Algebra Examples

$\frac{1}{6} + 3 \frac{2}{4}$

Step 1

Convert $3 \frac{2}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{6} + 3 + \frac{2}{4}$

Step 1.2

Add $3$ and $\frac{2}{4}$ .

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Step 1.2.1

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

$\frac{1}{6} + 3 \cdot \frac{4}{4} + \frac{2}{4}$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{1}{6} + \frac{3 \cdot 4}{4} + \frac{2}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1}{6} + \frac{3 \cdot 4 + 2}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$\frac{1}{6} + \frac{12 + 2}{4}$

Step 1.2.4.2

Add $12$ and $2$ .

$\frac{1}{6} + \frac{14}{4}$

Step 2

Cancel the common factor of $14$ and $4$ .

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Step 2.1

Factor $2$ out of $14$ .

$\frac{1}{6} + \frac{2 (7)}{4}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $4$ .

$\frac{1}{6} + \frac{2 \cdot 7}{2 \cdot 2}$

Step 2.2.2

Cancel the common factor.

$\frac{1}{6} + \frac{2 \cdot 7}{2 \cdot 2}$

Step 2.2.3

Rewrite the expression.

$\frac{1}{6} + \frac{7}{2}$

Step 3

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{6} + \frac{7}{2} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{2}$ by $\frac{3}{3}$ .

$\frac{1}{6} + \frac{7 \cdot 3}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{1}{6} + \frac{7 \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{1 + 7 \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $7$ by $3$ .

$\frac{1 + 21}{6}$

Step 6.2

Add $1$ and $21$ .

$\frac{22}{6}$

Step 7

Cancel the common factor of $22$ and $6$ .

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Step 7.1

Factor $2$ out of $22$ .

$\frac{2 (11)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 11}{2 \cdot 3}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 3}$

Step 7.2.3

Rewrite the expression.

$\frac{11}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{3}$

Decimal Form:

$3.\overline{6}$

Mixed Number Form:

$3 \frac{2}{3}$