Basic Math Examples

$1 \frac{1}{10} \cdot \frac{2 (\frac{7}{9})}{\frac{5}{11}} + \frac{1}{3}$

Step 1

Convert $1 \frac{1}{10}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$(1 + \frac{1}{10}) \cdot \frac{2 (\frac{7}{9})}{\frac{5}{11}} + \frac{1}{3}$

Step 1.2

Add $1$ and $\frac{1}{10}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{10}{10} + \frac{1}{10}) \cdot \frac{2 (\frac{7}{9})}{\frac{5}{11}} + \frac{1}{3}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{10 + 1}{10} \cdot \frac{2 (\frac{7}{9})}{\frac{5}{11}} + \frac{1}{3}$

Step 1.2.3

Add $10$ and $1$ .

$\frac{11}{10} \cdot \frac{2 (\frac{7}{9})}{\frac{5}{11}} + \frac{1}{3}$

Step 2

Simplify each term.

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Step 2.1

Combine $2$ and $\frac{7}{9}$ .

$\frac{11}{10} \cdot \frac{\frac{2 \cdot 7}{9}}{\frac{5}{11}} + \frac{1}{3}$

Step 2.2

Multiply $2$ by $7$ .

$\frac{11}{10} \cdot \frac{\frac{14}{9}}{\frac{5}{11}} + \frac{1}{3}$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{11}{10} \cdot (\frac{14}{9} \cdot \frac{11}{5}) + \frac{1}{3}$

Step 2.4

Multiply $\frac{14}{9} \cdot \frac{11}{5}$ .

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Step 2.4.1

Multiply $\frac{14}{9}$ by $\frac{11}{5}$ .

$\frac{11}{10} \cdot \frac{14 \cdot 11}{9 \cdot 5} + \frac{1}{3}$

Step 2.4.2

Multiply $14$ by $11$ .

$\frac{11}{10} \cdot \frac{154}{9 \cdot 5} + \frac{1}{3}$

Step 2.4.3

Multiply $9$ by $5$ .

$\frac{11}{10} \cdot \frac{154}{45} + \frac{1}{3}$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Factor $2$ out of $10$ .

$\frac{11}{2 (5)} \cdot \frac{154}{45} + \frac{1}{3}$

Step 2.5.2

Factor $2$ out of $154$ .

$\frac{11}{2 \cdot 5} \cdot \frac{2 \cdot 77}{45} + \frac{1}{3}$

Step 2.5.3

Cancel the common factor.

$\frac{11}{2 \cdot 5} \cdot \frac{2 \cdot 77}{45} + \frac{1}{3}$

Step 2.5.4

Rewrite the expression.

$\frac{11}{5} \cdot \frac{77}{45} + \frac{1}{3}$

Step 2.6

Multiply $\frac{11}{5}$ by $\frac{77}{45}$ .

$\frac{11 \cdot 77}{5 \cdot 45} + \frac{1}{3}$

Step 2.7

Multiply $11$ by $77$ .

$\frac{847}{5 \cdot 45} + \frac{1}{3}$

Step 2.8

Multiply $5$ by $45$ .

$\frac{847}{225} + \frac{1}{3}$

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{75}{75}$ .

$\frac{847}{225} + \frac{1}{3} \cdot \frac{75}{75}$

Step 4

Write each expression with a common denominator of $225$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{3}$ by $\frac{75}{75}$ .

$\frac{847}{225} + \frac{75}{3 \cdot 75}$

Step 4.2

Multiply $3$ by $75$ .

$\frac{847}{225} + \frac{75}{225}$

Step 5

Combine the numerators over the common denominator.

$\frac{847 + 75}{225}$

Step 6

Add $847$ and $75$ .

$\frac{922}{225}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{922}{225}$

Decimal Form:

$4.09\overline{7}$

Mixed Number Form:

$4 \frac{22}{225}$