Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $4$ by $3$ .

$2 (\frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4}) + 2$

Step 1.3.3

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

$2 (\frac{3}{12} + \frac{4}{3 \cdot 4}) + 2$

Step 1.3.4

Multiply $3$ by $4$ .

$2 (\frac{3}{12} + \frac{4}{12}) + 2$

Step 1.4

Combine the numerators over the common denominator.

$2 \frac{3 + 4}{12} + 2$

Step 1.5

Add $3$ and $4$ .

$2 (\frac{7}{12}) + 2$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $12$ .

$2 \frac{7}{2 (6)} + 2$

Step 1.6.2

Cancel the common factor.

$2 \frac{7}{2 \cdot 6} + 2$

Step 1.6.3

Rewrite the expression.

$\frac{7}{6} + 2$

Step 2

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{7}{6} + 2 \cdot \frac{6}{6}$

Step 3

Combine $2$ and $\frac{6}{6}$ .

$\frac{7}{6} + \frac{2 \cdot 6}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 + 2 \cdot 6}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $6$ .

$\frac{7 + 12}{6}$

Step 5.2

Add $7$ and $12$ .

$\frac{19}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{6}$

Decimal Form:

$3.1\overline{6}$

Mixed Number Form:

$3 \frac{1}{6}$