Algebra Examples

\frac{2}{3} + \frac{5}{6}

$\frac{2}{3} + \frac{5}{6}$

Step 1

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{5}{6}

$\frac{2}{3} \cdot \frac{2}{2} + \frac{5}{6}$

Step 2

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 2.1

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6}

$\frac{2 \cdot 2}{3 \cdot 2} + \frac{5}{6}$

Step 2.2

Multiply

3

$3$ by

2

$2$ .

\frac{2 \cdot 2}{6} + \frac{5}{6}

$\frac{2 \cdot 2}{6} + \frac{5}{6}$

\frac{2 \cdot 2}{6} + \frac{5}{6}

$\frac{2 \cdot 2}{6} + \frac{5}{6}$

Step 3

Combine the numerators over the common denominator.

\frac{2 \cdot 2 + 5}{6}

$\frac{2 \cdot 2 + 5}{6}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 + 5}{6}

$\frac{4 + 5}{6}$

Step 4.2

Add

4

$4$ and

5

$5$ .

\frac{9}{6}

$\frac{9}{6}$

\frac{9}{6}

$\frac{9}{6}$

Step 5

Cancel the common factor of

9

$9$ and

6

$6$ .

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Step 5.1

Factor

3

$3$ out of

9

$9$ .

\frac{3 (3)}{6}

$\frac{3 (3)}{6}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

3

$3$ out of

6

$6$ .

\frac{3 \cdot 3}{3 \cdot 2}

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{3}{2}$