Evaluate (2/5-1/10)*(3/4+1/2)

$(\frac{2}{5} - \frac{1}{10}) \cdot (\frac{3}{4} + \frac{1}{2})$

Step 1

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

$(\frac{2}{5} \cdot \frac{2}{2} - \frac{1}{10}) \cdot (\frac{3}{4} + \frac{1}{2})$

Step 2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$(\frac{2 \cdot 2}{5 \cdot 2} - \frac{1}{10}) \cdot (\frac{3}{4} + \frac{1}{2})$

Multiply $5$ by $2$ .

$(\frac{2 \cdot 2}{10} - \frac{1}{10}) \cdot (\frac{3}{4} + \frac{1}{2})$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 1}{10} \cdot (\frac{3}{4} + \frac{1}{2})$

Step 4

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 - 1}{10} \cdot (\frac{3}{4} + \frac{1}{2})$

Subtract $1$ from $4$ .

$\frac{3}{10} \cdot (\frac{3}{4} + \frac{1}{2})$

Step 5

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{10} \cdot (\frac{3}{4} + \frac{1}{2} \cdot \frac{2}{2})$

Step 6

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{3}{10} \cdot (\frac{3}{4} + \frac{2}{2 \cdot 2})$

Multiply $2$ by $2$ .

$\frac{3}{10} \cdot (\frac{3}{4} + \frac{2}{4})$

Step 7

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{3}{10} \cdot \frac{3 + 2}{4}$

Add $3$ and $2$ .

$\frac{3}{10} \cdot \frac{5}{4}$

Step 8

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$\frac{3}{5 (2)} \cdot \frac{5}{4}$

Cancel the common factor.

$\frac{3}{5 \cdot 2} \cdot \frac{5}{4}$

Rewrite the expression.

$\frac{3}{2} \cdot \frac{1}{4}$

Step 9

Multiply $\frac{3}{2}$ by $\frac{1}{4}$ .

$\frac{3}{2 \cdot 4}$

Step 10

Multiply $2$ by $4$ .

$\frac{3}{8}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$

Evaluate (2/5-1/10)*(3/4+1/2)

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