Pre-Algebra Examples

$(\frac{1}{2} + \frac{2}{7}) \cdot \frac{3}{4}$

Step 1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{1}{2} \cdot \frac{7}{7} + \frac{2}{7}) \cdot \frac{3}{4}$

Step 2

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{1}{2} \cdot \frac{7}{7} + \frac{2}{7} \cdot \frac{2}{2}) \cdot \frac{3}{4}$

Step 3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$(\frac{7}{2 \cdot 7} + \frac{2}{7} \cdot \frac{2}{2}) \cdot \frac{3}{4}$

Step 3.2

Multiply $2$ by $7$ .

$(\frac{7}{14} + \frac{2}{7} \cdot \frac{2}{2}) \cdot \frac{3}{4}$

Step 3.3

Multiply $\frac{2}{7}$ by $\frac{2}{2}$ .

$(\frac{7}{14} + \frac{2 \cdot 2}{7 \cdot 2}) \cdot \frac{3}{4}$

Step 3.4

Multiply $7$ by $2$ .

$(\frac{7}{14} + \frac{2 \cdot 2}{14}) \cdot \frac{3}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 + 2 \cdot 2}{14} \cdot \frac{3}{4}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $2$ .

$\frac{7 + 4}{14} \cdot \frac{3}{4}$

Step 5.2

Add $7$ and $4$ .

$\frac{11}{14} \cdot \frac{3}{4}$

Step 6

Multiply $\frac{11}{14} \cdot \frac{3}{4}$ .

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Step 6.1

Multiply $\frac{11}{14}$ by $\frac{3}{4}$ .

$\frac{11 \cdot 3}{14 \cdot 4}$

Step 6.2

Multiply $11$ by $3$ .

$\frac{33}{14 \cdot 4}$

Step 6.3

Multiply $14$ by $4$ .

$\frac{33}{56}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{56}$

Decimal Form:

$0.58928571 \dots$