Pre-Algebra Examples

\frac{2 x}{7} + \frac{9}{2}

$\frac{2 x}{7} + \frac{9}{2}$

Step 1

To write

\frac{2 x}{7}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 x}{7} \cdot \frac{2}{2} + \frac{9}{2}

$\frac{2 x}{7} \cdot \frac{2}{2} + \frac{9}{2}$

Step 2

To write

\frac{9}{2}

$\frac{9}{2}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{2 x}{7} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{7}{7}

$\frac{2 x}{7} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of

14

$14$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{2 x}{7}

$\frac{2 x}{7}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2 x \cdot 2}{7 \cdot 2} + \frac{9}{2} \cdot \frac{7}{7}

$\frac{2 x \cdot 2}{7 \cdot 2} + \frac{9}{2} \cdot \frac{7}{7}$

Step 3.2

Multiply

7

$7$ by

2

$2$ .

\frac{2 x \cdot 2}{14} + \frac{9}{2} \cdot \frac{7}{7}

$\frac{2 x \cdot 2}{14} + \frac{9}{2} \cdot \frac{7}{7}$

Step 3.3

Multiply

\frac{9}{2}

$\frac{9}{2}$ by

\frac{7}{7}

$\frac{7}{7}$ .

\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{2 \cdot 7}

$\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{2 \cdot 7}$

Step 3.4

Multiply

2

$2$ by

7

$7$ .

\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{14}

$\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{14}$

\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{14}

$\frac{2 x \cdot 2}{14} + \frac{9 \cdot 7}{14}$

Step 4

Combine the numerators over the common denominator.

\frac{2 x \cdot 2 + 9 \cdot 7}{14}

$\frac{2 x \cdot 2 + 9 \cdot 7}{14}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

\frac{4 x + 9 \cdot 7}{14}

$\frac{4 x + 9 \cdot 7}{14}$

Step 5.2

Multiply

9

$9$ by

7

$7$ .

\frac{4 x + 63}{14}

$\frac{4 x + 63}{14}$

\frac{4 x + 63}{14}

$\frac{4 x + 63}{14}$

\frac{2 x}{7} + \frac{9}{2}

$\frac{2 x}{7} + \frac{9}{2}$

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