Pre-Algebra Examples

$\frac{4}{15} + \frac{9}{10} + \frac{11}{12}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{4}{15}$ by $\frac{4}{4}$ .

$\frac{4}{15} \cdot \frac{4}{4} + \frac{9}{10} + \frac{11}{12}$

Step 1.2

Multiply $\frac{4}{15}$ by $\frac{4}{4}$ .

$\frac{4 \cdot 4}{15 \cdot 4} + \frac{9}{10} + \frac{11}{12}$

Step 1.3

Multiply $\frac{9}{10}$ by $\frac{6}{6}$ .

$\frac{4 \cdot 4}{15 \cdot 4} + \frac{9}{10} \cdot \frac{6}{6} + \frac{11}{12}$

Step 1.4

Multiply $\frac{9}{10}$ by $\frac{6}{6}$ .

$\frac{4 \cdot 4}{15 \cdot 4} + \frac{9 \cdot 6}{10 \cdot 6} + \frac{11}{12}$

Step 1.5

Multiply $\frac{11}{12}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 4}{15 \cdot 4} + \frac{9 \cdot 6}{10 \cdot 6} + \frac{11}{12} \cdot \frac{5}{5}$

Step 1.6

Multiply $\frac{11}{12}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 4}{15 \cdot 4} + \frac{9 \cdot 6}{10 \cdot 6} + \frac{11 \cdot 5}{12 \cdot 5}$

Step 1.7

Reorder the factors of $15 \cdot 4$ .

$\frac{4 \cdot 4}{4 \cdot 15} + \frac{9 \cdot 6}{10 \cdot 6} + \frac{11 \cdot 5}{12 \cdot 5}$

Step 1.8

Multiply $4$ by $15$ .

$\frac{4 \cdot 4}{60} + \frac{9 \cdot 6}{10 \cdot 6} + \frac{11 \cdot 5}{12 \cdot 5}$

Step 1.9

Reorder the factors of $10 \cdot 6$ .

$\frac{4 \cdot 4}{60} + \frac{9 \cdot 6}{6 \cdot 10} + \frac{11 \cdot 5}{12 \cdot 5}$

Step 1.10

Multiply $6$ by $10$ .

$\frac{4 \cdot 4}{60} + \frac{9 \cdot 6}{60} + \frac{11 \cdot 5}{12 \cdot 5}$

Step 1.11

Reorder the factors of $12 \cdot 5$ .

$\frac{4 \cdot 4}{60} + \frac{9 \cdot 6}{60} + \frac{11 \cdot 5}{5 \cdot 12}$

Step 1.12

Multiply $5$ by $12$ .

$\frac{4 \cdot 4}{60} + \frac{9 \cdot 6}{60} + \frac{11 \cdot 5}{60}$

Step 2

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 9 \cdot 6 + 11 \cdot 5}{60}$

Step 3

Simplify each term.

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Step 3.1

Multiply $4$ by $4$ .

$\frac{16 + 9 \cdot 6 + 11 \cdot 5}{60}$

Step 3.2

Multiply $9$ by $6$ .

$\frac{16 + 54 + 11 \cdot 5}{60}$

Step 3.3

Multiply $11$ by $5$ .

$\frac{16 + 54 + 55}{60}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $16$ and $54$ .

$\frac{70 + 55}{60}$

Step 4.2

Add $70$ and $55$ .

$\frac{125}{60}$

Step 4.3

Cancel the common factor of $125$ and $60$ .

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Step 4.3.1

Factor $5$ out of $125$ .

$\frac{5 (25)}{60}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $5$ out of $60$ .

$\frac{5 \cdot 25}{5 \cdot 12}$

Step 4.3.2.2

Cancel the common factor.

$\frac{5 \cdot 25}{5 \cdot 12}$

Step 4.3.2.3

Rewrite the expression.

$\frac{25}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{12}$

Decimal Form:

$2.08\overline{3}$

Mixed Number Form:

$2 \frac{1}{12}$