Pre-Algebra Examples

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

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

Step 1

Convert

2 \frac{1}{6}

$2 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{6}

$\frac{1}{6}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

6

$6$ .

\frac{2}{3} + \frac{12 + 1}{6}

$\frac{2}{3} + \frac{12 + 1}{6}$

Step 1.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{2}{3} + \frac{13}{6}

$\frac{2}{3} + \frac{13}{6}$

\frac{2}{3} + \frac{13}{6}

$\frac{2}{3} + \frac{13}{6}$

\frac{2}{3} + \frac{13}{6}

$\frac{2}{3} + \frac{13}{6}$

\frac{2}{3} + \frac{13}{6}

$\frac{2}{3} + \frac{13}{6}$

Step 2

To write

\frac{2}{3}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2}{3} \cdot \frac{2}{2} + \frac{13}{6}

$\frac{2}{3} \cdot \frac{2}{2} + \frac{13}{6}$

Step 3

Write each expression with a common denominator of

6

$6$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 \cdot 2}{3 \cdot 2} + \frac{13}{6}

$\frac{2 \cdot 2}{3 \cdot 2} + \frac{13}{6}$

Step 3.2

Multiply

3

$3$ by

2

$2$ .

\frac{2 \cdot 2}{6} + \frac{13}{6}

$\frac{2 \cdot 2}{6} + \frac{13}{6}$

\frac{2 \cdot 2}{6} + \frac{13}{6}

$\frac{2 \cdot 2}{6} + \frac{13}{6}$

Step 4

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 13}{6}

$\frac{2 \cdot 2 + 13}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 13}{6}

$\frac{4 + 13}{6}$

Step 5.2

Add

4

$4$ and

13

$13$ .

\frac{17}{6}

$\frac{17}{6}$

\frac{17}{6}

$\frac{17}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{17}{6}

$\frac{17}{6}$

Decimal Form:

2.8\overline{3}

$2.8\overline{3}$

Mixed Number Form:

2 \frac{5}{6}

$2 \frac{5}{6}$