac{3}{4} \cdot \frac{2}{5})}{2 \cdot 0.2 + 1}$

Step 5

Simplify the numerator.

Multiply $2$ by $1$ .

$\frac{2 + 2 (- \frac{3}{4} \cdot \frac{2}{5})}{2 \cdot 0.2 + 1}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{2 + 2 (\frac{- 3}{4} \cdot \frac{2}{5})}{2 \cdot 0.2 + 1}$

Factor $2$ out of $4$ .

$\frac{2 + 2 (\frac{- 3}{2 (2)} \cdot \frac{2}{5})}{2 \cdot 0.2 + 1}$

Cancel the common factor.

$\frac{2 + 2 (\frac{- 3}{2 \cdot 2} \cdot \frac{2}{5})}{2 \cdot 0.2 + 1}$

Rewrite the expression.

$\frac{2 + 2 (\frac{- 3}{2} \cdot \frac{1}{5})}{2 \cdot 0.2 + 1}$

Multiply $\frac{- 3}{2}$ by $\frac{1}{5}$ .

$\frac{2 + 2 \frac{- 3}{2 \cdot 5}}{2 \cdot 0.2 + 1}$

Multiply $2$ by $5$ .

$\frac{2 + 2 (\frac{- 3}{10})}{2 \cdot 0.2 + 1}$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{2 + 2 \frac{- 3}{2 (5)}}{2 \cdot 0.2 + 1}$

Cancel the common factor.

$\frac{2 + 2 \frac{- 3}{2 \cdot 5}}{2 \cdot 0.2 + 1}$

Rewrite the expression.

$\frac{2 + \frac{- 3}{5}}{2 \cdot 0.2 + 1}$

Move the negative in front of the fraction.

$\frac{2 - \frac{3}{5}}{2 \cdot 0.2 + 1}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 \cdot \frac{5}{5} - \frac{3}{5}}{2 \cdot 0.2 + 1}$

Combine $2$ and $\frac{5}{5}$ .

$\frac{\frac{2 \cdot 5}{5} - \frac{3}{5}}{2 \cdot 0.2 + 1}$

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 5 - 3}{5}}{2 \cdot 0.2 + 1}$

Simplify the numerator.

Multiply $2$ by $5$ .

$\frac{\frac{10 - 3}{5}}{2 \cdot 0.2 + 1}$

Subtract $3$ from $10$ .

$\frac{\frac{7}{5}}{2 \cdot 0.2 + 1}$

Step 6

Simplify the denominator.

Multiply $2$ by $0.2$ .

$\frac{\frac{7}{5}}{0.4 + 1}$

Add $0.4$ and $1$ .

$\frac{\frac{7}{5}}{1.4}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{5} \cdot \frac{1}{1.4}$

Step 8

Cancel the common factor of $1.4$ .

Factor $1.4$ out of $7$ .

$\frac{1.4 (5)}{5} \cdot \frac{1}{1.4}$

Cancel the common factor.

$\frac{1.4 \cdot 5}{5} \cdot \frac{1}{1.4}$

Rewrite the expression.

$\frac{5}{5}$

Step 9

Divide $5$ by $5$ .

$1$

Evaluate (1-3/4*2/5)÷(0.2+1/2)

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