Algebra Examples

$(\frac{11}{12} + \frac{11}{20}) \cdot \frac{15}{8}$

Step 1

To write $\frac{11}{12}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{11}{12} \cdot \frac{5}{5} + \frac{11}{20}) \cdot \frac{15}{8}$

Step 2

To write $\frac{11}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{11}{12} \cdot \frac{5}{5} + \frac{11}{20} \cdot \frac{3}{3}) \cdot \frac{15}{8}$

Step 3

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$(\frac{11 \cdot 5}{12 \cdot 5} + \frac{11}{20} \cdot \frac{3}{3}) \cdot \frac{15}{8}$

Step 3.2

Multiply $12$ by $5$ .

$(\frac{11 \cdot 5}{60} + \frac{11}{20} \cdot \frac{3}{3}) \cdot \frac{15}{8}$

Step 3.3

Multiply $\frac{11}{20}$ by $\frac{3}{3}$ .

$(\frac{11 \cdot 5}{60} + \frac{11 \cdot 3}{20 \cdot 3}) \cdot \frac{15}{8}$

Step 3.4

Multiply $20$ by $3$ .

$(\frac{11 \cdot 5}{60} + \frac{11 \cdot 3}{60}) \cdot \frac{15}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 \cdot 5 + 11 \cdot 3}{60} \cdot \frac{15}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $11$ by $5$ .

$\frac{55 + 11 \cdot 3}{60} \cdot \frac{15}{8}$

Step 5.2

Multiply $11$ by $3$ .

$\frac{55 + 33}{60} \cdot \frac{15}{8}$

Step 5.3

Add $55$ and $33$ .

$\frac{88}{60} \cdot \frac{15}{8}$

Step 6

Cancel the common factor of $8$ .

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Step 6.1

Factor $8$ out of $88$ .

$\frac{8 (11)}{60} \cdot \frac{15}{8}$

Step 6.2

Cancel the common factor.

$\frac{8 \cdot 11}{60} \cdot \frac{15}{8}$

Step 6.3

Rewrite the expression.

$\frac{11}{60} \cdot 15$

Step 7

Cancel the common factor of $15$ .

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Step 7.1

Factor $15$ out of $60$ .

$\frac{11}{15 (4)} \cdot 15$

Step 7.2

Cancel the common factor.

$\frac{11}{15 \cdot 4} \cdot 15$

Step 7.3

Rewrite the expression.

$\frac{11}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{4}$

Decimal Form:

$2.75$

Mixed Number Form:

$2 \frac{3}{4}$