Finite Math Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Add $2$ and $1$ .

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

Step 3

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

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

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

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

Step 4.2

Multiply $3$ by $2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $2$ .

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

Step 6.2

Add $6$ and $1$ .

$\frac{7}{6} + \frac{1}{12}$

Step 7

To write $\frac{7}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7}{6} \cdot \frac{2}{2} + \frac{1}{12}$

Step 8

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

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Step 8.1

Multiply $\frac{7}{6}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 2}{6 \cdot 2} + \frac{1}{12}$

Step 8.2

Multiply $6$ by $2$ .

$\frac{7 \cdot 2}{12} + \frac{1}{12}$

Step 9

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{12}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $7$ by $2$ .

$\frac{14 + 1}{12}$

Step 10.2

Add $14$ and $1$ .

$\frac{15}{12}$

Step 11

Cancel the common factor of $15$ and $12$ .

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Step 11.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{12}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 11.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 11.2.3

Rewrite the expression.

$\frac{5}{4}$